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<section id="base-structure-classes">
<h1>Base Structure Classes<a class="headerlink" href="#base-structure-classes" title="Link to this heading">¶</a></h1>
<section id="module-pgmpy.base.DAG">
<span id="directed-acyclic-graph-dag"></span><h2>Directed Acyclic Graph (DAG)<a class="headerlink" href="#module-pgmpy.base.DAG" title="Link to this heading">¶</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG">
<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pgmpy.base.DAG.</span></span><span class="sig-name descname"><span class="pre">DAG</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ebunch</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">latents</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">{}</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exposures</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">{}</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">outcomes</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">{}</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">roles</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG" title="Link to this definition">¶</a></dt>
<dd><p>Directed Graphical Model, graph with vertex roles.</p>
<p>Each node in the graph can represent either a random variable, <code class="docutils literal notranslate"><span class="pre">Factor</span></code>,
or a cluster of random variables. Edges in the graph represent the
dependencies between these.</p>
<p>Abstract roles can be assigned to nodes in the graph, such as
exposure, outcome, adjustment set, etc. These roles are used, or created,
by algorithms that use the graph, such as causal inference,
causal discovery, causal prediction.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>ebunch</strong> (<em>input graph</em><em>, </em><em>optional</em>) – Data to initialize graph. If None (default) an empty
graph is created. The data can be any format that is supported
by the to_networkx_graph() function, currently including edge list,
dict of dicts, dict of lists, NetworkX graph, 2D NumPy array, SciPy
sparse matrix, or PyGraphviz graph.</p></li>
<li><p><strong>latents</strong> (<em>set</em><em> of </em><em>nodes</em><em>, </em><em>default=set</em><em>(</em><em>)</em>) – A set of latent variables in the graph. These are not observed
variables but are used to represent unobserved confounding or
other latent structures.</p></li>
<li><p><strong>exposures</strong> (<em>set</em><em>, </em><em>default=set</em><em>(</em><em>)</em>) – Set of exposure variables in the graph. These are the variables
that represent the treatment or intervention being studied in a
causal analysis. Default is an empty set.</p></li>
<li><p><strong>outcomes</strong> (<em>set</em><em>, </em><em>default=set</em><em>(</em><em>)</em>) – Set of outcome variables in the graph. These are the variables
that represent the response or dependent variables being studied
in a causal analysis. Default is an empty set.</p></li>
<li><p><strong>roles</strong> (<em>dict</em><em>, </em><em>optional</em><em> (</em><em>default: None</em><em>)</em>) – A dictionary mapping roles to node names.
The keys are roles, and the values are role names (strings or iterables of str).
If provided, this will automatically assign roles to the nodes in the graph.
Passing a key-value pair via <code class="docutils literal notranslate"><span class="pre">roles</span></code> is equivalent to calling
<code class="docutils literal notranslate"><span class="pre">with_role(role,</span> <span class="pre">variables)</span></code> for each key-value pair in the dictionary.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Create an empty DAG with no nodes and no edges</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
</pre></div>
</div>
<p>Edges and vertices can be passed to the constructor as an edge list.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span><span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"b"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">)])</span>
</pre></div>
</div>
<p>G can be also grown incrementally, in several ways:</p>
<p><strong>Nodes:</strong></p>
<p>Add one node at a time:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="n">node</span><span class="o">=</span><span class="s2">"a"</span><span class="p">)</span>
</pre></div>
</div>
<p>Add the nodes from any container (a list, set or tuple or the nodes
from another graph).</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">nodes</span><span class="o">=</span><span class="p">[</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">])</span>
</pre></div>
</div>
<p><strong>Edges:</strong></p>
<p>G can also be grown by adding edges.</p>
<p>Add one edge,</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">u</span><span class="o">=</span><span class="s2">"a"</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
</pre></div>
</div>
<p>a list of edges,</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"b"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">)])</span>
</pre></div>
</div>
<p>If some edges connect nodes not yet in the model, the nodes
are added automatically. There are no errors when adding
nodes or edges that already exist.</p>
<p><strong>Shortcuts:</strong></p>
<p>Many common graph features allow python syntax for speed reporting.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="s2">"a"</span> <span class="ow">in</span> <span class="n">G</span> <span class="c1"># check if node in graph</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="c1"># number of nodes in graph</span>
<span class="go">3</span>
</pre></div>
</div>
<p>Roles can be assigned to nodes in the graph at construction or using methods.</p>
<p>At construction:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"U"</span><span class="p">,</span> <span class="s2">"X"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"M"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"M"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"U"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">)],</span>
<span class="gp">... </span> <span class="n">roles</span><span class="o">=</span><span class="p">{</span><span class="s2">"exposure"</span><span class="p">:</span> <span class="s2">"X"</span><span class="p">,</span> <span class="s2">"outcome"</span><span class="p">:</span> <span class="s2">"Y"</span><span class="p">},</span>
<span class="gp">... </span><span class="p">)</span>
</pre></div>
</div>
<p>Roles can also be assigned after creation using the <code class="docutils literal notranslate"><span class="pre">with_role</span></code> method.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">with_role</span><span class="p">(</span><span class="s2">"adjustment"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"U"</span><span class="p">,</span> <span class="s2">"M"</span><span class="p">})</span>
</pre></div>
</div>
<p>Vertices of a specific role can be retrieved using the <code class="docutils literal notranslate"><span class="pre">get_role</span></code> method.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">get_role</span><span class="p">(</span><span class="s2">"exposure"</span><span class="p">)</span>
<span class="go">['X']</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">get_role</span><span class="p">(</span><span class="s2">"adjustment"</span><span class="p">)</span>
<span class="go">['U', 'M']</span>
</pre></div>
</div>
<dl class="simple">
<dt><strong>Latents:</strong></dt><dd><p>Latent variables can be managed using the <cite>latents</cite> parameter at
initialization or by assigning the “latents” role to nodes. The
<cite>latents</cite> parameter is a convenient shortcut for <cite>roles={‘latents’: …}</cite>.</p>
</dd>
</dl>
<p>Create a graph with initial latent variables ‘U’ and ‘V’, and exposure ‘X’:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"U"</span><span class="p">,</span> <span class="s2">"X"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"M"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"M"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"U"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"V"</span><span class="p">,</span> <span class="s2">"M"</span><span class="p">)],</span>
<span class="gp">... </span> <span class="n">latents</span><span class="o">=</span><span class="p">{</span><span class="s2">"U"</span><span class="p">,</span> <span class="s2">"V"</span><span class="p">},</span>
<span class="gp">... </span> <span class="n">exposures</span><span class="o">=</span><span class="p">{</span><span class="s2">"X"</span><span class="p">},</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">latents</span><span class="p">)</span>
<span class="go">['U', 'V']</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">exposures</span>
<span class="go">{'X'}</span>
</pre></div>
</div>
<p>Add a new latent variable ‘Z’ using the role system:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="s2">"Z"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">with_role</span><span class="p">(</span><span class="n">role</span><span class="o">=</span><span class="s2">"latents"</span><span class="p">,</span> <span class="n">variables</span><span class="o">=</span><span class="s2">"Z"</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">latents</span><span class="p">)</span>
<span class="go">['U', 'V', 'Z']</span>
</pre></div>
</div>
<p>You can also check for latents using the <cite>get_role</cite> method:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">get_role</span><span class="p">(</span><span class="n">role</span><span class="o">=</span><span class="s2">"latents"</span><span class="p">))</span>
<span class="go">['U', 'V', 'Z']</span>
</pre></div>
</div>
<p>Remove a latent variable from the role:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">without_role</span><span class="p">(</span><span class="n">role</span><span class="o">=</span><span class="s2">"latents"</span><span class="p">,</span> <span class="n">variables</span><span class="o">=</span><span class="s2">"V"</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">latents</span><span class="p">)</span>
<span class="go">['U', 'Z']</span>
</pre></div>
</div>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.active_trail_nodes">
<span class="sig-name descname"><span class="pre">active_trail_nodes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">variables</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">observed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">include_latents</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.active_trail_nodes"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.active_trail_nodes" title="Link to this definition">¶</a></dt>
<dd><p>Returns a dictionary with the given variables as keys and all the nodes reachable
from that respective variable as values.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>variables</strong> (<em>str</em><em> or </em><em>array like</em>) – variables whose active trails are to be found.</p></li>
<li><p><strong>observed</strong> (<em>List</em><em> of </em><em>nodes</em><em> (</em><em>optional</em><em>)</em>) – If given the active trails would be computed assuming these nodes to be
observed.</p></li>
<li><p><strong>include_latents</strong> (<em>boolean</em><em> (</em><em>default: False</em><em>)</em>) – Whether to include the latent variables in the returned active trail nodes.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">student</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">([</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grades"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">([(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"grades"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grades"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">active_trail_nodes</span><span class="p">(</span><span class="s2">"diff"</span><span class="p">)</span>
<span class="go">{'diff': {'diff', 'grades'}}</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">active_trail_nodes</span><span class="p">([</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"intel"</span><span class="p">],</span> <span class="n">observed</span><span class="o">=</span><span class="s2">"grades"</span><span class="p">)</span>
<span class="go">{'diff': {'diff', 'intel'}, 'intel': {'diff', 'intel'}}</span>
</pre></div>
</div>
<p class="rubric">References</p>
<p>Details of the algorithm can be found in ‘Probabilistic Graphical Model
Principles and Techniques’ - Koller and Friedman
Page 75 Algorithm 3.1</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.add_edge">
<span class="sig-name descname"><span class="pre">add_edge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">float</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.add_edge"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.add_edge" title="Link to this definition">¶</a></dt>
<dd><p>Add an edge between u and v.</p>
<p>The nodes u and v will be automatically added if they are not already in the graph.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>u</strong> (<em>nodes</em>) – Nodes can be any hashable Python object.</p></li>
<li><p><strong>v</strong> (<em>nodes</em>) – Nodes can be any hashable Python object.</p></li>
<li><p><strong>weight</strong> (<em>int</em><em>, </em><em>float</em><em> (</em><em>default=None</em><em>)</em>) – The weight of the edge</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">nodes</span><span class="o">=</span><span class="p">[</span><span class="s2">"Alice"</span><span class="p">,</span> <span class="s2">"Bob"</span><span class="p">,</span> <span class="s2">"Charles"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">u</span><span class="o">=</span><span class="s2">"Alice"</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="s2">"Bob"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">()</span>
<span class="go">NodeView(('Alice', 'Bob', 'Charles'))</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">OutEdgeView([('Alice', 'Bob')])</span>
</pre></div>
</div>
<p>When the node is not already present in the graph:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">u</span><span class="o">=</span><span class="s2">"Alice"</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="s2">"Ankur"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">()</span>
<span class="go">NodeView(('Alice', 'Ankur', 'Bob', 'Charles'))</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">OutEdgeView([('Alice', 'Bob'), ('Alice', 'Ankur')])</span>
</pre></div>
</div>
<p>Adding edges with weight:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="s2">"Ankur"</span><span class="p">,</span> <span class="s2">"Maria"</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edge</span><span class="p">[</span><span class="s2">"Ankur"</span><span class="p">][</span><span class="s2">"Maria"</span><span class="p">]</span>
<span class="go">{'weight': 0.1}</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.add_edges_from">
<span class="sig-name descname"><span class="pre">add_edges_from</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ebunch</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.add_edges_from"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.add_edges_from" title="Link to this definition">¶</a></dt>
<dd><p>Add all the edges in ebunch.</p>
<p>If nodes referred in the ebunch are not already present, they
will be automatically added. Node names can be any hashable python
object.</p>
<p><a href="#id1"><span class="problematic" id="id2">**</span></a>The behavior of adding weights is different than networkx.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>ebunch</strong> (<em>container</em><em> of </em><em>edges</em>) – Each edge given in the container will be added to the graph.
The edges must be given as 2-tuples (u, v).</p></li>
<li><p><strong>weights</strong> (<em>list</em><em>, </em><em>tuple</em><em> (</em><em>default=None</em><em>)</em>) – A container of weights (int, float). The weight value at index i
is associated with the edge at index i.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">nodes</span><span class="o">=</span><span class="p">[</span><span class="s2">"Alice"</span><span class="p">,</span> <span class="s2">"Bob"</span><span class="p">,</span> <span class="s2">"Charles"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"Alice"</span><span class="p">,</span> <span class="s2">"Bob"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Bob"</span><span class="p">,</span> <span class="s2">"Charles"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">()</span>
<span class="go">NodeView(('Alice', 'Bob', 'Charles'))</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">OutEdgeView([('Alice', 'Bob'), ('Bob', 'Charles')])</span>
</pre></div>
</div>
<p>When the node is not already in the model:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"Alice"</span><span class="p">,</span> <span class="s2">"Ankur"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">()</span>
<span class="go">NodeView(('Alice', 'Bob', 'Charles', 'Ankur'))</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">OutEdgeView([('Alice', 'Bob'), ('Bob', 'Charles'), ('Alice', 'Ankur')])</span>
</pre></div>
</div>
<p>Adding edges with weights:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span>
<span class="gp">... </span> <span class="p">[(</span><span class="s2">"Ankur"</span><span class="p">,</span> <span class="s2">"Maria"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Maria"</span><span class="p">,</span> <span class="s2">"Mason"</span><span class="p">)],</span> <span class="n">weights</span><span class="o">=</span><span class="p">[</span><span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edge</span><span class="p">[</span><span class="s2">"Ankur"</span><span class="p">][</span><span class="s2">"Maria"</span><span class="p">]</span>
<span class="go">{'weight': 0.3}</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edge</span><span class="p">[</span><span class="s2">"Maria"</span><span class="p">][</span><span class="s2">"Mason"</span><span class="p">]</span>
<span class="go">{'weight': 0.5}</span>
</pre></div>
</div>
<p>or</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">([(</span><span class="s2">"Ankur"</span><span class="p">,</span> <span class="s2">"Maria"</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Maria"</span><span class="p">,</span> <span class="s2">"Mason"</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.copy">
<span class="sig-name descname"><span class="pre">copy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.copy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.copy" title="Link to this definition">¶</a></dt>
<dd><p>Returns a copy of the DAG object.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.do">
<span class="sig-name descname"><span class="pre">do</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nodes</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inplace</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.do"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.do" title="Link to this definition">¶</a></dt>
<dd><p>Applies the do operator to the graph and returns a new DAG with the
transformed graph.</p>
<p>The do-operator, do(X = x) has the effect of removing all edges from
the parents of X and setting X to the given value x.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>nodes</strong> (<em>list</em><em>, </em><em>array-like</em>) – The names of the nodes to apply the do-operator for.</p></li>
<li><p><strong>inplace</strong> (<em>boolean</em><em> (</em><em>default: False</em><em>)</em>) – If inplace=True, makes the changes to the current object,
otherwise returns a new instance.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>Modified DAG</strong> – A new instance of DAG modified by the do-operator</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="models/dag.html#pgmpy.base.DAG" title="pgmpy.base.DAG">pgmpy.base.DAG</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Initialize a DAG</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">graph</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">graph</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">([(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"A"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="c1"># Applying the do-operator will return a new DAG with the desired structure.</span>
<span class="gp">>>> </span><span class="n">graph_do_A</span> <span class="o">=</span> <span class="n">graph</span><span class="o">.</span><span class="n">do</span><span class="p">(</span><span class="s2">"A"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># Which we can verify is missing the edges we would expect.</span>
<span class="gp">>>> </span><span class="n">graph_do_A</span><span class="o">.</span><span class="n">edges</span>
<span class="go">OutEdgeView([('A', 'B'), ('A', 'Y')])</span>
</pre></div>
</div>
<p class="rubric">References</p>
<p>Causality: Models, Reasoning, and Inference, Judea Pearl (2000). p.70.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.edge_strength">
<span class="sig-name descname"><span class="pre">edge_strength</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">edges</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.edge_strength"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.edge_strength" title="Link to this definition">¶</a></dt>
<dd><p>Computes the strength of each edge in <cite>edges</cite>. The strength is bounded
between 0 and 1, with 1 signifying strong effect.</p>
<p>The edge strength is defined as the effect size measure of a
Conditional Independence test using the parents as the conditional set.
The strength quantifies the effect of edge[0] on edge[1] after
controlling for any other influence paths. We use a residualization-based
CI test[1] to compute the strengths.</p>
<p>Interpretation:
- The strength is the Pillai’s Trace effect size of partial correlation.
- Measures the strength of linear relationship between the residuals.
- Works for any mixture of categorical and continuous variables.
- The value is bounded between 0 and 1:
- Strength close to 1 → strong dependence.
- Strength close to 0 → conditional independence.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>data</strong> (<em>pandas.DataFrame</em>) – Dataset to compute edge strengths on.</p></li>
<li><p><strong>edges</strong> (<em>tuple</em><em>, </em><em>list</em><em>, or </em><em>None</em><em> (</em><em>default: None</em><em>)</em>) – <ul>
<li><p>None: Compute for all DAG edges.</p></li>
<li><p>Tuple (X, Y): Compute for edge X → Y.</p></li>
<li><p>List of tuples: Compute for selected edges.</p></li>
</ul>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Dictionary mapping edges to their strength values.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dict</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.models</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearGaussianBayesianNetwork</span> <span class="k">as</span> <span class="n">LGBN</span>
<span class="gp">>>> </span><span class="c1"># Create a linear Gaussian Bayesian network</span>
<span class="gp">>>> </span><span class="n">linear_model</span> <span class="o">=</span> <span class="n">LGBN</span><span class="p">([(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Z"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="c1"># Create CPDs with specific beta values</span>
<span class="gp">>>> </span><span class="n">x_cpd</span> <span class="o">=</span> <span class="n">LinearGaussianCPD</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="s2">"X"</span><span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">std</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y_cpd</span> <span class="o">=</span> <span class="n">LinearGaussianCPD</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">variable</span><span class="o">=</span><span class="s2">"Y"</span><span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">],</span> <span class="n">std</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">evidence</span><span class="o">=</span><span class="p">[</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Z"</span><span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">z_cpd</span> <span class="o">=</span> <span class="n">LinearGaussianCPD</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="s2">"Z"</span><span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">std</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># Add CPDs to the model</span>
<span class="gp">>>> </span><span class="n">linear_model</span><span class="o">.</span><span class="n">add_cpds</span><span class="p">(</span><span class="n">x_cpd</span><span class="p">,</span> <span class="n">y_cpd</span><span class="p">,</span> <span class="n">z_cpd</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># Simulate data from the model</span>
<span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="n">linear_model</span><span class="o">.</span><span class="n">simulate</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="nb">int</span><span class="p">(</span><span class="mf">1e4</span><span class="p">))</span>
<span class="gp">>>> </span><span class="c1"># Create DAG and compute edge strengths</span>
<span class="gp">>>> </span><span class="n">dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Z"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">strengths</span> <span class="o">=</span> <span class="n">dag</span><span class="o">.</span><span class="n">edge_strength</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="go">{('X', 'Y'): np.float64(0.14587166611282304),</span>
<span class="go"> ('Z', 'Y'): np.float64(0.25683780900125613)}</span>
</pre></div>
</div>
<p class="rubric">References</p>
<p>[1] Ankan, Ankur, and Johannes Textor. “A simple unified approach to testing high-dimensional
conditional independences for categorical and ordinal data.” Proceedings of the AAAI Conference
on Artificial Intelligence.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.from_dagitty">
<em class="property"><span class="k"><span class="pre">classmethod</span></span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_dagitty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">string</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">filename</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference internal" href="#pgmpy.base.DAG.DAG" title="pgmpy.base.DAG.DAG"><span class="pre">DAG</span></a></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.from_dagitty"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.from_dagitty" title="Link to this definition">¶</a></dt>
<dd><p>Initializes a <cite>DAG</cite> instance using DAGitty syntax.</p>
<p>Creates a <cite>DAG</cite> from the dagitty string. If parameter <cite>beta</cite> is specified in the DAGitty
string, the method returns a <cite>LinearGaussianBayesianNetwork</cite> instead of a plain <cite>DAG</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>string</strong> (<em>str</em><em> (</em><em>default: None</em><em>)</em>) – A <cite>DAGitty</cite> style multiline set of regression equation representing the model.
Refer <a class="reference external" href="https://www.dagitty.net/manual-3.x.pdf#page=3.58">https://www.dagitty.net/manual-3.x.pdf#page=3.58</a> and
<a class="reference external" href="https://github.com/jtextor/dagitty/blob/7a657776dc8f5e5ba4e323edb028e2c2aaf29327/gui/js/dagitty.js#L3417">https://github.com/jtextor/dagitty/blob/7a657776dc8f5e5ba4e323edb028e2c2aaf29327/gui/js/dagitty.js#L3417</a></p></li>
<li><p><strong>filename</strong> (<em>str</em><em> (</em><em>default: None</em><em>)</em>) – The filename of the file containing the model in DAGitty syntax.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="o">.</span><span class="n">from_dagitty</span><span class="p">(</span>
<span class="gp">... </span> <span class="s2">"dag{'carry matches' [latent] cancer [outcome] smoking -> 'carry matches' [beta=0.2] "</span>
<span class="gp">... </span> <span class="s2">"smoking -> cancer [beta=0.5] 'carry matches' -> cancer }"</span>
<span class="gp">... </span><span class="p">)</span>
</pre></div>
</div>
<p>Creating a Linear Gaussian Bayesian network from dagitty:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.models</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearGaussianBayesianNetwork</span> <span class="k">as</span> <span class="n">LGBN</span>
</pre></div>
</div>
<p># Specifying beta creates a LinearGaussianBayesianNetwork instance
>>> dag = DAG.from_dagitty(“dag{X -> Y [beta=0.3] Y -> Z [beta=0.1]}”)
>>> data = dag.simulate(n_samples=int(1e4))</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.models</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearGaussianBayesianNetwork</span> <span class="k">as</span> <span class="n">LGBN</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.from_lavaan">
<em class="property"><span class="k"><span class="pre">classmethod</span></span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_lavaan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">string</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">filename</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">PathLike</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference internal" href="#pgmpy.base.DAG.DAG" title="pgmpy.base.DAG.DAG"><span class="pre">DAG</span></a></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.from_lavaan"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.from_lavaan" title="Link to this definition">¶</a></dt>
<dd><p>Initializes a <cite>DAG</cite> instance using lavaan syntax.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>string</strong> (<em>str</em><em> (</em><em>default: None</em><em>)</em>) – A <cite>lavaan</cite> style multiline set of regression equation representing the model.
Refer <a class="reference external" href="http://lavaan.ugent.be/tutorial/syntax1.html">http://lavaan.ugent.be/tutorial/syntax1.html</a> for details.</p></li>
<li><p><strong>filename</strong> (<em>str</em><em> (</em><em>default: None</em><em>)</em>) – The filename of the file containing the model in lavaan syntax.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_ancestors">
<span class="sig-name descname"><span class="pre">get_ancestors</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nodes</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_ancestors"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_ancestors" title="Link to this definition">¶</a></dt>
<dd><p>Returns a dictionary of all ancestors of all the observed nodes including the
node itself.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>nodes</strong> (<em>string</em><em>, </em><em>list-type</em>) – name of all the observed nodes</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">model</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"D"</span><span class="p">,</span> <span class="s2">"G"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"I"</span><span class="p">,</span> <span class="s2">"G"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"G"</span><span class="p">,</span> <span class="s2">"L"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"I"</span><span class="p">,</span> <span class="s2">"L"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">model</span><span class="o">.</span><span class="n">get_ancestors</span><span class="p">(</span><span class="s2">"G"</span><span class="p">)</span>
<span class="go">{'D', 'G', 'I'}</span>
<span class="gp">>>> </span><span class="n">model</span><span class="o">.</span><span class="n">get_ancestors</span><span class="p">([</span><span class="s2">"G"</span><span class="p">,</span> <span class="s2">"I"</span><span class="p">])</span>
<span class="go">{'D', 'G', 'I'}</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_ancestral_graph">
<span class="sig-name descname"><span class="pre">get_ancestral_graph</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nodes</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_ancestral_graph"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_ancestral_graph" title="Link to this definition">¶</a></dt>
<dd><p>Returns the ancestral graph of the given <cite>nodes</cite>. The ancestral graph only
contains the nodes which are ancestors of at least one of the variables in
node.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>node</strong> (<em>iterable</em>) – List of nodes whose ancestral graph needs to be computed.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>Ancestral Graph</strong></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="models/dag.html#pgmpy.base.DAG" title="pgmpy.base.DAG">pgmpy.base.DAG</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"D"</span><span class="p">,</span> <span class="s2">"A"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"D"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">anc_dag</span> <span class="o">=</span> <span class="n">dag</span><span class="o">.</span><span class="n">get_ancestral_graph</span><span class="p">(</span><span class="n">nodes</span><span class="o">=</span><span class="p">[</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">anc_dag</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">OutEdgeView([('D', 'A'), ('D', 'B')])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_children">
<span class="sig-name descname"><span class="pre">get_children</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_children"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_children" title="Link to this definition">¶</a></dt>
<dd><p>Returns a list of children of node.
Throws an error if the node is not present in the graph.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>node</strong> (<em>string</em><em>, </em><em>int</em><em> or </em><em>any hashable python object.</em>) – The node whose children would be returned.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">g</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ebunch</span><span class="o">=</span><span class="p">[</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"C"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"D"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"E"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"F"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"E"</span><span class="p">,</span> <span class="s2">"G"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">g</span><span class="o">.</span><span class="n">get_children</span><span class="p">(</span><span class="n">node</span><span class="o">=</span><span class="s2">"B"</span><span class="p">)</span>
<span class="go">['D', 'E', 'F']</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_immoralities">
<span class="sig-name descname"><span class="pre">get_immoralities</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_immoralities"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_immoralities" title="Link to this definition">¶</a></dt>
<dd><p>Finds all the immoralities in the model
A v-structure X -> Z <- Y is an immorality if there is no direct edge between X and Y .</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>Immoralities</strong> – A set of all the immoralities in the model</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>set</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">student</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span>
<span class="gp">... </span> <span class="p">[</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"SAT"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"grade"</span><span class="p">,</span> <span class="s2">"letter"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">get_immoralities</span><span class="p">()</span>
<span class="go">{('diff', 'intel')}</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_independencies">
<span class="sig-name descname"><span class="pre">get_independencies</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">latex</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">include_latents</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Independencies</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_independencies"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_independencies" title="Link to this definition">¶</a></dt>
<dd><p>Computes independencies in the DAG, by checking minimal d-seperation.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>latex</strong> (<em>boolean</em>) – If latex=True then latex string of the independence assertion
would be created.</p></li>
<li><p><strong>include_latents</strong> (<em>boolean</em>) – If True, includes latent variables in the independencies. Otherwise,
only generates independencies on observed variables.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">chain</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Y"</span><span class="p">,</span> <span class="s2">"Z"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">chain</span><span class="o">.</span><span class="n">get_independencies</span><span class="p">()</span>
<span class="go">(X ⟂ Z | Y)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_leaves">
<span class="sig-name descname"><span class="pre">get_leaves</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_leaves"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_leaves" title="Link to this definition">¶</a></dt>
<dd><p>Returns a list of leaves of the graph.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">graph</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"D"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">graph</span><span class="o">.</span><span class="n">get_leaves</span><span class="p">()</span>
<span class="go">['C', 'D']</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_markov_blanket">
<span class="sig-name descname"><span class="pre">get_markov_blanket</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_markov_blanket"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_markov_blanket" title="Link to this definition">¶</a></dt>
<dd><p>Returns a markov blanket for a random variable. In the case
of Bayesian Networks, the markov blanket is the set of
node’s parents, its children and its children’s other parents.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>Markov Blanket</strong> – List of nodes in the markov blanket of <cite>node</cite>.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>list</p>
</dd>
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>node</strong> (<em>string</em><em>, </em><em>int</em><em> or </em><em>any hashable python object.</em>) – The node whose markov blanket would be returned.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.factors.discrete</span><span class="w"> </span><span class="kn">import</span> <span class="n">TabularCPD</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span>
<span class="gp">... </span> <span class="p">[</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"x"</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"z"</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"y"</span><span class="p">,</span> <span class="s2">"w"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"y"</span><span class="p">,</span> <span class="s2">"v"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"u"</span><span class="p">,</span> <span class="s2">"w"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"s"</span><span class="p">,</span> <span class="s2">"v"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"w"</span><span class="p">,</span> <span class="s2">"t"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"w"</span><span class="p">,</span> <span class="s2">"m"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"v"</span><span class="p">,</span> <span class="s2">"n"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"v"</span><span class="p">,</span> <span class="s2">"q"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">get_markov_blanket</span><span class="p">(</span><span class="s2">"y"</span><span class="p">)</span>
<span class="go">['s', 'w', 'x', 'u', 'z', 'v']</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_parents">
<span class="sig-name descname"><span class="pre">get_parents</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_parents"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_parents" title="Link to this definition">¶</a></dt>
<dd><p>Returns a list of parents of node.</p>
<p>Throws an error if the node is not present in the graph.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>node</strong> (<em>string</em><em>, </em><em>int</em><em> or </em><em>any hashable python object.</em>) – The node whose parents would be returned.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span><span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">get_parents</span><span class="p">(</span><span class="n">node</span><span class="o">=</span><span class="s2">"grade"</span><span class="p">)</span>
<span class="go">['diff', 'intel']</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_random">
<em class="property"><span class="k"><span class="pre">static</span></span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">get_random</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_nodes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">edge_prob</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">node_names</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">latents</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference internal" href="#pgmpy.base.DAG.DAG" title="pgmpy.base.DAG.DAG"><span class="pre">DAG</span></a></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_random"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_random" title="Link to this definition">¶</a></dt>
<dd><p>Returns a randomly generated DAG with <cite>n_nodes</cite> number of nodes with
edge probability being <cite>edge_prob</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n_nodes</strong> (<em>int</em>) – The number of nodes in the randomly generated DAG.</p></li>
<li><p><strong>edge_prob</strong> (<em>float</em>) – The probability of edge between any two nodes in the topologically
sorted DAG.</p></li>
<li><p><strong>node_names</strong> (<em>list</em><em> (</em><em>default: None</em><em>)</em>) – A list of variables names to use in the random graph.
If None, the node names are integer values starting from 0.</p></li>
<li><p><strong>latents</strong> (<em>bool</em><em> (</em><em>default: False</em><em>)</em>) – If True, includes latent variables in the generated DAG.</p></li>
<li><p><strong>seed</strong> (<em>int</em><em> (</em><em>default: None</em><em>)</em>) – The seed for the random number generator.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>Random DAG</strong> – The randomly generated DAG.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="models/dag.html#pgmpy.base.DAG" title="pgmpy.base.DAG">pgmpy.base.DAG</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">random_dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="o">.</span><span class="n">get_random</span><span class="p">(</span><span class="n">n_nodes</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">edge_prob</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">random_dag</span><span class="o">.</span><span class="n">nodes</span><span class="p">()</span>
<span class="go">NodeView((0, 1, 2, 3, 4, 5, 6, 7, 8, 9))</span>
<span class="gp">>>> </span><span class="n">random_dag</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">OutEdgeView([(0, 6), (1, 6), (1, 7), (7, 9), (2, 5), (2, 7), (2, 8), (5, 9), (3, 7)])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.get_roots">
<span class="sig-name descname"><span class="pre">get_roots</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.get_roots"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.get_roots" title="Link to this definition">¶</a></dt>
<dd><p>Returns a list of roots of the graph.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">graph</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"D"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"E"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">graph</span><span class="o">.</span><span class="n">get_roots</span><span class="p">()</span>
<span class="go">['A', 'E']</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.in_degree_iter">
<span class="sig-name descname"><span class="pre">in_degree_iter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nbunch</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.in_degree_iter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.in_degree_iter" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.is_dconnected">
<span class="sig-name descname"><span class="pre">is_dconnected</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">end</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">observed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">include_latents</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.is_dconnected"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.is_dconnected" title="Link to this definition">¶</a></dt>
<dd><p>Returns True if there is an active trail (i.e. d-connection) between
<cite>start</cite> and <cite>end</cite> node given that <cite>observed</cite> is observed.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>start</strong> (<em>int</em><em>, </em><em>str</em><em>, </em><em>any hashable python object.</em>) – The nodes in the DAG between which to check the d-connection/active trail.</p></li>
<li><p><strong>end</strong> (<em>int</em><em>, </em><em>str</em><em>, </em><em>any hashable python object.</em>) – The nodes in the DAG between which to check the d-connection/active trail.</p></li>
<li><p><strong>observed</strong> (<em>list</em><em>, </em><em>array-like</em><em> (</em><em>optional</em><em>)</em>) – If given the active trail would be computed assuming these nodes to
be observed.</p></li>
<li><p><strong>include_latents</strong> (<em>boolean</em><em> (</em><em>default: False</em><em>)</em>) – If true, latent variables are return as part of the active trail.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">student</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">([</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grades"</span><span class="p">,</span> <span class="s2">"letter"</span><span class="p">,</span> <span class="s2">"sat"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span>
<span class="gp">... </span> <span class="p">[</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"grades"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grades"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"grades"</span><span class="p">,</span> <span class="s2">"letter"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"sat"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">is_dconnected</span><span class="p">(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"intel"</span><span class="p">)</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">is_dconnected</span><span class="p">(</span><span class="s2">"grades"</span><span class="p">,</span> <span class="s2">"sat"</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.is_iequivalent">
<span class="sig-name descname"><span class="pre">is_iequivalent</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">model</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pgmpy.base.DAG.DAG" title="pgmpy.base.DAG.DAG"><span class="pre">DAG</span></a></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.is_iequivalent"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.is_iequivalent" title="Link to this definition">¶</a></dt>
<dd><p>Checks whether the given model is I-equivalent</p>
<p>Two graphs G1 and G2 are said to be I-equivalent if they have same skeleton
and have same set of immoralities.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>model</strong> (<em>A DAG object</em><em>, </em><em>for which you want to check I-equivalence</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>I-equivalence</strong> – True if both are I-equivalent, False otherwise</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>boolean</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">([(</span><span class="s2">"V"</span><span class="p">,</span> <span class="s2">"W"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"W"</span><span class="p">,</span> <span class="s2">"X"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Z"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">G1</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">G1</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">([(</span><span class="s2">"W"</span><span class="p">,</span> <span class="s2">"V"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"W"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Z"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">is_iequivalent</span><span class="p">(</span><span class="n">G1</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.local_independencies">
<span class="sig-name descname"><span class="pre">local_independencies</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">variables</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="p"><span class="pre">...</span></span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">str</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.local_independencies"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.local_independencies" title="Link to this definition">¶</a></dt>
<dd><p>Returns an instance of Independencies containing the local independencies
of each of the variables.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>variables</strong> (<em>str</em><em> or </em><em>array like</em>) – variables whose local independencies are to be found.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">student</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">student</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span>
<span class="gp">... </span> <span class="p">[</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"grade"</span><span class="p">,</span> <span class="s2">"letter"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"SAT"</span><span class="p">),</span>
<span class="gp">... </span> <span class="p">]</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ind</span> <span class="o">=</span> <span class="n">student</span><span class="o">.</span><span class="n">local_independencies</span><span class="p">(</span><span class="s2">"grade"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ind</span>
<span class="go">(grade ⟂ SAT | diff, intel)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.minimal_dseparator">
<span class="sig-name descname"><span class="pre">minimal_dseparator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">end</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Hashable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">include_latents</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.minimal_dseparator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.minimal_dseparator" title="Link to this definition">¶</a></dt>
<dd><p>Finds the minimal d-separating set for <cite>start</cite> and <cite>end</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>start</strong> (<em>node</em>) – The first node.</p></li>
<li><p><strong>end</strong> (<em>node</em>) – The second node.</p></li>
<li><p><strong>include_latents</strong> (<em>boolean</em><em> (</em><em>default: False</em><em>)</em>) – If true, latent variables are consider for minimal d-seperator.</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">dag</span><span class="o">.</span><span class="n">minimal_dseparator</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="s2">"A"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">"C"</span><span class="p">)</span>
<span class="go">{'B'}</span>
</pre></div>
</div>
<p class="rubric">References</p>
<dl class="simple">
<dt>[1] Algorithm 4, Page 10: Tian, Jin, Azaria Paz, and</dt><dd><dl class="simple">
<dt>Judea Pearl. Finding minimal d-separators. Computer Science Department,</dt><dd><p>University of California, 1998.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.moralize">
<span class="sig-name descname"><span class="pre">moralize</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.moralize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.moralize" title="Link to this definition">¶</a></dt>
<dd><p>Removes all the immoralities in the DAG and creates a moral
graph (UndirectedGraph).</p>
<p>A v-structure X->Z<-Y is an immorality if there is no directed edge
between X and Y.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">(</span><span class="n">ebunch</span><span class="o">=</span><span class="p">[(</span><span class="s2">"diff"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"intel"</span><span class="p">,</span> <span class="s2">"grade"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">moral_graph</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">moralize</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">moral_graph</span><span class="o">.</span><span class="n">edges</span><span class="p">()</span>
<span class="go">EdgeView([('intel', 'grade'), ('intel', 'diff'), ('grade', 'diff')])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.out_degree_iter">
<span class="sig-name descname"><span class="pre">out_degree_iter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nbunch</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.out_degree_iter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.out_degree_iter" title="Link to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.to_daft">
<span class="sig-name descname"><span class="pre">to_daft</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node_pos</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Hashable</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'circular'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">latex</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pgm_params</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">{}</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">edge_params</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">{}</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">node_params</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">{}</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_edge_strength</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.to_daft"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.to_daft" title="Link to this definition">¶</a></dt>
<dd><p>Returns a daft (<a class="reference external" href="https://docs.daft-pgm.org/en/latest/">https://docs.daft-pgm.org/en/latest/</a>) object which can be rendered for
publication quality plots. The returned object’s render method can be called to see the plots.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>node_pos</strong> (<em>str</em><em> or </em><em>dict</em><em> (</em><em>default: circular</em><em>)</em>) – <dl class="simple">
<dt>If str: Must be one of the following: circular, kamada_kawai, planar, random, shell, sprint,</dt><dd><dl class="simple">
<dt>spectral, spiral. Please refer:</dt><dd><dl class="simple">
<dt><a class="reference external" href="https://networkx.org/documentation/stable//reference/drawing.html#module-networkx.drawing.layout">https://networkx.org/documentation/stable//reference/drawing.html#module-networkx.drawing.layout</a></dt><dd><p>for details on these layouts.</p>
</dd>
</dl>
</dd>
</dl>
</dd>
</dl>
<p>If dict should be of the form {node: (x coordinate, y coordinate)} describing the x and y coordinate of each
node.</p>
<p>If no argument is provided uses circular layout.</p>
</p></li>
<li><p><strong>latex</strong> (<em>boolean</em>) – Whether to use latex for rendering the node names.</p></li>
<li><p><strong>pgm_params</strong> (<em>dict</em><em> (</em><em>optional</em><em>)</em>) – Any additional parameters that need to be passed to <cite>daft.PGM</cite> initializer.
Should be of the form: {param_name: param_value}</p></li>
<li><p><strong>edge_params</strong> (<em>dict</em><em> (</em><em>optional</em><em>)</em>) – Any additional edge parameters that need to be passed to <cite>daft.add_edge</cite> method.
Should be of the form: {(u1, v1): {param_name: param_value}, (u2, v2): {…} }</p></li>
<li><p><strong>node_params</strong> (<em>dict</em><em> (</em><em>optional</em><em>)</em>) – Any additional node parameters that need to be passed to <cite>daft.add_node</cite> method.
Should be of the form: {node1: {param_name: param_value}, node2: {…} }</p></li>
<li><p><strong>plot_edge_strength</strong> (<em>bool</em><em> (</em><em>default: False</em><em>)</em>) – If True, displays edge strength values as labels on edges.
Requires edge strengths to be computed first using the edge_strength() method.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>Daft object</strong> – Daft object for plotting the DAG.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>daft.PGM object</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"b"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"d"</span><span class="p">,</span> <span class="s2">"c"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="n">dag</span><span class="o">.</span><span class="n">to_daft</span><span class="p">(</span><span class="n">node_pos</span><span class="o">=</span><span class="p">{</span><span class="s2">"a"</span><span class="p">:</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="s2">"b"</span><span class="p">:</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="s2">"c"</span><span class="p">:</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="s2">"d"</span><span class="p">:</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)})</span>
<span class="go"><daft.PGM at 0x7fc756e936d0></span>
<span class="gp">>>> </span><span class="n">dag</span><span class="o">.</span><span class="n">to_daft</span><span class="p">(</span><span class="n">node_pos</span><span class="o">=</span><span class="s2">"circular"</span><span class="p">)</span>
<span class="go"><daft.PGM at 0x7f9bb48c5eb0></span>
<span class="gp">>>> </span><span class="n">dag</span><span class="o">.</span><span class="n">to_daft</span><span class="p">(</span><span class="n">node_pos</span><span class="o">=</span><span class="s2">"circular"</span><span class="p">,</span> <span class="n">pgm_params</span><span class="o">=</span><span class="p">{</span><span class="s2">"observed_style"</span><span class="p">:</span> <span class="s2">"inner"</span><span class="p">})</span>
<span class="go"><daft.PGM at 0x7f9bb48b0bb0></span>
<span class="gp">>>> </span><span class="n">dag</span><span class="o">.</span><span class="n">to_daft</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">node_pos</span><span class="o">=</span><span class="s2">"circular"</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">edge_params</span><span class="o">=</span><span class="p">{(</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"b"</span><span class="p">):</span> <span class="p">{</span><span class="s2">"label"</span><span class="p">:</span> <span class="mi">2</span><span class="p">}},</span>
<span class="gp">... </span> <span class="n">node_params</span><span class="o">=</span><span class="p">{</span><span class="s2">"a"</span><span class="p">:</span> <span class="p">{</span><span class="s2">"shape"</span><span class="p">:</span> <span class="s2">"rectangle"</span><span class="p">}},</span>
<span class="gp">... </span><span class="p">)</span>
<span class="go"><daft.PGM at 0x7f9bb48b0bb0></span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.to_dagitty">
<span class="sig-name descname"><span class="pre">to_dagitty</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.to_dagitty"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.to_dagitty" title="Link to this definition">¶</a></dt>
<dd><p>Convert the DAG to dagitty syntax representation.</p>
<p>The dagitty syntax represents directed acyclic graphs using
the dag { statements } format with -> for directed edges.
Isolated nodes (nodes with no edges) are included as standalone nodes.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>String representation of the DAG in dagitty syntax format.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">pgmpy.base</span><span class="w"> </span><span class="kn">import</span> <span class="n">DAG</span>
<span class="gp">>>> </span><span class="n">dag</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"X"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"Z"</span><span class="p">,</span> <span class="s2">"Y"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">dag</span><span class="o">.</span><span class="n">to_dagitty</span><span class="p">())</span>
<span class="go">dag {</span>
<span class="go">X -> Y</span>
<span class="go">Z -> Y</span>
<span class="go">}</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">dag2</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">([(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"B"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">)])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">dag2</span><span class="o">.</span><span class="n">to_dagitty</span><span class="p">())</span>
<span class="go">dag {</span>
<span class="go">A -> B</span>
<span class="go">B -> C</span>
<span class="go">}</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># DAG with isolated node</span>
<span class="gp">>>> </span><span class="n">dag3</span> <span class="o">=</span> <span class="n">DAG</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">dag3</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">([</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">dag3</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="s2">"A"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">dag3</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="s2">"C"</span><span class="p">)</span> <span class="c1"># Isolated node</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">dag3</span><span class="o">.</span><span class="n">to_dagitty</span><span class="p">())</span>
<span class="go">dag {</span>
<span class="go">A -> B</span>
<span class="go">C</span>
<span class="go">}</span>
</pre></div>
</div>
<p class="rubric">Notes</p>
<ul class="simple">
<li><p>Node names are converted to string representations using str().</p></li>
<li><p>If node names contain spaces or special characters, they will be used as-is.</p></li>
<li><p>Users should ensure node names are valid in R/dagitty context if needed.</p></li>
</ul>
<p class="rubric">References</p>
<p>dagitty syntax: <a class="reference external" href="https://cran.r-project.org/web/packages/dagitty/dagitty.pdf">https://cran.r-project.org/web/packages/dagitty/dagitty.pdf</a></p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pgmpy.base.DAG.DAG.to_graphviz">
<span class="sig-name descname"><span class="pre">to_graphviz</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">plot_edge_strength</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pgmpy/base/DAG.html#DAG.to_graphviz"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pgmpy.base.DAG.DAG.to_graphviz" title="Link to this definition">¶</a></dt>
<dd><p>Retuns a pygraphviz object for the DAG. pygraphviz is useful for
visualizing the network structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>plot_edge_strength</strong> (<em>bool</em><em> (</em><em>default: False</em><em>)</em>) – If True, displays edge strength values as labels on edges.
Requires edge strengths to be computed first using the edge_strength() method.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>AGraph object</strong> – pygraphviz object for plotting the DAG.</p>