diff --git a/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip b/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip
index 142c5251..5ff3ba73 100644
Binary files a/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip and b/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip differ
diff --git a/_downloads/2a4afa62d27b153aa605e093f9600e6b/plot_sim_red_syn.ipynb b/_downloads/2a4afa62d27b153aa605e093f9600e6b/plot_sim_red_syn.ipynb
index 197ff328..a4283453 100644
--- a/_downloads/2a4afa62d27b153aa605e093f9600e6b/plot_sim_red_syn.ipynb
+++ b/_downloads/2a4afa62d27b153aa605e093f9600e6b/plot_sim_red_syn.ipynb
@@ -15,14 +15,14 @@
},
"outputs": [],
"source": [
- "import numpy as np\n\nfrom hoi.metrics import Oinfo, GradientOinfo\n\nimport matplotlib.pyplot as plt\n\nnp.random.seed(42)\nplt.style.use(\"ggplot\")"
+ "import numpy as np\n\nfrom hoi.metrics import Oinfo, GradientOinfo\nfrom hoi.simulation import simulate_hoi_gauss\n\nimport matplotlib.pyplot as plt\n\nnp.random.seed(42)\nplt.style.use(\"ggplot\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Redundant and synergistic behavior\n\nIn this first part, we are going to create a random variable `x`, a network\ncomposed of three nodes (1, 2, 3). Then we need a function to estimate\nwhether the interactions between the three nodes are more redundant or more\nsynergistic. To estimate whether the interactions between the three nodes are\nredundant or # synergistic, we are gonig to use the\n:class:`hoi.metrics.Oinfo`. When the Oinfo is positive, it means that the\ninteractions are redundant and if the Oinfo is negative, the interactions are\nsynergistic.\n\n"
+ "## Redundant and synergistic behavior\n\nIn this first part, we are going to create a multivariate gaussian variable\n`x` with specific information patterns. Then we need a function to estimate\nwhether the interactions between the three nodes are more redundant or more\nsynergistic. To estimate whether the interactions between the three nodes are\nredundant or synergistic, we are gonig to use the\n:class:`hoi.metrics.Oinfo`. When the Oinfo is positive, it means that the\ninteractions are redundant and if the Oinfo is negative, the interactions are\nsynergistic.\n\n"
]
},
{
@@ -40,7 +40,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "### Simulating redundant behavior\n\nThe redundancy means that the nodes (1, 2, 3) in the system `x` are receiving\nmultiple copies of the same information. A simple way to simulate redundancy\nconsists in taking the signal of one node, let's say the first one, and copy\nthis signal to the two other nodes.\n\n"
+ "### Simulating synergistic behavior\n\nIn gaussian multivariate data, it is possible to generate synergy and\nredundancy by setting the parameters of the covariance matrix. This is\nwhat can be done using the function\n:class:`hoi.simulation.simulate_hoi_gauss`, in the following way:\n\n"
]
},
{
@@ -51,7 +51,68 @@
},
"outputs": [],
"source": [
- "# x = (n_samples, n_nodes)\nx = np.random.rand(1000, 3)\n\nx[:, 1] = x[:, 1] + x[:, 0] # 1 = 1 & 0\nx[:, 2] = x[:, 2] + x[:, 0] # 2 = 2 & 0"
+ "# x = (n_samples, n_nodes)\nx = simulate_hoi_gauss(\n target=False, n_samples=1000, triplet_character=\"synergy\"\n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "compute hoi using the Oinfo\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "hoi = compute_hoi_beh(x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Print HOI value\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"HOI between nodes (1, 2, 3) : {hoi}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As we can see, the estimated HOI is negative which is the hallmark of\nsynergy when using the Oinfo. Be careful because some metrics are positive\nfor synergistic interactions.\n\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Simulating redundant behavior\n\nAs for the redundancy, we can generate three gaussian variables, presenting\nsynergistic behavior, using the funciton,\n:class:`hoi.simulation.simulate_hoi_gauss`, in the following way:\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# x = (n_samples, n_nodes)\nx = simulate_hoi_gauss(\n target=False, n_samples=1000, triplet_character=\"redundancy\"\n)"
]
},
{
@@ -94,14 +155,14 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "As we can see, the estimated HOI is positive which is the hallmark of\nredundancy when using the Oinfo. Be careful because some metrics are negative\nfor redundant interactions.\n\n"
+ "Now HOI is positive, therefore the interaction between the three nodes is\ndominated by redundancy.\n\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "### Simulating synergistic behavior\n\nA synergy is obtained when elements of a system work together to produce an\neffect that is greater than the sum of their individual contributions. A\nsimple example is the sum. When a variable `A` is defined as the sum of two\nother variables $A = B + C$ then we need both `B` and `C` to know `A`.\nThat's what we are going to use here to simulate synergy.\n\n"
+ "### Simulating synergistic behavior by sum operation\n\nA synergy is obtained when elements of a system work together to produce an\neffect that is greater than the sum of their individual contributions. A\nsimple example is the sum. When a variable `A` is defined as the sum of two\nother variables $A = B + C$ then we need both `B` and `C` to know `A`.\nThat's what we are going to use here to simulate synergy.\n\n"
]
},
{
@@ -158,6 +219,67 @@
"Now HOI is negative, therefore the interaction between the three nodes is\ndominated by synergy.\n\n"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Simulating redundant behavior by copy operator\n\nRedundancy can emerge when nodes (1, 2, 3) in the system `x` are receiving\nmultiple copies of the same information. A simple way to simulate redundancy\nconsists in taking the signal of one node, let's say the first one, and copy\nthis signal to the two other nodes.\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# x = (n_samples, n_nodes)\nx = np.random.rand(1000, 3)\n\nx[:, 1] = x[:, 1] + x[:, 0] # 1 = 1 & 0\nx[:, 2] = x[:, 2] + x[:, 0] # 2 = 2 & 0"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "compute hoi using the Oinfo\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "hoi = compute_hoi_beh(x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Print HOI value\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"HOI between nodes (1, 2, 3) : {hoi}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As we can see, the estimated HOI is positive which is the hallmark of\nredundancy when using the Oinfo.\n\n"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
@@ -180,7 +302,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Redundant and synergistic encoding\n\nIn this second part, we are going to switch for encoding measure, in the sens\nthat elements of a network areg going to carry redundant or synergistic\ninformation about an external variable. To estimate HOI about a target\nvariable `y`, we're going to use the :class:`hoi.metrics.GradientOinfo`. To\nsimulate redundancy and synergy, we're going to use the same method as\nbefore.\n\n"
+ "## Redundant and synergistic encoding\n\nIn this second part, we are going to switch for encoding measure, in the sens\nthat elements of a network areg going to carry redundant or synergistic\ninformation about an external variable. To estimate HOI about a target\nvariable `y`, we're going to use the :class:`hoi.metrics.GradientOinfo`. To\nsimulate redundancy and synergy, we're going to use the same methods as\nbefore.\n\n"
]
},
{
@@ -198,7 +320,129 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "### Simulating redundant encoding\n\nTo simulate redundancy, we copy the y variable into each node of x\n\n"
+ "### Simulating redundant encoding\n\nTo simulate redundancy, between a triplet of variable `x` and a target\nvariable `y`\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# x = (n_samples, n_nodes)\nx, y = simulate_hoi_gauss(\n target=True, n_samples=1000, triplet_character=\"redundancy\"\n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "compute hoi\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "hoi = compute_hoi_enc(x, y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Print HOI value\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"HOI between nodes (1, 2, 3) about y : {hoi}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "the estimated HOI is positive which represents redundant interactions between\nthe three nodes about y.\n\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Simulating synergistic encoding\n\nTo simulate synergy, between a triplet of variable `x` and a target\nvariable `y`\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# x = (n_samples, n_nodes)\nx, y = simulate_hoi_gauss(\n target=True, n_samples=1000, triplet_character=\"synergy\"\n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "compute hoi\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "hoi = compute_hoi_enc(x, y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Print HOI value\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"HOI between nodes (1, 2, 3) about y : {hoi}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "the estimated HOI is negative which represents synergistic interactions\nbetween the three nodes about y.\n\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Simulating redundant encoding by copy operation\n\nTo simulate redundancy, we copy the y variable into each node of x\n\n"
]
},
{
@@ -259,7 +503,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "### Simulating synergistic encoding\n\nTo simulate synergy, we define the y variable as the sum of the three nodes\n\n"
+ "### Simulating synergistic encoding by sum operation\n\nTo simulate synergy, we define the y variable as the sum of the three nodes\n\n"
]
},
{
diff --git a/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip b/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip
index 75d1cc2e..18954099 100644
Binary files a/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip and b/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip differ
diff --git a/_downloads/f5814f7ad17220e2d429a4f0957c571e/plot_sim_red_syn.py b/_downloads/f5814f7ad17220e2d429a4f0957c571e/plot_sim_red_syn.py
index 4006fea8..c91dc3b8 100644
--- a/_downloads/f5814f7ad17220e2d429a4f0957c571e/plot_sim_red_syn.py
+++ b/_downloads/f5814f7ad17220e2d429a4f0957c571e/plot_sim_red_syn.py
@@ -16,6 +16,7 @@
import numpy as np
from hoi.metrics import Oinfo, GradientOinfo
+from hoi.simulation import simulate_hoi_gauss
import matplotlib.pyplot as plt
@@ -26,11 +27,11 @@
# Redundant and synergistic behavior
# ----------------------------------
#
-# In this first part, we are going to create a random variable `x`, a network
-# composed of three nodes (1, 2, 3). Then we need a function to estimate
+# In this first part, we are going to create a multivariate gaussian variable
+# `x` with specific information patterns. Then we need a function to estimate
# whether the interactions between the three nodes are more redundant or more
# synergistic. To estimate whether the interactions between the three nodes are
-# redundant or # synergistic, we are gonig to use the
+# redundant or synergistic, we are gonig to use the
# :class:`hoi.metrics.Oinfo`. When the Oinfo is positive, it means that the
# interactions are redundant and if the Oinfo is negative, the interactions are
# synergistic.
@@ -45,19 +46,44 @@ def compute_hoi_beh(x):
# %%
-# Simulating redundant behavior
-# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+# Simulating synergistic behavior
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
-# The redundancy means that the nodes (1, 2, 3) in the system `x` are receiving
-# multiple copies of the same information. A simple way to simulate redundancy
-# consists in taking the signal of one node, let's say the first one, and copy
-# this signal to the two other nodes.
+# In gaussian multivariate data, it is possible to generate synergy and
+# redundancy by setting the parameters of the covariance matrix. This is
+# what can be done using the function
+# :class:`hoi.simulation.simulate_hoi_gauss`, in the following way:
# x = (n_samples, n_nodes)
-x = np.random.rand(1000, 3)
+x = simulate_hoi_gauss(
+ target=False, n_samples=1000, triplet_character="synergy"
+)
-x[:, 1] = x[:, 1] + x[:, 0] # 1 = 1 & 0
-x[:, 2] = x[:, 2] + x[:, 0] # 2 = 2 & 0
+# %%
+# compute hoi using the Oinfo
+hoi = compute_hoi_beh(x)
+
+# %%
+# Print HOI value
+print(f"HOI between nodes (1, 2, 3) : {hoi}")
+
+# %%
+# As we can see, the estimated HOI is negative which is the hallmark of
+# synergy when using the Oinfo. Be careful because some metrics are positive
+# for synergistic interactions.
+
+# %%
+# Simulating redundant behavior
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+#
+# As for the redundancy, we can generate three gaussian variables, presenting
+# synergistic behavior, using the funciton,
+# :class:`hoi.simulation.simulate_hoi_gauss`, in the following way:
+
+# x = (n_samples, n_nodes)
+x = simulate_hoi_gauss(
+ target=False, n_samples=1000, triplet_character="redundancy"
+)
# %%
# compute hoi using the Oinfo
@@ -68,13 +94,12 @@ def compute_hoi_beh(x):
print(f"HOI between nodes (1, 2, 3) : {hoi}")
# %%
-# As we can see, the estimated HOI is positive which is the hallmark of
-# redundancy when using the Oinfo. Be careful because some metrics are negative
-# for redundant interactions.
+# Now HOI is positive, therefore the interaction between the three nodes is
+# dominated by redundancy.
# %%
-# Simulating synergistic behavior
-# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+# Simulating synergistic behavior by sum operation
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# A synergy is obtained when elements of a system work together to produce an
# effect that is greater than the sum of their individual contributions. A
@@ -100,6 +125,33 @@ def compute_hoi_beh(x):
# Now HOI is negative, therefore the interaction between the three nodes is
# dominated by synergy.
+# %%
+# Simulating redundant behavior by copy operator
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+#
+# Redundancy can emerge when nodes (1, 2, 3) in the system `x` are receiving
+# multiple copies of the same information. A simple way to simulate redundancy
+# consists in taking the signal of one node, let's say the first one, and copy
+# this signal to the two other nodes.
+
+# x = (n_samples, n_nodes)
+x = np.random.rand(1000, 3)
+
+x[:, 1] = x[:, 1] + x[:, 0] # 1 = 1 & 0
+x[:, 2] = x[:, 2] + x[:, 0] # 2 = 2 & 0
+
+# %%
+# compute hoi using the Oinfo
+hoi = compute_hoi_beh(x)
+
+# %%
+# Print HOI value
+print(f"HOI between nodes (1, 2, 3) : {hoi}")
+
+# %%
+# As we can see, the estimated HOI is positive which is the hallmark of
+# redundancy when using the Oinfo.
+
# %%
# Simulating dynamic redundancy and synergy
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -144,7 +196,7 @@ def compute_hoi_beh(x):
# that elements of a network areg going to carry redundant or synergistic
# information about an external variable. To estimate HOI about a target
# variable `y`, we're going to use the :class:`hoi.metrics.GradientOinfo`. To
-# simulate redundancy and synergy, we're going to use the same method as
+# simulate redundancy and synergy, we're going to use the same methods as
# before.
@@ -160,6 +212,54 @@ def compute_hoi_enc(x, y):
# Simulating redundant encoding
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
+# To simulate redundancy, between a triplet of variable `x` and a target
+# variable `y`
+
+# x = (n_samples, n_nodes)
+x, y = simulate_hoi_gauss(
+ target=True, n_samples=1000, triplet_character="redundancy"
+)
+
+# %%
+# compute hoi
+hoi = compute_hoi_enc(x, y)
+
+# %%
+# Print HOI value
+print(f"HOI between nodes (1, 2, 3) about y : {hoi}")
+
+# %%
+# the estimated HOI is positive which represents redundant interactions between
+# the three nodes about y.
+
+# %%
+# Simulating synergistic encoding
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+#
+# To simulate synergy, between a triplet of variable `x` and a target
+# variable `y`
+
+# x = (n_samples, n_nodes)
+x, y = simulate_hoi_gauss(
+ target=True, n_samples=1000, triplet_character="synergy"
+)
+
+# %%
+# compute hoi
+hoi = compute_hoi_enc(x, y)
+
+# %%
+# Print HOI value
+print(f"HOI between nodes (1, 2, 3) about y : {hoi}")
+
+# %%
+# the estimated HOI is negative which represents synergistic interactions
+# between the three nodes about y.
+
+# %%
+# Simulating redundant encoding by copy operation
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+#
# To simulate redundancy, we copy the y variable into each node of x
# x = (n_samples, n_nodes)
@@ -184,8 +284,8 @@ def compute_hoi_enc(x, y):
# the three nodes about y.
# %%
-# Simulating synergistic encoding
-# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+# Simulating synergistic encoding by sum operation
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# To simulate synergy, we define the y variable as the sum of the three nodes
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