part1/labs/11636785_11640758_lab2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Save this file as studentid1_studentid2_lab#.ipynb**\n",
    "(Your student-id is the number shown on your student card.)\n",
    "\n",
    "E.g. if you work with 3 people, the notebook should be named:\n",
    "12301230_3434343_1238938934_lab1.ipynb.\n",
    "\n",
    "**This will be parsed by a regexp, so please double check your filename.**\n",
    "\n",
    "Before you turn this problem in, please make sure everything runs correctly. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
    "\n",
    "**Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your names and email adresses below.**\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NAME = \"Gabriele Bani\"\n",
    "NAME2 = \"Andrii Skliar\"\n",
    "EMAIL = \"bani.gabri@gmail.com\"\n",
    "EMAIL2 = \"anreyws96@gmail.com\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "c39ec76a03b2143870009fb35729e8e0",
     "grade": false,
     "grade_id": "cell-8d856208da5d0763",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "# Lab 2: Classification\n",
    "\n",
    "### Machine Learning 1, September 17\n",
    "\n",
    "Notes on implementation:\n",
    "\n",
    "* You should write your code and answers in this IPython Notebook: http://ipython.org/notebook.html. If you have problems, please contact your teaching assistant.\n",
    "* Please write your answers right below the questions.\n",
    "* Among the first lines of your notebook should be \"%pylab inline\". This imports all required modules, and your plots will appear inline.\n",
    "* Use the provided test cells to check if your answers are correct\n",
    "* **Make sure your output and plots are correct before handing in your assignment with Kernel -> Restart & Run All**\n",
    "\n",
    "$\\newcommand{\\bx}{\\mathbf{x}}$\n",
    "$\\newcommand{\\bw}{\\mathbf{w}}$\n",
    "$\\newcommand{\\bt}{\\mathbf{t}}$\n",
    "$\\newcommand{\\by}{\\mathbf{y}}$\n",
    "$\\newcommand{\\bm}{\\mathbf{m}}$\n",
    "$\\newcommand{\\bb}{\\mathbf{b}}$\n",
    "$\\newcommand{\\bS}{\\mathbf{S}}$\n",
    "$\\newcommand{\\ba}{\\mathbf{a}}$\n",
    "$\\newcommand{\\bz}{\\mathbf{z}}$\n",
    "$\\newcommand{\\bv}{\\mathbf{v}}$\n",
    "$\\newcommand{\\bq}{\\mathbf{q}}$\n",
    "$\\newcommand{\\bp}{\\mathbf{p}}$\n",
    "$\\newcommand{\\bh}{\\mathbf{h}}$\n",
    "$\\newcommand{\\bI}{\\mathbf{I}}$\n",
    "$\\newcommand{\\bX}{\\mathbf{X}}$\n",
    "$\\newcommand{\\bT}{\\mathbf{T}}$\n",
    "$\\newcommand{\\bPhi}{\\mathbf{\\Phi}}$\n",
    "$\\newcommand{\\bW}{\\mathbf{W}}$\n",
    "$\\newcommand{\\bV}{\\mathbf{V}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "694e16c6fa7261b60747c28904049744",
     "grade": false,
     "grade_id": "cell-422dbc02437671ac",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "plt.rcParams[\"figure.figsize\"] = [9,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "17f77a32492fcf6ac989eab8a50e4dab",
     "grade": false,
     "grade_id": "cell-821f67d8cd14e4f7",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "# Part 1. Multiclass logistic regression\n",
    "\n",
    "Scenario: you have a friend with one big problem: she's completely blind. You decided to help her: she has a special smartphone for blind people, and you are going to develop a mobile phone app that can do _machine vision_ using the mobile camera: converting a picture (from the camera) to the meaning of the image. You decide to start with an app that can read handwritten digits, i.e. convert an image of handwritten digits to text (e.g. it would enable her to read precious handwritten phone numbers).\n",
    "\n",
    "A key building block for such an app would be a function `predict_digit(x)` that returns the digit class of an image patch $\\bx$. Since hand-coding this function is highly non-trivial, you decide to solve this problem using machine learning, such that the internal parameters of this function are automatically learned using machine learning techniques.\n",
    "\n",
    "The dataset you're going to use for this is the MNIST handwritten digits dataset (`http://yann.lecun.com/exdb/mnist/`). You can download the data with scikit learn, and load it as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "b82a7c9aec1e9157526d4fbe12f1d75d",
     "grade": false,
     "grade_id": "cell-bcdbc957165abae7",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "# Fetch the data\n",
    "mnist = fetch_mldata('MNIST original')\n",
    "data, target = mnist.data, mnist.target.astype('int')\n",
    "# Shuffle\n",
    "indices = np.arange(len(data))\n",
    "np.random.seed(123)\n",
    "np.random.shuffle(indices)\n",
    "data, target = data[indices].astype('float32'), target[indices]\n",
    "\n",
    "# Normalize the data between 0.0 and 1.0:\n",
    "data /= 255. \n",
    "\n",
    "# Split\n",
    "x_train, x_valid, x_test = data[:50000], data[50000:60000], data[60000: 70000]\n",
    "t_train, t_valid, t_test = target[:50000], target[50000:60000], target[60000: 70000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "5b20138af0810741223d2c2ddc82bf0f",
     "grade": false,
     "grade_id": "cell-b7b4a5a96dccf229",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "MNIST consists of small 28 by 28 pixel images of written digits (0-9). We split the dataset into a training, validation and testing arrays. The variables `x_train`, `x_valid` and `x_test` are $N \\times M$ matrices, where $N$ is the number of datapoints in the respective set, and $M = 28^2 = 784$ is the dimensionality of the data. The second set of variables `t_train`, `t_valid` and `t_test` contain the corresponding $N$-dimensional vector of integers, containing the true class labels.\n",
    "\n",
    "Here's a visualisation of the first 8 digits of the trainingset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "40e1628ec56b6d664edf9aaf496ea637",
     "grade": false,
     "grade_id": "cell-48a92c0a2a2bf4dd",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoEAAAFgCAYAAADEo6MCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERERRYhNIBEREVGE2AQSERERRej/A71lBRRy4hipAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ef356f358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data, num_cols, targets=None, shape=(28,28)):\n",
    "    num_digits = data.shape[0]\n",
    "    num_rows = int(num_digits/num_cols)\n",
    "    for i in range(num_digits):\n",
    "        plt.subplot(num_rows, num_cols, i+1)\n",
    "        plt.imshow(data[i].reshape(shape), interpolation='none', cmap='Greys')\n",
    "        if targets is not None:\n",
    "            plt.title(int(targets[i]))\n",
    "        plt.colorbar()\n",
    "        plt.axis('off')\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    \n",
    "plot_digits(x_train[0:40000:5000], num_cols=4, targets=t_train[0:40000:5000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "9908b1f7669980cd126946bf7983c096",
     "grade": false,
     "grade_id": "cell-3eb664a58e03bf42",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "In _multiclass_ logistic regression, the conditional probability of class label $j$ given the image $\\bx$ for some datapoint is given by:\n",
    "\n",
    "$ \\log p(t = j \\;|\\; \\bx, \\bb, \\bW) = \\log q_j - \\log Z$\n",
    "\n",
    "where $\\log q_j = \\bw_j^T \\bx + b_j$ (the log of the unnormalized probability of the class $j$), and $Z = \\sum_k q_k$ is the normalizing factor. $\\bw_j$ is the $j$-th column of $\\bW$ (a matrix of size $784 \\times 10$) corresponding to the class label, $b_j$ is the $j$-th element of $\\bb$.\n",
    "\n",
    "Given an input image, the multiclass logistic regression model first computes the intermediate vector $\\log \\bq$ (of size $10 \\times 1$), using $\\log q_j = \\bw_j^T \\bx + b_j$, containing the unnormalized log-probabilities per class. \n",
    "\n",
    "The unnormalized probabilities are then normalized by $Z$ such that $\\sum_j p_j = \\sum_j \\exp(\\log p_j) = 1$. This is done by $\\log p_j = \\log q_j - \\log Z$ where $Z = \\sum_i \\exp(\\log q_i)$. This is known as the _softmax_ transformation, and is also used as a last layer of many classifcation neural network models, to ensure that the output of the network is a normalized distribution, regardless of the values of second-to-last layer ($\\log \\bq$)\n",
    "\n",
    "**Warning**: when computing $\\log Z$, you are likely to encounter numerical problems. Save yourself countless hours of debugging and learn the [log-sum-exp trick](https://hips.seas.harvard.edu/blog/13/01/09/computing-log-sum-exp/ \"Title\").\n",
    "\n",
    "The network's output $\\log \\bp$ of size $10 \\times 1$ then contains the conditional log-probabilities $\\log p(t = j \\;|\\; \\bx, \\bb, \\bW)$ for each digit class $j$. In summary, the computations are done in this order:\n",
    "\n",
    "$\\bx \\rightarrow \\log \\bq \\rightarrow Z \\rightarrow \\log \\bp$\n",
    "\n",
    "Given some dataset with $N$ independent, identically distributed datapoints, the log-likelihood is given by:\n",
    "\n",
    "$ \\mathcal{L}(\\bb, \\bW) = \\sum_{n=1}^N \\mathcal{L}^{(n)}$\n",
    "\n",
    "where we use $\\mathcal{L}^{(n)}$ to denote the partial log-likelihood evaluated over a single datapoint. It is important to see that the log-probability of the class label $t^{(n)}$ given the image, is given by the $t^{(n)}$-th element of the network's output $\\log \\bp$, denoted by $\\log p_{t^{(n)}}$:\n",
    "\n",
    "$\\mathcal{L}^{(n)} = \\log p(t = t^{(n)} \\;|\\; \\bx = \\bx^{(n)}, \\bb, \\bW) = \\log p_{t^{(n)}} = \\log q_{t^{(n)}} - \\log Z^{(n)}$\n",
    "\n",
    "where $\\bx^{(n)}$ and $t^{(n)}$ are the input (image) and class label (integer) of the $n$-th datapoint, and $Z^{(n)}$ is the normalizing constant for the distribution over $t^{(n)}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "dfb50b2b2d11a7b8d1fe9bf5e9586442",
     "grade": false,
     "grade_id": "cell-17766ee789f11384",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## 1.1 Gradient-based stochastic optimization\n",
    "### 1.1.1 Derive gradient equations ( points)\n",
    "\n",
    "Derive the equations for computing the (first) partial derivatives of the log-likelihood w.r.t. all the parameters, evaluated at a _single_ datapoint $n$.\n",
    "\n",
    "You should start deriving the equations for $\\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j}$ for each $j$. For clarity, we'll use the shorthand $\\delta^q_j = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j}$.\n",
    "\n",
    "For $j = t^{(n)}$:\n",
    "$\n",
    "\\delta^q_j\n",
    "= \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log p_j}\n",
    "\\frac{\\partial \\log p_j}{\\partial \\log q_j}\n",
    "+ \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log Z}\n",
    "\\frac{\\partial \\log Z}{\\partial Z} \n",
    "\\frac{\\partial Z}{\\partial \\log q_j} \n",
    "= \\frac{\\partial \\log q_i}{\\partial \\log q_j} - \\frac{\\partial \\log Z}{\\partial Z} \n",
    "\\frac{\\partial Z}{\\partial \\log q_j}\n",
    "= 1 - \\frac{\\partial \\log Z}{\\partial Z} \n",
    "\\frac{\\partial Z}{\\partial \\log q_j}\n",
    "$\n",
    "\n",
    "For $j \\neq t^{(n)}$:\n",
    "$\n",
    "\\delta^q_j\n",
    "= \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log Z}\n",
    "\\frac{\\partial \\log Z}{\\partial Z} \n",
    "\\frac{\\partial Z}{\\partial \\log q_j} \n",
    "= - \\frac{\\partial \\log Z}{\\partial Z} \n",
    "\\frac{\\partial Z}{\\partial \\log q_j}\n",
    "$\n",
    "\n",
    "Complete the above derivations for $\\delta^q_j$ by furtherly developing $\\frac{\\partial \\log Z}{\\partial Z}$ and $\\frac{\\partial Z}{\\partial \\log q_j}$. Both are quite simple. For these it doesn't matter whether $j = t^{(n)}$ or not.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "f394ea0423ed2b17c80bbe8f1193cc81",
     "grade": true,
     "grade_id": "cell-e40110444a1e1d3f",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "We have that\n",
    "\\begin{align*}\n",
    "\\frac{\\partial \\log Z}{\\partial Z} = \\frac{1}{Z}\n",
    "\\end{align*}\n",
    "and\n",
    "\\begin{align*}\n",
    "    &\\frac{\\partial Z}{\\partial \\log q_j} \\\\\n",
    "    &=\\frac{\\partial \\sum_k q_k}{\\partial \\log q_j} \\\\\n",
    "    &=\\frac{\\partial \\sum_k \\exp ( \\log ( q_k) )}{\\partial \\log q_j} \\\\\n",
    "    &= \\exp(\\log(q_j))\n",
    "\\end{align*}\n",
    "\n",
    "For $j = t^{(n)}$:\n",
    "\\begin{align}\n",
    "\\delta^q_j\n",
    "&= 1 - \\frac{\\partial \\log Z}{\\partial Z} \\frac{\\partial Z}{\\partial \\log q_j} \\\\\n",
    "&= 1 - \\frac{1}{Z} \\exp(\\log(q_j)) \\\\\n",
    "&= 1 - \\frac{\\exp(\\log(q_j))}{\\sum_k q_k} \\\\\n",
    "&= 1 - \\frac{\\exp(\\log(q_j))}{\\exp(\\log(Z))} \n",
    "\\end{align}\n",
    "For $j \\neq t^{(n)}$:\n",
    "\\begin{align}\n",
    "\\delta^q_j\n",
    "&= - \\frac{\\partial \\log Z}{\\partial Z} \\frac{\\partial Z}{\\partial \\log q_j} \\\\\n",
    "&= - \\frac{1}{Z} \\exp(\\log(q_j)) \\\\\n",
    "&= - \\frac{\\exp(\\log(q_j))}{\\sum_k q_k} \\\\\n",
    "&= \\frac{\\exp(\\log(q_j))}{\\exp(\\log(Z))} \n",
    "\\end{align}\n",
    "\n",
    "\n",
    "**Note**: we have left the exponents of logarithms for consistency with implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "d46c028e9830445397d7b2275815990d",
     "grade": false,
     "grade_id": "cell-c770cfe1389ca4ff",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Given your equations for computing the gradients $\\delta^q_j$ it should be quite straightforward to derive the equations for the gradients of the parameters of the model, $\\frac{\\partial \\mathcal{L}^{(n)}}{\\partial W_{ij}}$ and $\\frac{\\partial \\mathcal{L}^{(n)}}{\\partial b_j}$. The gradients for the biases $\\bb$ are given by:\n",
    "\n",
    "$\n",
    "\\frac{\\partial \\mathcal{L}^{(n)}}{\\partial b_j}\n",
    "= \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j}\n",
    "\\frac{\\partial \\log q_j}{\\partial b_j}\n",
    "= \\delta^q_j\n",
    "\\cdot 1\n",
    "= \\delta^q_j\n",
    "$\n",
    "\n",
    "The equation above gives the derivative of $\\mathcal{L}^{(n)}$ w.r.t. a single element of $\\bb$, so the vector $\\nabla_\\bb \\mathcal{L}^{(n)}$ with all derivatives of $\\mathcal{L}^{(n)}$ w.r.t. the bias parameters $\\bb$ is: \n",
    "\n",
    "$\n",
    "\\nabla_\\bb \\mathcal{L}^{(n)} = \\mathbf{\\delta}^q\n",
    "$\n",
    "\n",
    "where $\\mathbf{\\delta}^q$ denotes the vector of size $10 \\times 1$ with elements $\\mathbf{\\delta}_j^q$.\n",
    "\n",
    "The (not fully developed) equation for computing the derivative of $\\mathcal{L}^{(n)}$ w.r.t. a single element $W_{ij}$ of $\\bW$ is:\n",
    "\n",
    "$\n",
    "\\frac{\\partial \\mathcal{L}^{(n)}}{\\partial W_{ij}} =\n",
    "\\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j}\n",
    "\\frac{\\partial \\log q_j}{\\partial W_{ij}}\n",
    "= \\mathbf{\\delta}_j^q\n",
    "\\frac{\\partial \\log q_j}{\\partial W_{ij}}\n",
    "$\n",
    "\n",
    "What is $\\frac{\\partial \\log q_j}{\\partial W_{ij}}$? Complete the equation above.\n",
    "\n",
    "If you want, you can give the resulting equation in vector format ($\\nabla_{\\bw_j} \\mathcal{L}^{(n)} = ...$), like we did for $\\nabla_\\bb \\mathcal{L}^{(n)}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "70fc98e5b227736e2bb92964a3c7174d",
     "grade": true,
     "grade_id": "cell-e40110444a1asdfasdfd3f",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "$\\frac{\\partial \\log q_j}{\\partial W_{ij}} = \\frac{\\partial \\mathbf{w}_j^T \\mathbf{x} + b_j}{\\partial W_{ij}}  = \n",
    "\\frac{\\partial \\sum_k^L w_{kj} x_{k} + b_k}{\\partial W_{ij}} = x_i$\n",
    "\n",
    "If we want to use vector notation, we have then\n",
    "\n",
    "$\\nabla_{\\bw_j} \\mathcal{L}^{(n)} = \\delta_J^q  \\mathbf{x} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "99387b4094640d8cd71bfd15687abc31",
     "grade": false,
     "grade_id": "cell-b0f28b0924b9983d",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.1.2 Implement gradient computations (10 points)\n",
    "\n",
    "Implement the gradient calculations you derived in the previous question. Write a function `logreg_gradient(x, t, w, b)` that returns the gradients $\\nabla_{\\bw_j} \\mathcal{L}^{(n)}$ (for each $j$) and $\\nabla_{\\bb} \\mathcal{L}^{(n)}$, i.e. the first partial derivatives of the log-likelihood w.r.t. the parameters $\\bW$ and $\\bb$, evaluated at a single datapoint (`x`, `t`).\n",
    "The computation will contain roughly the following intermediate variables:\n",
    "\n",
    "$\n",
    "\\log \\bq \\rightarrow Z \\rightarrow \\log \\bp\\,,\\, \\mathbf{\\delta}^q\n",
    "$\n",
    "\n",
    "followed by computation of the gradient vectors $\\nabla_{\\bw_j} \\mathcal{L}^{(n)}$ (contained in a $784 \\times 10$ matrix) and $\\nabla_{\\bb} \\mathcal{L}^{(n)}$ (a $10 \\times 1$ vector).\n",
    "\n",
    "For maximum points, ensure the function is numerically stable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "46b3dd32a8837896ac75063695c150f8",
     "grade": false,
     "grade_id": "cell-6858f885be587480",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "# 1.1.2 Compute gradient of log p(t|x;w,b) wrt w and b\n",
    "def logreg_gradient(x, t, w, b):\n",
    "    # YOUR CODE HERE\n",
    "    logq = np.dot(x, w) + b\n",
    "    \n",
    "    #log exp trick for numerical stability of logZ calculation\n",
    "    a = np.max(logq)\n",
    "    logZ = a + np.log(np.sum(np.exp(logq - a)))\n",
    "    \n",
    "    logp = logq - logZ\n",
    "    Z = np.exp(logZ)\n",
    "    deltaq = -np.exp(logq) / Z\n",
    "    # here deltaq is a matrix of dimension 1x10 \n",
    "    deltaq[0, t] += 1\n",
    "    dL_db = deltaq\n",
    "    dL_dw = np.outer(x, deltaq)\n",
    "    return logp[:,t].squeeze(), dL_dw, dL_db.squeeze()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "bcebc974c2a0ac928c9f0381e7e86eec",
     "grade": true,
     "grade_id": "cell-1c9659f607b151a2",
     "locked": true,
     "points": 4,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test gradient on one point\n",
      "Log Likelihood:\t -2.2959726720744777\n",
      "\n",
      "Grad_W_ij\t (784, 10) matrix\n",
      "Grad_W_ij[0,152:158]=\t [-0.04518971 -0.06758809 -0.07819784 -0.09077237 -0.07584012 -0.06365855]\n",
      "\n",
      "Grad_B_i shape\t (10,) vector\n",
      "Grad_B_i=\t [-0.10020327 -0.09977827 -0.1003198   0.89933657 -0.10037941 -0.10072863\n",
      " -0.09982729 -0.09928672 -0.09949324 -0.09931994]\n",
      "i in {0,...,9}; j in M\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "# scalar, 10 X 768  matrix, 10 X 1 vector\n",
    "w = np.random.normal(size=(28*28,10), scale=0.001)\n",
    "# w = np.zeros((784,10))\n",
    "b = np.zeros((10,))\n",
    "\n",
    "# test gradients, train on 1 sample\n",
    "logpt, grad_w, grad_b = logreg_gradient(x_train[0:1,:], t_train[0:1], w, b)\n",
    "\n",
    "print(\"Test gradient on one point\")\n",
    "print(\"Log Likelihood:\\t\", logpt)\n",
    "print(\"\\nGrad_W_ij\\t\",grad_w.shape,\"matrix\")\n",
    "print(\"Grad_W_ij[0,152:158]=\\t\", grad_w[152:158,0])\n",
    "print(\"\\nGrad_B_i shape\\t\",grad_b.shape,\"vector\")\n",
    "print(\"Grad_B_i=\\t\", grad_b.T)\n",
    "print(\"i in {0,...,9}; j in M\")\n",
    "\n",
    "assert logpt.shape == (), logpt.shape\n",
    "assert grad_w.shape == (784, 10), grad_w.shape\n",
    "assert grad_b.shape == (10,), grad_b.shape\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "72121207fa6163adf16cb3381ddde510",
     "grade": true,
     "grade_id": "cell-fd59c3a03a87ab83",
     "locked": true,
     "points": 4,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finite difference error grad_b: 5.23511748609e-08\n",
      "Finite difference error grad_w: 6.3612946893e-07\n"
     ]
    }
   ],
   "source": [
    "# It's always good to check your gradient implementations with finite difference checking:\n",
    "# Scipy provides the check_grad function, which requires flat input variables.\n",
    "# So we write two helper functions that provide can compute the gradient and output with 'flat' weights:\n",
    "from scipy.optimize import check_grad\n",
    "\n",
    "np.random.seed(123)\n",
    "# scalar, 10 X 768  matrix, 10 X 1 vector\n",
    "w = np.random.normal(size=(28*28,10), scale=0.001)\n",
    "# w = np.zeros((784,10))\n",
    "b = np.zeros((10,))\n",
    "\n",
    "def func(b):\n",
    "    logpt, grad_w, grad_b = logreg_gradient(x_train[0:1,:], t_train[0:1], w, b)\n",
    "    return logpt\n",
    "def grad(b):\n",
    "    logpt, grad_w, grad_b = logreg_gradient(x_train[0:1,:], t_train[0:1], w, b)\n",
    "    return grad_b.flatten()\n",
    "finite_diff_error = check_grad(func, grad, b)\n",
    "print('Finite difference error grad_b:', finite_diff_error)\n",
    "assert finite_diff_error < 1e-3, 'Your gradient computation for b seems off'\n",
    "\n",
    "\n",
    "\n",
    "def func(w):\n",
    "    logpt, grad_w, grad_b = logreg_gradient(x_train[0:1,:], t_train[0:1], w.reshape(784,10), b)\n",
    "    return logpt\n",
    "def grad(w):\n",
    "    logpt, grad_w, grad_b = logreg_gradient(x_train[0:1,:], t_train[0:1], w.reshape(784,10), b)\n",
    "    return grad_w.flatten()\n",
    "finite_diff_error = check_grad(func, grad, w.flatten())\n",
    "print('Finite difference error grad_w:', finite_diff_error)\n",
    "assert finite_diff_error < 1e-3, 'Your gradient computation for w seems off'\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "1aedefd481635db2e213dacbca5959d4",
     "grade": false,
     "grade_id": "cell-bdce061b39aaacec",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "\n",
    "### 1.1.3 Stochastic gradient descent (10 points)\n",
    "\n",
    "Write a function `sgd_iter(x_train, t_train, w, b)` that performs one iteration of stochastic gradient descent (SGD), and returns the new weights. It should go through the trainingset once in randomized order, call `logreg_gradient(x, t, w, b)` for each datapoint to get the gradients, and update the parameters **using a small learning rate of `1E-6`**. Note that in this case we're maximizing the likelihood function, so we should actually performing gradient ___ascent___... For more information about SGD, see Bishop 5.2.4 or an online source (i.e. https://en.wikipedia.org/wiki/Stochastic_gradient_descent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "a1fd10093bd350a24e4a718bc0133738",
     "grade": true,
     "grade_id": "cell-86bf84658f1c5bc8",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def sgd_iter(x_train, t_train, W, b):\n",
    "    p = np.random.permutation(x_train.shape[0])\n",
    "    xp, tp = x_train[p], t_train[p]\n",
    "    logp_train = 0\n",
    "    lr = 1E-6\n",
    "    N = x_train.shape[0]\n",
    "    for i in range(N):\n",
    "        x, t = xp[i], tp[i]\n",
    "        # convert from column vector (784,) to row vector (1, 784)\n",
    "        x = x[np.newaxis]\n",
    "        logp, dw, db = logreg_gradient(x, t, W, b)\n",
    "        logp_train += logp\n",
    "        W += lr*dw\n",
    "        b += lr*db\n",
    "    return logp_train / N, W , b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "f4eb4ba6aee968be7e896cb4ef74e745",
     "grade": true,
     "grade_id": "cell-2f7bbc264cc887a0",
     "locked": true,
     "points": 5,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# Sanity check:\n",
    "np.random.seed(1243)\n",
    "w = np.zeros((28*28, 10))\n",
    "b = np.zeros(10)\n",
    "    \n",
    "logp_train, W, b = sgd_iter(x_train[:5], t_train[:5], w, b)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "32ce2e1e1bc8ee7c2ed647ea65c6f943",
     "grade": false,
     "grade_id": "cell-81634c804e1f93fc",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## 1.2. Train\n",
    "\n",
    "### 1.2.1 Train (10 points)\n",
    "Perform 10 SGD iterations through the trainingset. Plot (in one graph) the conditional log-probability of the trainingset and validation set after each iteration.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Function for just calculating the log probabilities\n",
    "# Function is equivalent to SGD with learning rate 0 (so, without updating weights)\n",
    "def calc_prob(x_train, t_train, W, b):\n",
    "    logp_train = 0\n",
    "    lr = 1E-6\n",
    "    N = x_train.shape[0]\n",
    "    for i in range(N):\n",
    "        x, t = x_train[i], t_train[i]\n",
    "        # convert from column vector (784,) to row vector (1, 784)\n",
    "        x = x[np.newaxis] \n",
    "        logp, dw, db = logreg_gradient(x, t, W, b)\n",
    "        logp_train += logp\n",
    "    return logp_train / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "nbgrader": {
     "checksum": "02d6fffcf7065691be87ea236459d3e1",
     "grade": true,
     "grade_id": "cell-20a347ba4db6e82c",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1edeb707f0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAicAAAEyCAYAAAAho3BoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\no6ScRERERKOknERERESjpJxEREREo/wF3GZpldl6sYkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edf0566d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def test_sgd(x_train, t_train, w, b):\n",
    "    #list of log probabilities\n",
    "    tlist = []\n",
    "    vlist = []\n",
    "    for i in range(10):\n",
    "        logp_train, w, b = sgd_iter(x_train, t_train, w, b)\n",
    "        tlist.append(logp_train)\n",
    "        logp_valid = calc_prob(x_valid, t_valid, w, b)\n",
    "        vlist.append(logp_valid)\n",
    "    \n",
    "    return w, b, tlist, vlist\n",
    "\n",
    "np.random.seed(1243)\n",
    "w = np.zeros((28*28, 10))\n",
    "b = np.zeros(10)\n",
    "w,b, tlist, vlist = test_sgd(x_train, t_train, w, b)\n",
    "\n",
    "train, = plt.plot(tlist, 'r', label='Train')\n",
    "test, = plt.plot(vlist, 'g', label='Validation')\n",
    "plt.legend(handles=[train, test])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "a6d85bbd97cad35d524b65b23f64e75f",
     "grade": false,
     "grade_id": "cell-cf7f3da57d19493a",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.2.2 Visualize weights (10 points)\n",
    "Visualize the resulting parameters $\\bW$ after a few iterations through the training set, by treating each column of $\\bW$ as an image. If you want, you can use or edit the `plot_digits(...)` above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "nbgrader": {
     "checksum": "4e554436500eebe1527a31039570a264",
     "grade": true,
     "grade_id": "cell-b10656f35fac065e",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAFgCAYAAABHfSWNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlNio0lAURVFi8/8B+9YTa/zMDakAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edefec080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(w.T, num_cols=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "de187afcf5ae1e34b80bc10610760e7a",
     "grade": true,
     "grade_id": "cell-eb131c8b7303da38",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "**Describe in less than 100 words why these weights minimize the loss**\n",
    "\n",
    "First of all, the weights have been optimized by SGD in order to minimize the loss. We have 10 sets of weights, one for every class. We can see that for every class, the corresponding weights are higher for the features of the pixels most used for that class. Even more, the weights resemble the training numbers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "2bb485340ba8ee90a0d8cbc90fc7a7af",
     "grade": false,
     "grade_id": "cell-f36d974d9ef34c97",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.2.3. Visualize the 8 hardest and 8 easiest digits (10 points)\n",
    "Visualize the 8 digits in the validation set with the highest probability of the true class label under the model.\n",
    "Also plot the 8 digits that were assigned the lowest probability.\n",
    "Ask yourself if these results make sense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "nbgrader": {
     "checksum": "7fe3011f6f3ef6f6b00f58bb5dea7b76",
     "grade": true,
     "grade_id": "cell-3802d61680deeff5",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoEAAAFgCAYAAADEo6MCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEVGE2AQSERERRYhNIBEREVGE/j9Ezc7XC0TZ9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edefec400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoEAAAFgCAYAAADEo6MCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edf48d748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = x_valid.shape[0]\n",
    "logs = np.zeros(N)\n",
    "for i in range(N):\n",
    "    x, t = x_valid[i], t_valid[i]\n",
    "    x = x[np.newaxis]\n",
    "    logp, _, _ = logreg_gradient(x, t, w, b)\n",
    "    logs[i] = logp\n",
    "\n",
    "logs_min = np.argsort(logs)\n",
    "logs_max = np.argsort(-logs)\n",
    "\n",
    "plot_digits(x_valid[logs_min[:8]], num_cols=4, targets=t_valid[logs_min[:8]])\n",
    "plot_digits(x_valid[logs_max[:8]], num_cols=4, targets=t_valid[logs_max[:8]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "8d3b971f8daced95f5020cfffcb89d02",
     "grade": false,
     "grade_id": "cell-2c525344c99e5b26",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "# Part 2. Multilayer perceptron\n",
    "\n",
    "\n",
    "You discover that the predictions by the logistic regression classifier are not good enough for your application: the model is too simple. You want to increase the accuracy of your predictions by using a better model. For this purpose, you're going to use a multilayer perceptron (MLP), a simple kind of neural network. The perceptron wil have a single hidden layer $\\bh$ with $L$ elements. The parameters of the model are $\\bV$ (connections between input $\\bx$ and hidden layer $\\bh$), $\\ba$ (the biases/intercepts of $\\bh$), $\\bW$ (connections between $\\bh$ and $\\log q$) and $\\bb$ (the biases/intercepts of $\\log q$.\n",
    "\n",
    "The conditional probability of the class label $j$ is given by:\n",
    "\n",
    "$\\log p(t = j \\;|\\; \\bx, \\bb, \\bW) = \\log q_j - \\log Z$\n",
    "\n",
    "where $q_j$ are again the unnormalized probabilities per class, and $Z = \\sum_j q_j$ is again the probability normalizing factor. Each $q_j$ is computed using:\n",
    "\n",
    "$\\log q_j = \\bw_j^T \\bh + b_j$\n",
    "\n",
    "where $\\bh$ is a $L \\times 1$ vector with the hidden layer activations (of a hidden layer with size $L$), and $\\bw_j$ is the $j$-th column of $\\bW$ (a $L \\times 10$ matrix). Each element of the hidden layer is computed from the input vector $\\bx$ using:\n",
    "\n",
    "$h_j = \\sigma(\\bv_j^T \\bx + a_j)$\n",
    "\n",
    "where $\\bv_j$ is the $j$-th column of $\\bV$ (a $784 \\times L$ matrix), $a_j$ is the $j$-th element of $\\ba$, and $\\sigma(.)$ is the so-called sigmoid activation function, defined by:\n",
    "\n",
    "$\\sigma(x) = \\frac{1}{1 + \\exp(-x)}$\n",
    "\n",
    "Note that this model is almost equal to the multiclass logistic regression model, but with an extra 'hidden layer' $\\bh$. The activations of this hidden layer can be viewed as features computed from the input, where the feature transformation ($\\bV$ and $\\ba$) is learned.\n",
    "\n",
    "## 2.1 Derive gradient equations (20 points)\n",
    "\n",
    "State (shortly) why $\\nabla_{\\bb} \\mathcal{L}^{(n)}$ is equal to the earlier (multiclass logistic regression) case, and why $\\nabla_{\\bw_j} \\mathcal{L}^{(n)}$ is almost equal to the earlier case.\n",
    "\n",
    "Like in multiclass logistic regression, you should use intermediate variables $\\mathbf{\\delta}_j^q$. In addition, you should use intermediate variables $\\mathbf{\\delta}_j^h = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial h_j}$.\n",
    "\n",
    "Given an input image, roughly the following intermediate variables should be computed:\n",
    "\n",
    "$\n",
    "\\log \\bq \\rightarrow Z \\rightarrow \\log \\bp \\rightarrow \\mathbf{\\delta}^q \\rightarrow \\mathbf{\\delta}^h\n",
    "$\n",
    "\n",
    "where $\\mathbf{\\delta}_j^h = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\bh_j}$.\n",
    "\n",
    "Give the equations for computing $\\mathbf{\\delta}^h$, and for computing the derivatives of $\\mathcal{L}^{(n)}$ w.r.t. $\\bW$, $\\bb$, $\\bV$ and $\\ba$. \n",
    "\n",
    "You can use the convenient fact that $\\frac{\\partial}{\\partial x} \\sigma(x) = \\sigma(x) (1 - \\sigma(x))$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "bb7ce29f01484f94a6357784ddaf6412",
     "grade": true,
     "grade_id": "cell-48f48bb8ec75cc3c",
     "locked": false,
     "points": 20,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "The values of $\\delta_j^q$ are the same as for logistic regression.\n",
    "\n",
    "$ \\frac{\\partial }{\\partial b_j} \\mathcal{L}^{(n)} = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j} \\frac{\\partial \\log q_j}{\\partial b_j } = \\delta_j^q \\frac{\\bw_j^T \\bh + b_j}{\\partial b_j} = \\delta_j^q$\n",
    "\n",
    "in vector form, we have then\n",
    "$\\frac{\\partial }{\\partial \\bb} \\mathcal{L}^{(n)} = \\boldsymbol{\\delta}^q$\n",
    "\n",
    "for $\\bW$, we have\n",
    "\n",
    "$ \\frac{\\partial }{\\partial W_{ij}} \\mathcal{L}^{(n)} = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j} \\frac{\\partial \\log q_j}{\\partial W_{ij} } = \\delta_j^q \\frac{\\partial (\\bw_j^T \\bh + \\bb_j)}{\\partial W_{ij}} = \\frac{\\partial ((\\sum_k w_{ij}h_i) + bj)}{\\partial W_{ij}}= \\delta_j^q h_i$\n",
    "\n",
    "which, in vector form, can be written as\n",
    "\n",
    "$\\frac{\\partial }{\\partial \\bW} = \\bh (\\boldsymbol{\\delta}^q)^T$\n",
    "\n",
    "for $\\delta_i^h$ we have\n",
    "\n",
    "$\\delta_i^h = \\frac{\\partial}{\\partial h_i} \\mathcal{L}^{(n)} = \\sum_j \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j} \\frac{\\partial \\log q_j}{\\partial h_i} = \\sum_j \\delta_j^q \\frac{\\partial (\\bw_j^T \\bh + b_j)}{\\partial h_i} = \\sum_j \\delta_j^q \\frac{\\partial ((\\sum_k w_{kj} h_k ) + b_j)}{\\partial h_i} = \\sum_j \\delta_j^q w_{ij} = \\bw_{i, :} \\delta^q  $\n",
    "\n",
    "where $\\bw_{i, :}$ denotes the $i^{th}$ row of $\\bW$\n",
    "in vectorized form, we have\n",
    "\n",
    "$\\boldsymbol{\\delta}^h = \\bW \\boldsymbol{\\delta}^q$\n",
    "\n",
    "$ \\frac{\\partial }{\\partial a_i} \\mathcal{L}^{(n)} = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial h_i} \\frac{\\partial  h_i}{\\partial a_i } = \\delta_i^h \\frac{\\partial \\sigma (\\bv_i^T \\bx + a_i) }{\\partial a_i} = \\delta_i^h \\cdot \\sigma(\\bv_i^T \\bx + a_i) \\cdot (1 - \\sigma(\\bv_i^T \\bx + a_i))$\n",
    "\n",
    "in vector form, we have then\n",
    "\n",
    "$\\frac{\\partial }{\\partial \\ba} \\mathcal{L}^{(n)} = \\boldsymbol{\\delta}^h * \\sigma(\\bV^T \\bx + a) * (1 - \\sigma(\\bV^T \\bx + a))$\n",
    "\n",
    "where we use the symbol $*$ for denoting the element wise multiplication between two vectors\n",
    "\n",
    "for $\\bV$, we have\n",
    "\n",
    "$ \\frac{\\partial }{\\partial V_{ki}} \\mathcal{L}^{(n)} = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial h_i} \\frac{\\partial  h_i}{\\partial V_{ki} } = \\delta_i^h \\frac{\\partial \\sigma (\\bv_i^T \\bx + a_i) }{\\partial V_{ki}} = \\delta_i^h \\cdot \\sigma(\\bv_i^T \\bx + a_i) \\cdot (1 - \\sigma(\\bv_i^T \\bx + a_i)) \\frac{\\partial (\\sum_m w_{mi}x_m)) + a_i}{\\partial V_{ki}} = \\delta_i^h \\cdot \\sigma(\\bv_i^T \\bx + a_i) \\cdot (1 - \\sigma(\\bv_i^T \\bx + a_i)) x_k$\n",
    "\n",
    "which, in vector form, can be written as\n",
    "\n",
    "$\\frac{\\partial }{\\partial V} = \\bx \\big( \\boldsymbol{\\delta}^h * \\sigma(\\bV^T \\bx + \\ba) *  (1 - \\sigma(\\bV^T \\bx + \\ba)) \\big)^T $ \n",
    "\n",
    "where we use the symbol $*$ for denoting the element wise multiplication between two vectors\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "cfcfec5959134f7f3fca2ba585a94fba",
     "grade": false,
     "grade_id": "cell-0bff945081e993fc",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## 2.2 MAP optimization (10 points)\n",
    "\n",
    "You derived equations for finding the _maximum likelihood_ solution of the parameters. Explain, in a few sentences, how you could extend this approach so that it optimizes towards a _maximum a posteriori_ (MAP) solution of the parameters, with a Gaussian prior on the parameters. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "49d6376929b1cdf60a9ca9282512f1b4",
     "grade": true,
     "grade_id": "cell-1daef2744c010b73",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "We know that introducing a prior $p(\\theta | \\alpha) = \\mathcal{N}(0, \\alpha^{-1} I)$ over vector of parameters $\\theta$ corresponds to adding the term $- \\frac{\\alpha}{2} \\mathcal{\\theta}^T\\mathcal{\\theta}$ to the function we are optimizing, in this case to $\\mathcal{L}^{(n)}$. This is because with MAP there is an additional term regarding the log of the prior.\n",
    "We assume a different gaussian prior for $\\bW$ and $\\bV$.\n",
    "\n",
    "\\begin{align}\n",
    "&p(\\mathbf{V} | \\alpha_1) = \\mathcal{N}(0, \\alpha_1^{-1} I) \\\\\n",
    "&p(\\mathbf{W} | \\alpha_2) = \\mathcal{N}(0, \\alpha_2^{-1} I) \\\\\n",
    "\\end{align}\n",
    "\n",
    "This will result in adding the term $ -\\frac{\\alpha_1}{2} \\|\\bV\\|^2 -\\frac{\\alpha_2}{2} \\|\\bW\\|^2$ to $L^{(n)}$.\n",
    "Notice that mathematically, we should treat $\\bW$ and $\\bV$ as vectors. However, the final update will be anyways done element by element \n",
    "The updates that we get are\n",
    "\n",
    "$\\bW = \\bW + \\eta ( \\frac{\\partial }{\\partial \\bW} \\mathcal{L}^{(n)} - \\alpha \\bW)$\n",
    "\n",
    "$\\bV = \\bV + \\eta ( \\frac{\\partial }{\\partial \\bV} \\mathcal{L}^{(n)} - \\alpha \\bV)$\n",
    "\n",
    "where $\\eta$ is the learning rate. Thus, MAP for SGD would mean weight decay for parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "02e47e2058c064a6f9518077e62a9357",
     "grade": false,
     "grade_id": "cell-2e56d8a567e2fb08",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## 2.3. Implement and train a MLP (15 points)\n",
    "\n",
    "Implement a MLP model with a single hidden layer of ** neurons**. \n",
    "Train the model for **10 epochs**.\n",
    "Plot (in one graph) the conditional log-probability of the trainingset and validation set after each two iterations, as well as the weights.\n",
    "\n",
    "- 10 points: Working MLP that learns with plots\n",
    "- +5 points: Fast, numerically stable, vectorized implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "f8772d3e65d7f1bef5b739a62c2e192f",
     "grade": true,
     "grade_id": "cell-5d1924ace9e216e2",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1. / (1. + np.exp(-x))\n",
    "\n",
    "def forward(x, V, a, W, b):\n",
    "    h = sigmoid(V.transpose().dot(x) + a)\n",
    "    logq = W.transpose().dot(h) + b\n",
    "    aa = np.max(logq)\n",
    "    logZ = aa + np.log(np.sum(np.exp(logq - aa)))\n",
    "    logp = logq - logZ\n",
    "    return logp, logq, logZ, h\n",
    "\n",
    "def backward(x, h, t, V, a, W, b, logq, logZ):\n",
    "    # here we are using properties of exponentials and logarithms.\n",
    "    # equivalent to -np.exp(logq) / np.exp(logZ)\n",
    "    deltaq = - np.exp(logq - logZ)\n",
    "    deltaq[t] += 1\n",
    "    db = deltaq\n",
    "    dw = np.outer(h, deltaq)\n",
    "    deltah = W.dot(deltaq)\n",
    "    sigm2 = h*(1-h)\n",
    "    da = deltah * sigm2\n",
    "    dv = np.outer(x, deltah * sigm2)\n",
    "    return dv, da, dw, db\n",
    "\n",
    "\n",
    "def sgd_iter_train(x_train, t_train, V, a, W, b, lr=1E-2):\n",
    "    p = np.random.permutation(x_train.shape[0])\n",
    "    xp, tp = x_train[p], t_train[p]\n",
    "    logp_train = 0\n",
    "    for i in range(xp.shape[0]):\n",
    "        x, t = xp[i], tp[i]\n",
    "        logp, logq, logZ, h = forward(x, V, a, W, b)\n",
    "        dv, da, dw, db = backward(x, h, t, V, a, W, b, logq, logZ)\n",
    "        logp_train += logp[t]\n",
    "        V += lr*dv\n",
    "        a += lr*da\n",
    "        W += lr*dw\n",
    "        b += lr*db\n",
    "    return logp_train / x_train.shape[0], V, a, W, b\n",
    "\n",
    "def sgd_iter_loss(x_train, t_train, V, a, W, b, lr=1E-2):\n",
    "    p = np.random.permutation(x_train.shape[0])\n",
    "    xp, tp = x_train[p], t_train[p]\n",
    "    logp_train = 0\n",
    "    for i in range(xp.shape[0]):\n",
    "        x, t = xp[i], tp[i]\n",
    "        logp, logq, logZ, h = forward(x, V, a, W, b)\n",
    "        logp_train += logp[t]\n",
    "    return logp_train / x_train.shape[0], V, a, W, b\n",
    "\n",
    "def test_sgd(x_train, t_train, x_valid, t_valid, V, a, W, b):\n",
    "    tlist = []\n",
    "    vlist = []\n",
    "    for i in range(10):\n",
    "        logp_train, V, a, W, b = sgd_iter_train(x_train, t_train, V, a, W, b)\n",
    "        tlist.append(logp_train)\n",
    "        logp_valid, _, _, _, _ = sgd_iter_loss(x_valid, t_valid, V, a, W, b, lr=0)\n",
    "        vlist.append(logp_valid)\n",
    "    return tlist, vlist, V, a, W, b\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "301c1950ea79e09141e8ed170bd8b21b",
     "grade": true,
     "grade_id": "cell-e9b2125a5ea8a22c",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "L = 20\n",
    "V = np.random.normal(np.zeros((x_train.shape[1], L)), 0.1)\n",
    "a = np.random.normal(np.zeros(L), 0.1)\n",
    "W = np.random.normal(np.zeros((L, 10)), 0.1)\n",
    "b = np.random.normal(np.zeros(10), 0.1)\n",
    "\n",
    "tloglike, vloglike, V, a, W, b = test_sgd(x_train, t_train, x_valid, t_valid, V, a, W, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAi0AAAEyCAYAAAA2geChAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edf1e9d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoMAAAFgCAYAAADAVnM/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edeb31710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train, = plt.plot([x for i,x in enumerate(tloglike) if i % 2 == 0], 'r', label='Train')\n",
    "test, = plt.plot([x for i,x in enumerate(vloglike) if i % 2 == 0], 'g', label='Validation')\n",
    "plt.legend(handles=[train, test])\n",
    "plt.show()\n",
    "plot_digits(V.T, num_cols=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "555a73588f1a55d1185064f5a6192cac",
     "grade": false,
     "grade_id": "cell-6ae8cb5a4c246b97",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.3.1. Explain the weights (5 points)\n",
    "In less than 80 words, explain how and why the weights of the hidden layer of the MLP differ from the logistic regression model, and relate this to the stronger performance of the MLP."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "7f6cbf48a398f8722f4d403b957b2075",
     "grade": true,
     "grade_id": "cell-c4fdc27b1aab6828",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "The weights of logistic regression define a linear transformation of the input variables, while the weights of the  hidden layer of the MLP do the same for the features in the hidden layer, which are nonlinear function of the input. In the hidden layer, we have an intermediate representation that is also optimized during training. This allows the MLP to learn  which parts of the input are more informative than others in order to classify images."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "fa501d2127075b733105148f21adbaf2",
     "grade": false,
     "grade_id": "cell-df7f372be57b921b",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.3.1. Less than 250 misclassifications on the test set (10 bonus points)\n",
    "\n",
    "You receive an additional 10 bonus points if you manage to train a model with very high accuracy: at most 2.5% misclasified digits on the test set. Note that the test set contains 10000 digits, so you model should misclassify at most 250 digits. This should be achievable with a MLP model with one hidden layer. See results of various models at : `http://yann.lecun.com/exdb/mnist/index.html`. To reach such a low accuracy, you probably need to have a very high $L$ (many hidden units), probably $L > 0$, and apply a strong Gaussian prior on the weights. In this case you are allowed to use the validation set for training.\n",
    "You are allowed to add additional layers, and use convolutional networks, although that is probably not required to reach 2.5% misclassifications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "L = 300\n",
    "np.random.seed(1234)\n",
    "V = np.random.normal(np.zeros((x_train.shape[1], L)), 0.001)\n",
    "a = np.zeros(L)\n",
    "W = np.random.normal(np.zeros((L, 10)), 0.001)\n",
    "b = np.zeros(10)\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1. / (1. + np.exp(-x))\n",
    "\n",
    "def forward(x, V, a, W, b):\n",
    "    h = sigmoid(V.transpose().dot(x) + a)\n",
    "    logq = W.transpose().dot(h) + b\n",
    "    aa = np.max(logq)\n",
    "    logZ = aa + np.log(np.sum(np.exp(logq - aa)))\n",
    "    logp = logq - logZ\n",
    "    return logp, logq, logZ, h\n",
    "\n",
    "def backward(x, h, t, V, a, W, b, logq, logZ):\n",
    "    deltaq = - np.exp(logq - logZ)\n",
    "    deltaq[t] += 1\n",
    "    db = deltaq\n",
    "    dw = np.outer(h, deltaq)\n",
    "    deltah = W.dot(deltaq)\n",
    "    sigm2 = h*(1-h)\n",
    "    da = deltah * sigm2\n",
    "    dv = np.outer(x, deltah * sigm2)\n",
    "    return dv, da, dw, db\n",
    "\n",
    "def sgd_iter_train(x_train, t_train, V, a, W, b, lr=1E-1):\n",
    "    N = x_train.shape[0]\n",
    "    p = np.random.permutation(N)\n",
    "    xp, tp = x_train[p], t_train[p]\n",
    "    logp_train = 0\n",
    "    predicted = np.zeros(N)\n",
    "    for i in range(N):\n",
    "        x, t = xp[i], tp[i]\n",
    "        logp, logq, logZ, h = forward(x, V, a, W, b)\n",
    "        dv, da, dw, db = backward(x, h, t, V, a, W, b, logq, logZ)\n",
    "        logp_train += logp[t]\n",
    "        V += lr*dv\n",
    "        a += lr*da\n",
    "        W += lr*dw\n",
    "        b += lr*db\n",
    "    return logp_train/N, V, a, W, b\n",
    "\n",
    "def sgd_iter_loss(x_train, t_train, V, a, W, b, lr=1E-3):\n",
    "    N = x_train.shape[0]\n",
    "    p = np.random.permutation(N)\n",
    "    xp, tp = x_train[p], t_train[p]\n",
    "    logp_train = 0\n",
    "    predicted = np.zeros(N)\n",
    "    for i in range(N):\n",
    "        x, t = xp[i], tp[i]\n",
    "        logp, logq, logZ, h = forward(x, V, a, W, b)\n",
    "        logp_train += logp[t]\n",
    "    return logp_train/N, V, a, W, b\n",
    "\n",
    "def test_sgd(x_train, t_train, x_valid, t_valid, V, a, W, b):\n",
    "    tlist = []\n",
    "    vlist = []\n",
    "    for i in range(13):\n",
    "        logp_train, V, a, W, b = sgd_iter_train(x_train, t_train, V, a, W, b)\n",
    "        tlist.append(logp_train)\n",
    "        logp_valid, _, _, _, _ = sgd_iter_loss(x_test, t_test, V, a, W, b, lr=0)\n",
    "        vlist.append(logp_valid)\n",
    "    return tlist, vlist, V, a, W, b\n",
    "\n",
    "\n",
    "tloglike, vloglike, V, a, W, b = test_sgd(data[:60000], target[:60000], x_test, t_test, V, a, W, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predict_test = np.zeros(len(t_test))\n",
    "\n",
    "for i in range(x_test.shape[0]):\n",
    "    x, t = x_test[i], t_test[i]\n",
    "    logp, logq, logZ, h = forward(x, V, a, W, b)\n",
    "    predict_test[i] = np.argmax(logp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "b540e8fc73d65a4cc4139d9841e4aaba",
     "grade": true,
     "grade_id": "cell-4ad977cd0b7d27df",
     "locked": true,
     "points": 10,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test errors: 239\n"
     ]
    }
   ],
   "source": [
    "assert predict_test.shape == t_test.shape\n",
    "n_errors = np.sum(predict_test != t_test)\n",
    "print('Test errors: %d' % n_errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAogAAAFgCAYAAAA4tojIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1edf187ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(V.T[:20], num_cols=5)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}