Lab2.ipynb

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      "# Lab 2: Classification\n",
      "\n",
      "### Machine Learning 1, September 2015\n",
      "\n",
      "* The lab exercises should be made in groups of two, three or four people.\n",
      "* The deadline is October 4th (Sunday) 23:59.\n",
      "* Assignment should be sent to Philip Versteeg (p.j.j.p.versteeg@uva.nl). The subject line of your email should be \"lab\\#\\_lastname1\\_lastname2\\_lastname3\".\n",
      "* Put your and your teammates' names in the body of the email\n",
      "* Attach the .IPYNB (IPython Notebook) file containing your code and answers. Naming of the file follows the same rule as the subject line. For example, if the subject line is \"lab01\\_Kingma\\_Hu\", the attached file should be \"lab01\\_Kingma\\_Hu.ipynb\". Only use underscores (\"\\_\") to connect names, otherwise the files cannot be parsed.\n",
      "\n",
      "Notes on implementation:\n",
      "\n",
      "* For this notebook you need to answer a few theory questions, add them in the Markdown cell's below the question. Note: you can use Latex-style code in here.\n",
      "* Focus on Part 1 the first week, and Part 2 the second week!\n",
      "* You should write your code and answers below the questions in this IPython Notebook.\n",
      "* Among the first lines of your notebook should be \"%pylab inline\". This imports all required modules, and your plots will appear inline.\n",
      "* If you have questions outside of the labs, post them on blackboard or email me.\n",
      "* NOTE: Make sure we can run your notebook / scripts!\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",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import gzip, cPickle\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "from pylab import *\n",
      "rcParams['legend.loc'] = 'best'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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 load the data from `mnist.pkl.gz` we provided, using: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def load_mnist():\n",
      "    f = gzip.open('mnist.pkl.gz', 'rb')\n",
      "    data = cPickle.load(f)\n",
      "    f.close()\n",
      "    return data\n",
      "\n",
      "(x_train, t_train), (x_valid, t_valid), (x_test, t_test) = load_mnist()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The tuples represent train, validation and test sets. The first element (`x_train`, `x_valid`, `x_test`) of each tuple is a $N \\times M$ matrix, where $N$ is the number of datapoints and $M = 28^2 = 784$ is the dimensionality of the data. The second element (`t_train`, `t_valid`, `t_test`) of each tuple is 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",
     "collapsed": false,
     "input": [
      "def plot_digits(data, numcols, shape=(28,28)):\n",
      "    numdigits = data.shape[0]\n",
      "    numrows = int(numdigits/numcols)\n",
      "    for i in range(0, numdigits):\n",
      "        plt.subplot(numrows, numcols, i)\n",
      "        plt.axis('off')\n",
      "        plt.imshow(data[i].reshape(shape), interpolation='nearest', cmap='Greys')\n",
      "    plt.show()\n",
      "    \n",
      "plot_digits(x_train[0:8], numcols=4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/lib64/python2.7/site-packages/matplotlib/axes/_subplots.py:69: MatplotlibDeprecationWarning: The use of 0 (which ends up being the _last_ sub-plot) is deprecated in 1.4 and will raise an error in 1.5\n",
        "  mplDeprecation)\n"
       ]
      },
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       "text": [
        "<matplotlib.figure.Figure at 0x7fefb2bef150>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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 $Z = \\sum_j \\exp(\\log q_j)$. 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/2013/01/09/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": {},
     "source": [
      "## 1.1 Gradient-based stochastic optimization\n",
      "\n",
      "### 1.1.1 Derive gradient equations (20 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",
      "$\n",
      "\\delta^q_j\n",
      "= \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log p_j}\n",
      "\\frac{\\partial \\log p_j}{\\partial \\log q_j}\n",
      "+ \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log Z}\n",
      "\\frac{\\partial \\log Z}{\\partial Z} \n",
      "\\frac{\\partial Z}{\\partial \\log q_j} \n",
      "= 1 \\cdot 1 - \\frac{\\partial \\log Z}{\\partial Z} \n",
      "\\frac{\\partial Z}{\\partial \\log q_j}\n",
      "= 1 - \\frac{\\partial \\log Z}{\\partial Z} \n",
      "\\frac{\\partial Z}{\\partial \\log q_j}\n",
      "$\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",
      "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",
      "##### Answer: "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\dfrac{\\partial \\log Z}{\\partial Z} = \\dfrac{1}{Z}$\n",
      "\n",
      "$\\dfrac{\\partial Z}{\\partial \\log q_j} = \\dfrac{\\partial \\sum_k q_k}{\\partial \\log q_j} = \\dfrac{\\partial q_j}{\\partial \\log q_j} = \\dfrac{\\partial exp(\\log q_j)}{\\partial \\log q_j} = exp(\\log q_j)$\n",
      "\n",
      "For $j = t^{(n)}$: $\\delta_j^q = 1 - \\dfrac{1}{Z}exp(\\log q_j)$\n",
      "\n",
      "For $j \\neq t^{(n)}$: $\\delta_j^q = -\\dfrac{1}{Z}exp(\\log q_j)$\n",
      "\n",
      "$ \\log q_j = \\mathbf{w}_j^T \\mathbf{x} = b_j + \\sum_{i} W_{ij} x_i \\Rightarrow \\dfrac{\\partial \\log q_j}{\\partial W_{ij}} = x_i \\Rightarrow \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial W_{ij}} = \\delta_j^q x_i$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logreg_gradient(x, t, W, b):\n",
      "    log_q = W.T.dot(x) + b\n",
      "\n",
      "    # Log-sum-exp trick\n",
      "    a = np.max(log_q)\n",
      "    logZ = a + np.log(np.sum(np.exp(log_q - a)))\n",
      "    Z = np.exp(logZ)\n",
      "    grad_b = -np.exp(log_q) / Z\n",
      "    grad_b[t] += 1\n",
      "    grad_w = x[np.newaxis].T.dot(grad_b[np.newaxis])\n",
      "    return grad_w, grad_b\n",
      "\n",
      "def init_weights(num_of_features, num_of_class):\n",
      "    w = (np.random.random_sample((num_of_features, num_of_class)) - 0.5) * 0.001\n",
      "    b = (np.random.random_sample(num_of_class) - 0.5) * 0.001\n",
      "    return w, b\n",
      "\n",
      "np.random.seed(0)\n",
      "num_of_features = x_train.shape[1]\n",
      "num_of_class = 10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "# Test\n",
      "w, b = init_weights(num_of_features, num_of_class)\n",
      "\n",
      "random_item_id = np.random.randint(x_train.shape[0])\n",
      "grad_w, grad_b = logreg_gradient(x_train[random_item_id], t_train[random_item_id], w, b)\n",
      "print grad_w.shape, grad_b.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(784, 10) (10,)\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 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 (e.g. `1E-4`). 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",
     "collapsed": false,
     "input": [
      "def compute_log_likelihood(x, t, w, b):\n",
      "    log_q = x.dot(w) + b\n",
      "    a = np.max(log_q, axis=1)\n",
      "    log_Z = a + np.log(np.sum(np.exp((log_q.T - a).T)))\n",
      "    #print log_Z\n",
      "    log_likelihood = np.sum(np.array([log_q[index, value] for (index,), value in np.ndenumerate(t)]) - log_Z)\n",
      "    return log_likelihood\n",
      "\n",
      "def sgd_iter(x_train, t_train, w, b, lr=0.001):\n",
      "    \"\"\"\n",
      "    Don't need to return w and b. They are modified by reference\n",
      "    \"\"\"\n",
      "    indexes = np.arange(len(x_train))\n",
      "    np.random.shuffle(indexes)\n",
      "\n",
      "    for index in indexes:\n",
      "        grad_w, delta = logreg_gradient(x_train[index], t_train[index], w, b)\n",
      "        w += lr * grad_w\n",
      "        b += lr * delta"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "# Test\n",
      "w, b = init_weights(num_of_features, num_of_class)\n",
      "print 'Likelihood:', compute_log_likelihood(x_train, t_train, w, b)\n",
      "sgd_iter(x_train, t_train, w, b)\n",
      "print 'Likelihood:', compute_log_likelihood(x_train, t_train, w, b)\n",
      "\n",
      "print w.shape, b.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Likelihood: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-656101.475887\n",
        "Likelihood:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " -563579.176356\n",
        "(784, 10) (10,)\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 1.2. Train\n",
      "\n",
      "### 1.2.1 Train (10 points)\n",
      "Perform a handful of training 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",
     "collapsed": false,
     "input": [
      "w, b = init_weights(num_of_features, num_of_class)\n",
      "\n",
      "loglik_train = [compute_log_likelihood(x_train, t_train, w, b)]\n",
      "loglik_valid = [compute_log_likelihood(x_valid, t_valid, w, b)]\n",
      "\n",
      "for i in xrange(20):\n",
      "    sgd_iter(x_train, t_train, w, b)\n",
      "    loglik_train.append(compute_log_likelihood(x_train, t_train, w, b))\n",
      "    loglik_valid.append(compute_log_likelihood(x_valid, t_valid, w, b))\n",
      "print loglik_train\n",
      "print loglik_valid"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-656127.78796885256, -563489.54004502413, -560710.70819607517, -559476.86415083136, -558672.87133309408, -558126.77589244605, -557778.31006429915, -557503.29501747712, -557221.17392680771, -557006.95308198209, -556857.89457949984, -556652.54276553483, -556608.59091926157, -556414.18220701138, -556325.04402379564, -556193.87064407591, -556191.2871871643, -556029.22706000751, -555984.25005778333, -555919.39343924192, -555812.71085594292]\n",
        "[-115131.3188426539, -96225.157424292818, -95739.368808260973, -95537.644802986848, -95416.687431804312, -95324.357970577519, -95276.300002378557, -95226.403100354655, -95198.58238510575, -95163.42667403337, -95141.45578611338, -95106.095667088433, -95110.736190914176, -95081.876999509084, -95069.190430164759, -95048.415419227094, -95048.645472410601, -95033.776317953481, -95019.125260893954, -95011.934854917476, -95003.694336871093]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = np.arange(len(loglik_valid))\n",
      "figure = plt.figure()\n",
      "figure.set_size_inches((14, 10))\n",
      "plt.subplot(221)\n",
      "plt.plot(r, loglik_train, label='Training set')\n",
      "plt.plot(r, loglik_valid, label='Validation set')\n",
      "plt.ylabel('Likelihood')\n",
      "plt.xlabel('Iteration')\n",
      "plt.grid(True)\n",
      "plt.legend()\n",
      "\n",
      "plt.subplot(222)\n",
      "plt.plot(r, loglik_train)\n",
      "plt.title('log likelihood changes for the training set')\n",
      "plt.ylabel('Likelihood')\n",
      "plt.xlabel('Iteration')\n",
      "plt.grid(True)\n",
      "\n",
      "plt.subplot(223)\n",
      "plt.plot(r, loglik_valid)\n",
      "plt.title('log likelihood changes for the validation set')\n",
      "\n",
      "plt.ylabel('Likelihood')\n",
      "plt.xlabel('Iteration')\n",
      "plt.grid(True)\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GMWAfAW5L67sDi8v2LQbGVElfktJJj4sAImItsErS6DrXGgV0R8T6KtcyMzNr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       "text": [
        "<matplotlib.figure.Figure at 0x7fefb26f6190>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_digits(w.T, numcols=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fefb2be12d0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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",
     "collapsed": false,
     "input": [
      "# Ranking by highest probability is the same like ranking log(q(j = t)), therefore we are taking log_qt to make\n",
      "# it easier from the computational perspective\n",
      "log_q = x_valid.dot(w) + b\n",
      "\n",
      "log_qt = np.array([log_q[index, value] for (index,), value in np.ndenumerate(t_valid)]) \n",
      "sorted_by_log_qt = np.argsort(log_qt)\n",
      "easiest = sorted_by_log_qt[-8:]\n",
      "for i in range(8):\n",
      "    plt.subplot(1, 8, i)\n",
      "    plt.axis('off')\n",
      "    plt.imshow(x_train[easiest[i]].reshape((28, 28)), interpolation='nearest', cmap='Greys')\n",
      "plt.title('Easiest 8 digits')\n",
      "plt.show()\n",
      "\n",
      "hardest = sorted_by_log_qt[:8]\n",
      "for i in range(8):\n",
      "    plt.subplot(1, 8, i)\n",
      "    plt.axis('off')\n",
      "    plt.imshow(x_train[hardest[i]].reshape((28, 28)), interpolation='nearest', cmap='Greys')\n",
      "plt.title('Hardest 8 digits')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fefb22f3710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fefb2aa6e90>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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 $\\frac{\\partial}{\\partial x} \\sigma(x) = \\sigma(x) (1 - \\sigma(x))$.\n",
      "\n",
      "##### Answer: "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathcal{L}^{(n)} = \\log q_j - \\log Z = \\mathbf{w}_j^T \\mathbf{h} + b_j - \\log Z = \\sum_{i=1}^L W_{ij}\\sigma(\\mathbf{v}_i^T \\mathbf{x} + a_i) + b_j - \\log Z = \\sum_{i=1}^L W_{ij}\\sigma(\\sum_{k=1}^{784} v_{ki}x_k + a_i) + b_j - \\log Z$\n",
      "\n",
      "$\\delta^q_j = \\frac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j}$\n",
      "\n",
      "For $j = t^{(n)}$: $\\delta_j^q = 1 - \\dfrac{1}{Z}exp(\\log q_j)$\n",
      "\n",
      "For $j \\neq t^{(n)}$: $\\delta_j^q = -\\dfrac{1}{Z}exp(\\log q_j)$\n",
      "\n",
      "$\\delta_i^h = \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial h_i} = \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j} \\dfrac{\\partial \\log q_j}{\\partial h_i} = \\delta_j^q W_{ij}$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial b_j} = \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j} \\dfrac{\\partial \\log q_j}{\\partial b_j} = \\delta_j^q$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial W_{ij}} = \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial \\log q_j}\\dfrac{\\partial \\log q_j}{\\partial \\log W_{ij}} = \\delta_j^q h_i$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial a_i} = \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial h_i} \\dfrac{\\partial h_i}{\\partial (\\mathbf{v_i}^T\\mathbf{x} + a_i)}  \\dfrac{\\partial(\\mathbf{v_i}^T\\mathbf{x} + a_i)}{\\partial a_i} = \\delta_i^h \\sigma(\\mathbf{v_i}^T\\mathbf{x} + a_i)(1 - \\sigma(\\mathbf{v_i}^T\\mathbf{x} + a_i)) = \\delta_i^h h_i (1 - h_i)$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial v_{ki}} = \\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial h_i} \\dfrac{\\partial h_i}{\\partial(\\mathbf{v_i}^T\\mathbf{x} + a_i)}  \\dfrac{\\partial(\\mathbf{v_i}^T\\mathbf{x} + a_i)}{\\partial a_i} = \\delta_i^h \\sigma(\\mathbf{v_i}^T\\mathbf{x} + a_i)(1 - \\sigma(\\mathbf{v_i}^T\\mathbf{x} + a_i))x_k = \\delta_i^h h_i(1 - h_i)x_k$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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. \n",
      "\n",
      "##### Answer: "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathcal{L}^{(n)} = \\log q_j - \\log Z - \\dfrac{\\alpha_1}{2}\\sum_{k=1}^{784}\\sum_{i=0}^L v_{ki}^2 - \\dfrac{\\alpha_2}{2} \\sum_{i=0}^L\\sum_{j=1}^{10} W_{ij}^2 $\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial b_j} = \\delta_j^q$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial W_{ij}} = \\delta_j^q h_i - \\alpha_2 W_{ij}$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial a_i} = \\delta_i^h h_i (1 - h_i)$\n",
      "\n",
      "$\\dfrac{\\partial \\mathcal{L}^{(n)}}{\\partial v_{ki}} = \\delta_i^h h_i (1 - h_i)x_k - \\alpha_1 v_{ki}$\n",
      "\n",
      "<!-- Bishop 5.5.1 Section -->"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 2.3. Implement and train a MLP (15 points)\n",
      "\n",
      "Implement a MLP model with a single hidden layer, and code to train the model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mlperceptron_gradient(x, t, W, b, V, a, a1=0.001, a2=0.001):\n",
      "    h = 1 / (1 + np.exp(-x.dot(V) - a))\n",
      "    log_q = h.dot(W) + b\n",
      "\n",
      "    a = np.max(log_q)\n",
      "    logZ = a + np.log(np.sum(np.exp(log_q - a)))\n",
      "    Z = np.exp(logZ) \n",
      "\n",
      "    grad_b = -np.exp(log_q) / Z\n",
      "    grad_b[t] += 1\n",
      "\n",
      "    grad_W = h[np.newaxis].T.dot(grad_b[np.newaxis]) - a2 * W\n",
      "\n",
      "    grad_h = W[:,t].dot(grad_b[t])\n",
      "    grad_a = grad_h * h * (1 - h)\n",
      "\n",
      "    grad_V = x[np.newaxis].T.dot(grad_a[np.newaxis]) - a1 * V\n",
      "    return grad_W, grad_b, grad_V, grad_a\n",
      "\n",
      "def init_mlperceptron_weights(num_of_features, num_of_class, L):\n",
      "    W = (np.random.random_sample((L, num_of_class)) - 0.5) * 0.001\n",
      "    b = (np.random.random_sample(num_of_class) - 0.5) * 0.001\n",
      "    V = (np.random.random_sample((num_of_features, L)) - 0.5) * 0.001\n",
      "    a = (np.random.random_sample(L) - 0.5) * 0.001\n",
      "    return W, b, V, a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Test\n",
      "np.random.seed(0)\n",
      "L = 50\n",
      "W, b, V, a = init_mlperceptron_weights(num_of_features, num_of_class, L)\n",
      "grad_W, grad_b, grad_V, grad_a = mlperceptron_gradient(x_train[0], t_train[0], W, b, V, a)\n",
      "print grad_W.shape, grad_b.shape, grad_V.shape, grad_a.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(50, 10) (10,) (784, 50) (50,)\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sgd_mlperceptron_iter(x_train, t_train, W, b, V, a, a1=0.001, a2=0.001, lr=0.001):\n",
      "    indexes = np.arange(len(x_train))\n",
      "    np.random.shuffle(indexes)\n",
      "\n",
      "    for index in indexes:\n",
      "        grad_W, grad_b, grad_V, grad_a = mlperceptron_gradient(x_train[index], t_train[index], W, b, V, a, a1, a2)\n",
      "        W += lr * grad_W\n",
      "        b += lr * grad_b\n",
      "        V += lr * grad_V\n",
      "        a += lr * grad_a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "# Test\n",
      "np.random.seed(0)\n",
      "L = 50\n",
      "W, b, V, a = init_mlperceptron_weights(num_of_features, num_of_class, L)\n",
      "sgd_mlperceptron_iter(x_train, t_train, W, b, V, a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "def compute_log_likelihood(x, t, W, b, V, a):\n",
      "    h = 1 / (1 + np.exp(-x.dot(V) - a))\n",
      "    log_q = h.dot(W) + b\n",
      "\n",
      "    a = np.max(log_q)\n",
      "    log_Z = a + np.log(np.sum(np.exp(log_q - a)))\n",
      "\n",
      "    log_likelihood = np.sum(np.array([log_q[index, value] for (index,), value in np.ndenumerate(t)]) - log_Z)\n",
      "    return log_likelihood"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Test\n",
      "compute_log_likelihood(x_train, t_train, W, b, V, a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "-647362.6658047433"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "import time\n",
      "def train_mlperceptron(W, b, V, a, a1=0.001, a2=0.001, lr=0.001, num_iter=20, cl=True):\n",
      "    loglik_train = []\n",
      "    if cl:\n",
      "        loglik_train.append(compute_log_likelihood(x_train, t_train, W, b, V, a))\n",
      "    for i in xrange(num_iter):\n",
      "        t1 = time.time()\n",
      "        sgd_mlperceptron_iter(x_train, t_train, W, b, V, a, a1, a2, lr)\n",
      "        print 'dt =', (time.time() - t1)\n",
      "        if cl:\n",
      "            loglik_train.append(compute_log_likelihood(x_train, t_train, W, b, V, a))\n",
      "\n",
      "    return loglik_train"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Test\n",
      "W, b, V, a = init_mlperceptron_weights(num_of_features, num_of_class, L)\n",
      "likelihood = train_mlperceptron(W, b, V, a, num_iter=20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dt = 11.749341011\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7022368908\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7554790974\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7140228748\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7579360008\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.762294054\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7154080868\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7621219158\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7620649338\n",
        "dt ="
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7433152199\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7541389465\n",
        "dt ="
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7270381451\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7738518715\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7657809258\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7822918892\n",
        "dt ="
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.769810915\n",
        "dt ="
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.7125301361\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.6957070827\n",
        "dt ="
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.9570178986\n",
        "dt ="
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11.763520956\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = np.arange(len(likelihood))\n",
      "figure = plt.figure()\n",
      "figure.set_size_inches((14, 10))\n",
      "plt.plot(r, likelihood)\n",
      "plt.title('log likelihood changes for the training set')\n",
      "plt.ylabel('Likelihood')\n",
      "plt.xlabel('Iteration')\n",
      "plt.grid(True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bTrm77z7485/z17/9DYYPz63TV1oJVl6597/2VpBTXZfVfmvfHjYM3vSm169k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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fefb23c22d0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def predict_mlperceptron(W, b, V, a, x):\n",
      "    h = 1 / (1 + np.exp(-x.dot(V) - a))\n",
      "    log_q = h.dot(W) + b\n",
      "    return np.argmax(log_q, axis=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We got 91.9% of accuracy on validation set without model selection:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Test\n",
      "prediction = predict_mlperceptron(W, b, V, a, x_valid)\n",
      "correctness = t_valid == prediction\n",
      "accuracy = len(correctness[correctness == True]) / float(len(t_valid))\n",
      "print accuracy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.919\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure = plt.figure()\n",
      "figure.set_size_inches((16, 10))\n",
      "plot_digits(V.T, numcols=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xoliv1+1nH0kExjK+vb0NAHjw4AEAoNFoABjrfer5w6It3gsuxKwJoyFRFJkd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\npe5aAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fefb1fc5b50>"
       ]
      }
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "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 $L > 200$, 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",
     "collapsed": false,
     "input": [
      "# Ignore this cell if you don't want to wait for a century\n",
      "best_L = 0\n",
      "best_a1 = 0\n",
      "best_a2 = 0\n",
      "best_accuracy = 0\n",
      "\n",
      "for a1 in [0.001, 0.005, 0.01]:\n",
      "    for a2 in [0.001, 0.005, 0.01]:\n",
      "        for L in [150, 200, 250, 300]:\n",
      "            np.random.seed(0)\n",
      "            W, b, V, a = init_mlperceptron_weights(num_of_features, num_of_class, L)\n",
      "            train_mlperceptron(W, b, V, a, a1=a1, a2=a2, num_iter=5, cl=False)\n",
      "            prediction = predict_mlperceptron(W, b, V, a, x_valid)\n",
      "            correctness = t_valid == prediction\n",
      "            accuracy = len(correctness[correctness == True]) / float(len(t_valid))\n",
      "            print 'L =', L, 'a1 =', a1, 'a2 =', a2, 'accuracy =', accuracy\n",
      "            if accuracy > best_accuracy:\n",
      "                best_L = L\n",
      "                best_a1 = a1\n",
      "                best_a2 = a2\n",
      "                best_accuracy = accuracy\n",
      "\n",
      "print best_a1, best_a2, best_L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dt = 36.1404809952\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 36.4526309967\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 36.081289053\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35.7838938236\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35.6864190102\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 150 a1 = 0.001 a2 = 0.001 accuracy = 0.8807\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 59.0064771175\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 59.9170291424\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 59.9129788876\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 58.1051089764\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 59.1668610573\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 200 a1 = 0.001 a2 = 0.001 accuracy = 0.8813\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 94.0111758709\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 91.4698078632\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85.9305830002\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85.7214310169\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 91.5173709393\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 250 a1 = 0.001 a2 = 0.001 accuracy = 0.8806\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 115.118833065\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 112.193403006\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 110.160282135\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 110.108178854\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 110.097103119\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 300 a1 = 0.001 a2 = 0.001 accuracy = 0.8789\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 34.7444028854\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35.1943128109\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35.2584700584\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35.273624897\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35.2362449169\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 150 a1 = 0.001 a2 = 0.005 accuracy = 0.8738\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 57.7591640949\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 57.6998641491\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 57.3350760937\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 58.3718030453\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 57.7873208523\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 200 a1 = 0.001 a2 = 0.005 accuracy = 0.8779\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85.1471838951\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85.2267768383\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85.265212059\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85.0255630016\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 84.4933559895\n",
        "L ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 250 a1 = 0.001 a2 = 0.005 accuracy = 0.8761\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 120.142332077\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 122.890453815\n",
        "dt ="
       ]
      }
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(0)\n",
      "best_a1 = 0.001\n",
      "best_a2 = 0.001\n",
      "best_L = 200\n",
      "W, b, V, a = init_mlperceptron_weights(num_of_features, num_of_class, best_L)\n",
      "# L = 150 a1 = 0.001 a2 = 0.001 accuracy = 0.8807\n",
      "# L = 200 a1 = 0.001 a2 = 0.001 accuracy = 0.8813\n",
      "# L = 250 a1 = 0.001 a2 = 0.001 accuracy = 0.8806\n",
      "# L = 300 a1 = 0.001 a2 = 0.001 accuracy = 0.8789\n",
      "# L = 150 a1 = 0.001 a2 = 0.005 accuracy = 0.8738\n",
      "# L = 200 a1 = 0.001 a2 = 0.005 accuracy = 0.8779\n",
      "# L = 250 a1 = 0.001 a2 = 0.005 accuracy = 0.8761\n",
      "\n",
      "train_mlperceptron(W, b, V, a, a1=best_a1, a2=best_a2, num_iter=20, cl=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dt = 64.8666241169\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.7134349346\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.4661099911\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.2972989082\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.8289330006\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.6778249741\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 65.1156840324\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.2937319279\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.8534121513\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.4524497986\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.1453700066\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.9153909683\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.5796968937\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.261963129\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 63.4503080845\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 62.8272130489\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 63.8530681133\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.3897378445\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.5703201294\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64.4503500462\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "[]"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prediction = predict_mlperceptron(W, b, V, a, x_valid)\n",
      "correctness = t_valid == prediction\n",
      "accuracy = len(correctness[correctness == True]) / float(len(t_valid))\n",
      "print accuracy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.9179\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W1 = np.copy(W)\n",
      "b1 = np.copy(b)\n",
      "V1 = np.copy(V)\n",
      "a1 = np.copy(a)\n",
      "train_mlperceptron(W1, b1, V1, a1, a1=best_a1, a2=best_a2, num_iter=5, cl=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dt = 55.5144901276\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 55.3634490967\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 55.3930630684\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 54.1291520596\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 54.125690937\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "[]"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prediction = predict_mlperceptron(W1, b1, V1, a1, x_valid)\n",
      "correctness = t_valid == prediction\n",
      "accuracy = len(correctness[correctness == True]) / float(len(t_valid))\n",
      "print accuracy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.92\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W2 = np.copy(W1)\n",
      "b2 = np.copy(b1)\n",
      "V2 = np.copy(V1)\n",
      "a2 = np.copy(a1)\n",
      "train_mlperceptron(W2, b2, V2, a2, a1=best_a1, a2=best_a2, num_iter=5, cl=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dt = 54.5731868744\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 55.0300350189\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 54.8870930672\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 54.5760028362\n",
        "dt ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 54.5074689388\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "[]"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prediction = predict_mlperceptron(W2, b2, V2, a2, x_valid)\n",
      "correctness = t_valid == prediction\n",
      "accuracy = len(correctness[correctness == True]) / float(len(t_valid))\n",
      "print accuracy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.9205\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}