part2/labs/11636785_11640758_lab3.ipynb

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    "### Lab 3: Expectation Maximization and Variational Autoencoder\n",
    "\n",
    "### Machine Learning 2 (2017/2018)\n",
    "\n",
    "* The lab exercises should be made in groups of two or three people.\n",
    "* The deadline is Friday, 01.06.\n",
    "* Assignment should be submitted through BlackBoard! Make sure to include your and your teammates' names with the submission.\n",
    "* Attach the .IPYNB (IPython Notebook) file containing your code and answers. Naming of the file should be \"studentid1\\_studentid2\\_lab#\", for example, the attached file should be \"12345\\_12346\\_lab1.ipynb\". Only use underscores (\"\\_\") to connect ids, otherwise the files cannot be parsed.\n",
    "\n",
    "Notes on implementation:\n",
    "\n",
    "* You should write your code and answers in an IPython Notebook: http://ipython.org/notebook.html. If you have problems, please ask.\n",
    "* Use __one cell__ for code and markdown answers only!\n",
    "    * Put all code in the cell with the ```# YOUR CODE HERE``` comment and overwrite the ```raise NotImplementedError()``` line.\n",
    "    * For theoretical questions, put your solution using LaTeX style formatting in the YOUR ANSWER HERE cell.\n",
    "* Among the first lines of your notebook should be \"%pylab inline\". This imports all required modules, and your plots will appear inline.\n",
    "* Large parts of you notebook will be graded automatically. Therefore it is important that your notebook can be run completely without errors and within a reasonable time limit. To test your notebook before submission, select Kernel -> Restart \\& Run All.\n",
    "$\\newcommand{\\bx}{\\mathbf{x}} \\newcommand{\\bpi}{\\mathbf{\\pi}} \\newcommand{\\bmu}{\\mathbf{\\mu}} \\newcommand{\\bX}{\\mathbf{X}} \\newcommand{\\bZ}{\\mathbf{Z}} \\newcommand{\\bz}{\\mathbf{z}}$"
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   "source": [
    "Authors:\n",
    "Gabriele Bani, 11640758\n",
    "Andrii Skliar, 11636785"
   ]
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   "source": [
    "### Installing PyTorch\n",
    "\n",
    "In this lab we will use PyTorch. PyTorch is an open source deep learning framework primarily developed by Facebook's artificial-intelligence research group. In order to install PyTorch in your conda environment go to https://pytorch.org and select your operating system, conda, Python 3.6, no cuda. Copy the text from the \"Run this command:\" box. Now open a terminal and activate your 'ml2labs' conda environment. Paste the text and run. After the installation is done you should restart Jupyter."
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    "### MNIST data\n",
    "\n",
    "In this Lab we will use several methods for unsupervised learning on the MNIST dataset of written digits. The dataset contains digital images of handwritten numbers $0$ through $9$. Each image has 28x28 pixels that each take 256 values in a range from white ($= 0$) to  black ($=1$). The labels belonging to the images are also included. \n",
    "Fortunately, PyTorch comes with a MNIST data loader. The first time you run the box below it will download the MNIST data set. That can take a couple of minutes.\n",
    "The main data types in PyTorch are tensors. For Part 1, we will convert those tensors to numpy arrays. In Part 2, we will use the torch module to directly work with PyTorch tensors."
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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
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      "/home/hiryugan/anaconda3/envs/ml2labs/lib/python3.6/site-packages/IPython/core/magics/pylab.py:160: UserWarning: pylab import has clobbered these variables: ['figure', 'norm', 'pi', 'sample', 'gamma', 'axes']\n",
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      "  \"\\n`%matplotlib` prevents importing * from pylab and numpy\"\n"
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   "source": [
    "%pylab inline\n",
    "import torch\n",
    "from torchvision import datasets, transforms\n",
    "\n",
    "train_dataset = datasets.MNIST('../data', train=True, download=True,\n",
    "                   transform=transforms.Compose([\n",
    "                       transforms.ToTensor(),\n",
    "                       transforms.Normalize((0.1307,), (0.3081,))\n",
    "                   ]))\n",
    "\n",
    "train_labels = train_dataset.train_labels.numpy()\n",
    "train_data = train_dataset.train_data.numpy()\n",
    "# For EM we will use flattened data\n",
    "train_data = train_data.reshape(train_data.shape[0], -1)\n"
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   "source": [
    "## Part 1: Expectation Maximization\n",
    "We will use the Expectation Maximization (EM) algorithm for the recognition of handwritten digits in the MNIST dataset. The images are modelled as a Bernoulli mixture model (see Bishop $\\S9.3.3$):\n",
    "$$\n",
    "p(\\bx|\\bmu, \\bpi) = \\sum_{k=1}^K  \\pi_k \\prod_{i=1}^D \\mu_{ki}^{x_i}(1-\\mu_{ki})^{(1-x_i)}\n",
    "$$\n",
    "where $x_i$ is the value of pixel $i$ in an image, $\\mu_{ki}$ represents the probability that pixel $i$ in class $k$ is black, and $\\{\\pi_1, \\ldots, \\pi_K\\}$ are the mixing coefficients of classes in the data. We want to use this data set to classify new images of handwritten numbers."
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   "source": [
    "### 1.1 Binary data (5 points)\n",
    "As we like to apply our Bernoulli mixture model, write a function `binarize` to convert the (flattened) MNIST data to binary images, where each pixel $x_i \\in \\{0,1\\}$, by thresholding at an appropriate level."
   ]
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   "source": [
    "def binarize(X):\n",
    "    return np.around(train_data/255)"
   ]
  },
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   "source": [
    "# Test test test!\n",
    "bin_train_data = binarize(train_data)\n",
    "assert bin_train_data.dtype == np.float\n",
    "assert bin_train_data.shape == train_data.shape\n"
   ]
  },
  {
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   "source": [
    "Sample a few images of digits $2$, $3$ and $4$; and show both the original and the binarized image together with their label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "matplotlib.rcParams['figure.figsize'] = (12, 8)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 55,
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   "source": [
    "def sample_digits_indices(start, stop, num_samples):\n",
    "    sampled_indices = np.array([]).astype(int)\n",
    "    \n",
    "    sampled_sizes = []\n",
    "    for i in range(start, stop+1):\n",
    "        indices = np.where(train_labels == i)[0]\n",
    "        if num_samples is not None:\n",
    "            indices = np.random.choice(indices, num_samples)\n",
    "        sampled_sizes.append(len(indices))\n",
    "        sampled_indices = np.hstack((sampled_indices, indices))\n",
    "        \n",
    "    return sampled_indices, sampled_sizes"
   ]
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   "execution_count": 56,
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   "source": [
    "def sample_digits(sampled_indices, binary = False):\n",
    "    samples = train_data[sampled_indices]\n",
    "    sampled_labels = train_labels[sampled_indices]\n",
    "    \n",
    "    if binary:\n",
    "        bin_samples = bin_train_data[sampled_indices]\n",
    "        return sampled_labels, samples, bin_samples\n",
    "    else:\n",
    "        return sampled_labels, samples"
   ]
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   "source": [
    "def sample_data(start, stop, num_samples, binary):\n",
    "    range_digits = stop - start + 1\n",
    "    \n",
    "    sampled_indices, sampled_sizes = sample_digits_indices(start, stop, num_samples)\n",
    "    if binary:\n",
    "        sampled_labels, samples, bin_samples = sample_digits(sampled_indices, binary)\n",
    "        return sampled_labels, samples, bin_samples, sampled_sizes\n",
    "    else:\n",
    "        sampled_labels, samples = sample_digits(sampled_indices, binary)\n",
    "        return sampled_labels, samples, sampled_sizes"
   ]
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\n",
      "text/plain": [
       "<Figure size 864x576 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_samples = 3\n",
    "start_digit = 2\n",
    "stop_digit = 4\n",
    "range_digits = stop_digit - start_digit + 1\n",
    "\n",
    "sampled_labels, samples, bin_samples, _ =  sample_data(start_digit, stop_digit, \n",
    "                                                    num_samples, binary = True)\n",
    "\n",
    "sampled_labels = sampled_labels.reshape(range_digits, num_samples)\n",
    "samples = samples.reshape(range_digits, num_samples, 28, 28)\n",
    "bin_samples = bin_samples.reshape(range_digits, num_samples, 28, 28)\n",
    "\n",
    "fig, axes = plt.subplots(range_digits, num_samples * 2)\n",
    "\n",
    "for i in range(range_digits):\n",
    "    for j in range(num_samples):\n",
    "        k = 2*j\n",
    "        \n",
    "        axes[i, k].axis('off')\n",
    "        axes[i, k + 1].axis('off')\n",
    "        \n",
    "        axes[i, k].imshow(samples[i, j], cmap='Greys')\n",
    "        axes[i, k + 1].imshow(bin_samples[i, j], cmap='Greys')\n",
    "        \n",
    "        axes[i, k].set_title(f'Original {sampled_labels[i, j]}')\n",
    "        axes[i, k+1].set_title(f'Binarized {sampled_labels[i, j]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "4b9da574d24193df76e96ed8ca62c7b0",
     "grade": false,
     "grade_id": "cell-56b33654497d4052",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.2 Implementation (40 points)\n",
    "You are going to write a function ```EM(X, K, max_iter)``` that implements the EM algorithm on the Bernoulli mixture model. \n",
    "\n",
    "The only parameters the function has are:\n",
    "* ```X``` :: (NxD) array of input training images\n",
    "* ```K``` :: size of the latent space\n",
    "* ```max_iter``` :: maximum number of iterations, i.e. one E-step and one M-step\n",
    "\n",
    "You are free to specify your return statement.\n",
    "\n",
    "Make sure you use a sensible way of terminating the iteration process early to prevent unnecessarily running through all epochs. Vectorize computations using ```numpy``` as  much as possible.\n",
    "\n",
    "You should implement the `E_step(X, mu, pi)` and `M_step(X, gamma)` separately in the functions defined below. These you can then use in your function `EM(X, K, max_iter)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "316c9131692747c363b5db8e9091d362",
     "grade": false,
     "grade_id": "cell-882b13c117a73cc4",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def E_step(X, mu, pi):\n",
    "    \n",
    "    # expand dimensions for vectorizing (N x D -> N x 1 x D)\n",
    "    X_expanded = np.expand_dims(X, axis=1)\n",
    "\n",
    "    # calculate unnormalized responsibilities\n",
    "    gamma_unnorm = pi * np.prod((mu ** X_expanded) * ((1 - mu) ** (1 - X_expanded)),\n",
    "                                     axis = 2)\n",
    "    \n",
    "    # these lines are for avoiding underflow errors of the product\n",
    "    # uncomment when having such errors\n",
    "#     bern = (mu ** X_expanded) * ((1 - mu) ** (1 - X_expanded))\n",
    "#     gamma_unnorm = pi * (np.exp(np.sum(np.log(bern), axis = 2)))    \n",
    "\n",
    "    # calculate normalization constant\n",
    "    norm_constant = np.sum(gamma_unnorm, axis = 1)\n",
    "\n",
    "    # expand normalization constant dimensions for vectorizing (N -> N x 1)\n",
    "    norm_expanded = np.expand_dims(norm_constant, axis = 1)\n",
    "\n",
    "    # normalize responsibilities\n",
    "    gamma = np.divide(gamma_unnorm, norm_expanded, where = norm_expanded!=0)\n",
    "\n",
    "    return gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "1418f4014e98024fc97446ce27766c1d",
     "grade": true,
     "grade_id": "cell-f7c7dd52d82e2498",
     "locked": true,
     "points": 15,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# Let's test on 5 datapoints\n",
    "n_test = 5\n",
    "X_test = bin_train_data[:n_test]\n",
    "D_test, K_test = X_test.shape[1], 10\n",
    "\n",
    "np.random.seed(2018)\n",
    "mu_test = np.random.uniform(low=.25, high=.75, size=(K_test,D_test))\n",
    "pi_test = np.ones(K_test) / K_test\n",
    "\n",
    "gamma_test = E_step(X_test, mu_test, pi_test)\n",
    "assert gamma_test.shape == (n_test, K_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "2c426a613653174795cd9c8327ab6e20",
     "grade": false,
     "grade_id": "cell-f1b11b8765bd1ef6",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def M_step(X, gamma):\n",
    "    # sum over n\n",
    "    N_k = gamma.sum(axis = 0)\n",
    "\n",
    "    # calculate pi as N_k/N\n",
    "    pi = N_k / np.sum(N_k)\n",
    "    \n",
    "    # expand dimensions and repeat for vectorizing (N x D -> N x K x D)\n",
    "    # where c is the second dimension of vector gamma (N in Bishop's notation)\n",
    "    X_expanded = np.repeat(np.expand_dims(X, axis=1), gamma.shape[1], axis=1)\n",
    "    \n",
    "    # expand dimensions for vectorizing (N x K -> N x K x 1)\n",
    "    gamma_expanded = np.expand_dims(gamma, axis=2)\n",
    "\n",
    "    # calculate unnormalized values for mu\n",
    "    # results in K x D dimensional vector\n",
    "    mu_unnorm = np.sum(X_expanded * gamma_expanded, axis = 0)\n",
    "\n",
    "    # expand dimensions for vectorizing (K -> K x 1)\n",
    "    N_k_expanded = np.expand_dims(N_k, axis=1)\n",
    "\n",
    "    # normalize mu\n",
    "    mu = mu_unnorm / N_k_expanded\n",
    "    \n",
    "    return mu, pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "0f60d48b8b22063cef560b42944a0aa4",
     "grade": true,
     "grade_id": "cell-6e7c751b30acfd45",
     "locked": true,
     "points": 15,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# Oh, let's test again\n",
    "mu_test, pi_test = M_step(X_test, gamma_test)\n",
    "\n",
    "assert mu_test.shape == (K_test,D_test)\n",
    "assert pi_test.shape == (K_test, )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_MNIST_latent_representation(mu, iter = None):\n",
    "    K = mu.shape[0]\n",
    "    mu = mu.reshape(mu.shape[0], 28, 28)\n",
    "        \n",
    "    fig, axes = plt.subplots(1, K)\n",
    "    \n",
    "    for i in range(K):\n",
    "        if iter is not None:\n",
    "            axes[i].set_title(f'After iteration {iter}')\n",
    "        axes[i].axis('off')\n",
    "        axes[i].imshow(mu[i], cmap='Greys')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "acfec6384b058cb0ce1932006fbfebc4",
     "grade": true,
     "grade_id": "cell-d6c4368246dee7e6",
     "locked": false,
     "points": 10,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def EM(X, K, max_iter, eps = 1e-5, mu=None, pi=None, plot=False):\n",
    "    N, D = X.shape[0], X.shape[1]\n",
    "    \n",
    "    if mu is None:\n",
    "        mu = np.random.uniform(low=.25, high=.75, size=(K, D))\n",
    "    \n",
    "    if pi is None:\n",
    "        pi = np.ones(K) / K\n",
    "        \n",
    "    gamma_prev = np.zeros((N, K))\n",
    "    for i in range(max_iter):\n",
    "        if plot and not (i % 5):\n",
    "            plot_MNIST_latent_representation(mu, i)\n",
    "        gamma = E_step(X, mu, pi)\n",
    "        mu, pi = M_step(X, gamma)\n",
    "        \n",
    "        delta = np.linalg.norm(gamma - gamma_prev) / gamma.shape[0]\n",
    "        print(f'Epoch {i}/{max_iter}: delta of gamma - {delta}, tolerance - {eps}')\n",
    "        if delta < eps:\n",
    "            break\n",
    "        gamma_prev = gamma\n",
    "\n",
    "    return mu, pi, gamma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "b4fc12faa0da660f7a4d9cc7deb41b25",
     "grade": false,
     "grade_id": "cell-e1077ed3b83489be",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.3 Three digits experiment (10 points)\n",
    "In analogue with Bishop $\\S9.3.3$, sample a training set consisting of only __binary__ images of written digits $2$, $3$, and $4$. Run your EM algorithm and show the reconstructed digits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "bdbce0fad0ed151063d4c489ce999e3e",
     "grade": true,
     "grade_id": "cell-477155d0264d7259",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/500: delta of gamma - 0.0070490424913507155, tolerance - 1e-05\n",
      "Epoch 1/500: delta of gamma - 0.0051387241732246845, tolerance - 1e-05\n",
      "Epoch 2/500: delta of gamma - 0.004088840820088166, tolerance - 1e-05\n",
      "Epoch 3/500: delta of gamma - 0.003436397103838344, tolerance - 1e-05\n",
      "Epoch 4/500: delta of gamma - 0.002408677835739104, tolerance - 1e-05\n",
      "Epoch 5/500: delta of gamma - 0.001363267126487797, tolerance - 1e-05\n",
      "Epoch 6/500: delta of gamma - 0.0006892379917515429, tolerance - 1e-05\n",
      "Epoch 7/500: delta of gamma - 0.0002604341881501465, tolerance - 1e-05\n",
      "Epoch 8/500: delta of gamma - 9.748415266967077e-05, tolerance - 1e-05\n",
      "Epoch 9/500: delta of gamma - 4.015764175495793e-05, tolerance - 1e-05\n",
      "Epoch 10/500: delta of gamma - 9.746428292658852e-05, tolerance - 1e-05\n",
      "Epoch 11/500: delta of gamma - 6.556884193446168e-05, tolerance - 1e-05\n",
      "Epoch 12/500: delta of gamma - 7.856660129090118e-05, tolerance - 1e-05\n",
      "Epoch 13/500: delta of gamma - 8.237123611978988e-06, tolerance - 1e-05\n",
      "Mixing coefficients: [0.34751217 0.31859832 0.33388951]\n",
      "Final result:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# None corresponds to getting all samples of specified digits\n",
    "num_samples = None\n",
    "\n",
    "start_digit = 2\n",
    "stop_digit = 4\n",
    "range_digits = stop_digit - start_digit + 1\n",
    "\n",
    "max_iter = 500\n",
    "latent_size = range_digits\n",
    "\n",
    "_, _, bin_samples, _ =  sample_data(start_digit, stop_digit, num_samples, binary = True)\n",
    "mu, pi, gamma = EM(bin_samples, latent_size, max_iter = max_iter, plot = False)\n",
    "print(f'Mixing coefficients: {pi}')\n",
    "print('Final result:')\n",
    "plot_MNIST_latent_representation(mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "485543f4893938d2a9dc1c17d8221cbc",
     "grade": false,
     "grade_id": "cell-88c9664f995b1909",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Can you identify which element in the latent space corresponds to which digit? What are the identified mixing coefficients for digits $2$, $3$ and $4$, and how do these compare to the true ones?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "ae7b5acea6089e2590059f90b0d0a0be",
     "grade": true,
     "grade_id": "cell-3680ae2159c48193",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "Yes, it is easy to see from this latent space visualizations above that the first digit is a 4, the second a 2 and the thrid a 3. The calculated mixing coefficients are 0.34751217 0.31859832 0.33388951. If we assume that the data contain every digit in equal number, then the true mixing coefficients would be all 1/3, which is true in our case, since we sample data in equal number for every digit. So, the difference between the true mixing coefficients and the calculated ones is relatively small with our implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "98e04feb59a36867367b3027df9e226d",
     "grade": false,
     "grade_id": "cell-0891dda1c3e80e9a",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.4 Experiments (20 points)\n",
    "Perform the follow-up experiments listed below using your implementation of the EM algorithm. For each of these, describe/comment on the obtained results and give an explanation. You may still use your dataset with only digits 2, 3 and 4 as otherwise computations can take very long."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "439067186fa3ef1d7261a9bcf5a84ea6",
     "grade": false,
     "grade_id": "cell-06fe1b1355689928",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.4.1 Size of the latent space (5 points)\n",
    "Run EM with $K$ larger or smaller than the true number of classes. Describe your results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "791512aeadd30c4b586b966ca10e6fad",
     "grade": true,
     "grade_id": "cell-6c9057f2546b7215",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/500: delta of gamma - 0.007144744590750588, tolerance - 1e-05\n",
      "Epoch 1/500: delta of gamma - 0.004779654926787, tolerance - 1e-05\n",
      "Epoch 2/500: delta of gamma - 0.0024882583181318084, tolerance - 1e-05\n",
      "Epoch 3/500: delta of gamma - 0.0022324971529000498, tolerance - 1e-05\n",
      "Epoch 4/500: delta of gamma - 0.0022835379677800917, tolerance - 1e-05\n",
      "Epoch 5/500: delta of gamma - 0.002151058735035688, tolerance - 1e-05\n",
      "Epoch 6/500: delta of gamma - 0.0018296689358845918, tolerance - 1e-05\n",
      "Epoch 7/500: delta of gamma - 0.001386186344403166, tolerance - 1e-05\n",
      "Epoch 8/500: delta of gamma - 0.0009759272094159891, tolerance - 1e-05\n",
      "Epoch 9/500: delta of gamma - 0.0006955222436021928, tolerance - 1e-05\n",
      "Epoch 10/500: delta of gamma - 0.0005707264176081586, tolerance - 1e-05\n",
      "Epoch 11/500: delta of gamma - 0.0005288460145955689, tolerance - 1e-05\n",
      "Epoch 12/500: delta of gamma - 0.0004988628924039905, tolerance - 1e-05\n",
      "Epoch 13/500: delta of gamma - 0.0004766444775863425, tolerance - 1e-05\n",
      "Epoch 14/500: delta of gamma - 0.0004670913100419411, tolerance - 1e-05\n",
      "Epoch 15/500: delta of gamma - 0.00042388687717678656, tolerance - 1e-05\n",
      "Epoch 16/500: delta of gamma - 0.0004091096635607695, tolerance - 1e-05\n",
      "Epoch 17/500: delta of gamma - 0.00042287078947736136, tolerance - 1e-05\n",
      "Epoch 18/500: delta of gamma - 0.0003918385336358374, tolerance - 1e-05\n",
      "Epoch 19/500: delta of gamma - 0.00036933939668811866, tolerance - 1e-05\n",
      "Epoch 20/500: delta of gamma - 0.00032307309525652077, tolerance - 1e-05\n",
      "Epoch 21/500: delta of gamma - 0.00032701369928666706, tolerance - 1e-05\n",
      "Epoch 22/500: delta of gamma - 0.000354141577733489, tolerance - 1e-05\n",
      "Epoch 23/500: delta of gamma - 0.0003911919282659982, tolerance - 1e-05\n",
      "Epoch 24/500: delta of gamma - 0.000411601369677907, tolerance - 1e-05\n",
      "Epoch 25/500: delta of gamma - 0.00040407000034738203, tolerance - 1e-05\n",
      "Epoch 26/500: delta of gamma - 0.0004128994040413564, tolerance - 1e-05\n",
      "Epoch 27/500: delta of gamma - 0.0004259556715320405, tolerance - 1e-05\n",
      "Epoch 28/500: delta of gamma - 0.0004625943216139471, tolerance - 1e-05\n",
      "Epoch 29/500: delta of gamma - 0.0005396386499560137, tolerance - 1e-05\n",
      "Epoch 30/500: delta of gamma - 0.0006364854565514206, tolerance - 1e-05\n",
      "Epoch 31/500: delta of gamma - 0.0007201820209596188, tolerance - 1e-05\n",
      "Epoch 32/500: delta of gamma - 0.0007810187665382894, tolerance - 1e-05\n",
      "Epoch 33/500: delta of gamma - 0.0007465860881387331, tolerance - 1e-05\n",
      "Epoch 34/500: delta of gamma - 0.0007413091938619359, tolerance - 1e-05\n",
      "Epoch 35/500: delta of gamma - 0.0006792661377471598, tolerance - 1e-05\n",
      "Epoch 36/500: delta of gamma - 0.0005224327060848067, tolerance - 1e-05\n",
      "Epoch 37/500: delta of gamma - 0.0003767659971063931, tolerance - 1e-05\n",
      "Epoch 38/500: delta of gamma - 0.00028274606733557863, tolerance - 1e-05\n",
      "Epoch 39/500: delta of gamma - 0.00021731314820181585, tolerance - 1e-05\n",
      "Epoch 40/500: delta of gamma - 0.0001093157293422588, tolerance - 1e-05\n",
      "Epoch 41/500: delta of gamma - 5.698017515990999e-05, tolerance - 1e-05\n",
      "Epoch 42/500: delta of gamma - 0.00011471905544535734, tolerance - 1e-05\n",
      "Epoch 43/500: delta of gamma - 0.00010615735587016173, tolerance - 1e-05\n",
      "Epoch 44/500: delta of gamma - 2.2138941322456886e-05, tolerance - 1e-05\n",
      "Epoch 45/500: delta of gamma - 9.361030123234992e-06, tolerance - 1e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_samples = None\n",
    "max_iter = 500\n",
    "\n",
    "latent_size = 2\n",
    "\n",
    "_, _, bin_samples, _ =  sample_data(start_digit, stop_digit, num_samples, binary = True)\n",
    "mu, _, _ = EM(bin_samples, latent_size, max_iter = max_iter, plot = False)\n",
    "plot_MNIST_latent_representation(mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/500: delta of gamma - 0.006754877053127517, tolerance - 1e-05\n",
      "Epoch 1/500: delta of gamma - 0.00757841750983632, tolerance - 1e-05\n",
      "Epoch 2/500: delta of gamma - 0.003947350775148579, tolerance - 1e-05\n",
      "Epoch 3/500: delta of gamma - 0.0028395653533175485, tolerance - 1e-05\n",
      "Epoch 4/500: delta of gamma - 0.002429701579530734, tolerance - 1e-05\n",
      "Epoch 5/500: delta of gamma - 0.002250506459919134, tolerance - 1e-05\n",
      "Epoch 6/500: delta of gamma - 0.0020988478345393977, tolerance - 1e-05\n",
      "Epoch 7/500: delta of gamma - 0.002045659636048078, tolerance - 1e-05\n",
      "Epoch 8/500: delta of gamma - 0.001885141505463226, tolerance - 1e-05\n",
      "Epoch 9/500: delta of gamma - 0.0015578157663286248, tolerance - 1e-05\n",
      "Epoch 10/500: delta of gamma - 0.0012147851862863743, tolerance - 1e-05\n",
      "Epoch 11/500: delta of gamma - 0.0009137315623055044, tolerance - 1e-05\n",
      "Epoch 12/500: delta of gamma - 0.0007342119528952707, tolerance - 1e-05\n",
      "Epoch 13/500: delta of gamma - 0.000613314523037607, tolerance - 1e-05\n",
      "Epoch 14/500: delta of gamma - 0.0005398110733064115, tolerance - 1e-05\n",
      "Epoch 15/500: delta of gamma - 0.0004779577238332128, tolerance - 1e-05\n",
      "Epoch 16/500: delta of gamma - 0.00042572549409920145, tolerance - 1e-05\n",
      "Epoch 17/500: delta of gamma - 0.0003711630880889386, tolerance - 1e-05\n",
      "Epoch 18/500: delta of gamma - 0.00035933010121210547, tolerance - 1e-05\n",
      "Epoch 19/500: delta of gamma - 0.00032306793630421316, tolerance - 1e-05\n",
      "Epoch 20/500: delta of gamma - 0.00030140288625423866, tolerance - 1e-05\n",
      "Epoch 21/500: delta of gamma - 0.00027586848196966564, tolerance - 1e-05\n",
      "Epoch 22/500: delta of gamma - 0.00027176325491164724, tolerance - 1e-05\n",
      "Epoch 23/500: delta of gamma - 0.0002879933675329066, tolerance - 1e-05\n",
      "Epoch 24/500: delta of gamma - 0.00023403316051324327, tolerance - 1e-05\n",
      "Epoch 25/500: delta of gamma - 0.0001863619579350264, tolerance - 1e-05\n",
      "Epoch 26/500: delta of gamma - 0.0001552950856829872, tolerance - 1e-05\n",
      "Epoch 27/500: delta of gamma - 0.00014553934873322573, tolerance - 1e-05\n",
      "Epoch 28/500: delta of gamma - 0.00018472984215766786, tolerance - 1e-05\n",
      "Epoch 29/500: delta of gamma - 0.00014036221120146658, tolerance - 1e-05\n",
      "Epoch 30/500: delta of gamma - 0.00014133339700441174, tolerance - 1e-05\n",
      "Epoch 31/500: delta of gamma - 0.00014451672355022432, tolerance - 1e-05\n",
      "Epoch 32/500: delta of gamma - 0.0001685525182397856, tolerance - 1e-05\n",
      "Epoch 33/500: delta of gamma - 0.0002163937791774255, tolerance - 1e-05\n",
      "Epoch 34/500: delta of gamma - 0.00023065534959132295, tolerance - 1e-05\n",
      "Epoch 35/500: delta of gamma - 0.00021764598817185904, tolerance - 1e-05\n",
      "Epoch 36/500: delta of gamma - 0.00021301604937478988, tolerance - 1e-05\n",
      "Epoch 37/500: delta of gamma - 0.00022900827704891652, tolerance - 1e-05\n",
      "Epoch 38/500: delta of gamma - 0.00024274416071841046, tolerance - 1e-05\n",
      "Epoch 39/500: delta of gamma - 0.0002546594412008258, tolerance - 1e-05\n",
      "Epoch 40/500: delta of gamma - 0.00024758761099684504, tolerance - 1e-05\n",
      "Epoch 41/500: delta of gamma - 0.00027359555618727935, tolerance - 1e-05\n",
      "Epoch 42/500: delta of gamma - 0.0003022521562335065, tolerance - 1e-05\n",
      "Epoch 43/500: delta of gamma - 0.00033344601177253265, tolerance - 1e-05\n",
      "Epoch 44/500: delta of gamma - 0.00036281863111162763, tolerance - 1e-05\n",
      "Epoch 45/500: delta of gamma - 0.0003675863486247605, tolerance - 1e-05\n",
      "Epoch 46/500: delta of gamma - 0.0003913478403590397, tolerance - 1e-05\n",
      "Epoch 47/500: delta of gamma - 0.0004619336019666824, tolerance - 1e-05\n",
      "Epoch 48/500: delta of gamma - 0.0005467803433095116, tolerance - 1e-05\n",
      "Epoch 49/500: delta of gamma - 0.0005338133660591144, tolerance - 1e-05\n",
      "Epoch 50/500: delta of gamma - 0.0005262543393059028, tolerance - 1e-05\n",
      "Epoch 51/500: delta of gamma - 0.0005067313075063531, tolerance - 1e-05\n",
      "Epoch 52/500: delta of gamma - 0.0005025039191292878, tolerance - 1e-05\n",
      "Epoch 53/500: delta of gamma - 0.00045155748431349686, tolerance - 1e-05\n",
      "Epoch 54/500: delta of gamma - 0.0003857356700546121, tolerance - 1e-05\n",
      "Epoch 55/500: delta of gamma - 0.00029187032191307373, tolerance - 1e-05\n",
      "Epoch 56/500: delta of gamma - 0.00023336975979970146, tolerance - 1e-05\n",
      "Epoch 57/500: delta of gamma - 0.00018504340307128742, tolerance - 1e-05\n",
      "Epoch 58/500: delta of gamma - 0.0001567507866273801, tolerance - 1e-05\n",
      "Epoch 59/500: delta of gamma - 0.00014119029196183768, tolerance - 1e-05\n",
      "Epoch 60/500: delta of gamma - 0.0002190462970855749, tolerance - 1e-05\n",
      "Epoch 61/500: delta of gamma - 0.00016859434400586353, tolerance - 1e-05\n",
      "Epoch 62/500: delta of gamma - 0.00014305136148862145, tolerance - 1e-05\n",
      "Epoch 63/500: delta of gamma - 0.00012707234358024587, tolerance - 1e-05\n",
      "Epoch 64/500: delta of gamma - 0.00011600493441798424, tolerance - 1e-05\n",
      "Epoch 65/500: delta of gamma - 0.00010202459230608064, tolerance - 1e-05\n",
      "Epoch 66/500: delta of gamma - 9.149031197278156e-05, tolerance - 1e-05\n",
      "Epoch 67/500: delta of gamma - 9.164465734697155e-05, tolerance - 1e-05\n",
      "Epoch 68/500: delta of gamma - 0.00011558028198328458, tolerance - 1e-05\n",
      "Epoch 69/500: delta of gamma - 0.00010385427918037123, tolerance - 1e-05\n",
      "Epoch 70/500: delta of gamma - 0.00010588048878998556, tolerance - 1e-05\n",
      "Epoch 71/500: delta of gamma - 0.00011380552010511619, tolerance - 1e-05\n",
      "Epoch 72/500: delta of gamma - 0.00011779947093167398, tolerance - 1e-05\n",
      "Epoch 73/500: delta of gamma - 0.00010858446595362048, tolerance - 1e-05\n",
      "Epoch 74/500: delta of gamma - 0.00010968068779214395, tolerance - 1e-05\n",
      "Epoch 75/500: delta of gamma - 0.00010169474277177547, tolerance - 1e-05\n",
      "Epoch 76/500: delta of gamma - 8.368393462773473e-05, tolerance - 1e-05\n",
      "Epoch 77/500: delta of gamma - 8.153718936711895e-05, tolerance - 1e-05\n",
      "Epoch 78/500: delta of gamma - 6.985221021277597e-05, tolerance - 1e-05\n",
      "Epoch 79/500: delta of gamma - 5.4397429051657864e-05, tolerance - 1e-05\n",
      "Epoch 80/500: delta of gamma - 7.924183242932883e-05, tolerance - 1e-05\n",
      "Epoch 81/500: delta of gamma - 4.647020014686744e-05, tolerance - 1e-05\n",
      "Epoch 82/500: delta of gamma - 4.200260223640429e-05, tolerance - 1e-05\n",
      "Epoch 83/500: delta of gamma - 4.1639624742571206e-05, tolerance - 1e-05\n",
      "Epoch 84/500: delta of gamma - 4.182208422724666e-05, tolerance - 1e-05\n",
      "Epoch 85/500: delta of gamma - 4.1710040682925736e-05, tolerance - 1e-05\n",
      "Epoch 86/500: delta of gamma - 4.1324255692369105e-05, tolerance - 1e-05\n",
      "Epoch 87/500: delta of gamma - 4.113932106430801e-05, tolerance - 1e-05\n",
      "Epoch 88/500: delta of gamma - 4.1466792373811685e-05, tolerance - 1e-05\n",
      "Epoch 89/500: delta of gamma - 8.540220942061665e-05, tolerance - 1e-05\n",
      "Epoch 90/500: delta of gamma - 4.814321899977782e-05, tolerance - 1e-05\n",
      "Epoch 91/500: delta of gamma - 4.9363782010013584e-05, tolerance - 1e-05\n",
      "Epoch 92/500: delta of gamma - 5.3023097733656146e-05, tolerance - 1e-05\n",
      "Epoch 93/500: delta of gamma - 5.8353367178756775e-05, tolerance - 1e-05\n",
      "Epoch 94/500: delta of gamma - 6.351163920379305e-05, tolerance - 1e-05\n",
      "Epoch 95/500: delta of gamma - 6.626542022244861e-05, tolerance - 1e-05\n",
      "Epoch 96/500: delta of gamma - 6.862646981511196e-05, tolerance - 1e-05\n",
      "Epoch 97/500: delta of gamma - 6.952265813303708e-05, tolerance - 1e-05\n",
      "Epoch 98/500: delta of gamma - 6.954420873475966e-05, tolerance - 1e-05\n",
      "Epoch 99/500: delta of gamma - 6.870626174915706e-05, tolerance - 1e-05\n",
      "Epoch 100/500: delta of gamma - 6.448432226506345e-05, tolerance - 1e-05\n",
      "Epoch 101/500: delta of gamma - 5.84249597856985e-05, tolerance - 1e-05\n",
      "Epoch 102/500: delta of gamma - 5.3190322925917076e-05, tolerance - 1e-05\n",
      "Epoch 103/500: delta of gamma - 4.71378596687925e-05, tolerance - 1e-05\n",
      "Epoch 104/500: delta of gamma - 3.864503850610039e-05, tolerance - 1e-05\n",
      "Epoch 105/500: delta of gamma - 3.337680921049574e-05, tolerance - 1e-05\n",
      "Epoch 106/500: delta of gamma - 2.8996246444777368e-05, tolerance - 1e-05\n",
      "Epoch 107/500: delta of gamma - 2.565921072589273e-05, tolerance - 1e-05\n",
      "Epoch 108/500: delta of gamma - 2.3407811678317682e-05, tolerance - 1e-05\n",
      "Epoch 109/500: delta of gamma - 2.2271133494460404e-05, tolerance - 1e-05\n",
      "Epoch 110/500: delta of gamma - 2.1956944401227344e-05, tolerance - 1e-05\n",
      "Epoch 111/500: delta of gamma - 2.1092051577290294e-05, tolerance - 1e-05\n",
      "Epoch 112/500: delta of gamma - 1.859928320317024e-05, tolerance - 1e-05\n",
      "Epoch 113/500: delta of gamma - 1.624257865133663e-05, tolerance - 1e-05\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 114/500: delta of gamma - 1.4448205055839004e-05, tolerance - 1e-05\n",
      "Epoch 115/500: delta of gamma - 1.2736654447977601e-05, tolerance - 1e-05\n",
      "Epoch 116/500: delta of gamma - 1.113823432779032e-05, tolerance - 1e-05\n",
      "Epoch 117/500: delta of gamma - 9.72047096532438e-06, tolerance - 1e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_samples = None\n",
    "max_iter = 500\n",
    "\n",
    "latent_size = 8\n",
    "\n",
    "_, _, bin_samples, _ =  sample_data(start_digit, stop_digit, num_samples, binary = True)\n",
    "mu, _, _= EM(bin_samples, latent_size, max_iter = max_iter, plot = False)\n",
    "plot_MNIST_latent_representation(mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "e12e40c2d2165e3bb500b5504128910d",
     "grade": true,
     "grade_id": "cell-f01c37653160244b",
     "locked": false,
     "points": 3,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "When K is less than the number of labels, we can see that we get hidden spaces that correspond to more than one digit. In particular, the first visualization looks like a mix of digits 3 and 2 while the second one looks like a four. In general, the representation of a missing digit can infuence more than one single hidden vector.\n",
    "\n",
    "When K is greater than the number of classes, we obtain mutiple hidden representations for the same digit. However, those capture different characteristics among the same labels. For example they can represent different styles of writing, as we can see from the figure. We have in fact different types of four, which include one with wider white space in the top, one with smaller one, and one that is inclinated to the right. Also we have different types of 2s, such as with or without an overlap of the line in the lower part of the image. In general, we could also find mixed representations of digits."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "b306681523a2e35eea310ac10bb68999",
     "grade": false,
     "grade_id": "cell-cf478d67239b7f2e",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.4.2 Identify misclassifications (10 points)\n",
    "How can you use the data labels to assign a label to each of the clusters/latent variables? Use this to identify images that are 'misclassified' and try to understand why they are. Report your findings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "000c11bd8756a4e24296c7c55d3ee17e",
     "grade": true,
     "grade_id": "cell-daa1a492fbba5c7e",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "\n",
    "def find_inferred_labels(gamma):\n",
    "    mapping = {}\n",
    "    \n",
    "    inferred_labels = np.argmax(gamma, axis=1)\n",
    "    matches_counter = Counter(zip(inferred_labels, labels)).most_common()\n",
    "\n",
    "    for k, v in matches_counter: \n",
    "        inferred_label, true_label = k\n",
    "        if inferred_label not in mapping:\n",
    "            mapping[inferred_label] = true_label\n",
    "        if len(mapping) == gamma.shape[0]:\n",
    "            break\n",
    "            \n",
    "    map_function = np.vectorize(lambda x: mapping[x])\n",
    "    return map_function(inferred_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/500: delta of gamma - 0.007037781547180154, tolerance - 1e-05\n",
      "Epoch 1/500: delta of gamma - 0.00527394434295638, tolerance - 1e-05\n",
      "Epoch 2/500: delta of gamma - 0.0035627569378913664, tolerance - 1e-05\n",
      "Epoch 3/500: delta of gamma - 0.0034087886552452242, tolerance - 1e-05\n",
      "Epoch 4/500: delta of gamma - 0.002715058694992901, tolerance - 1e-05\n",
      "Epoch 5/500: delta of gamma - 0.0017693330150239555, tolerance - 1e-05\n",
      "Epoch 6/500: delta of gamma - 0.0011088506613732138, tolerance - 1e-05\n",
      "Epoch 7/500: delta of gamma - 0.0007161957319071086, tolerance - 1e-05\n",
      "Epoch 8/500: delta of gamma - 0.000519849438466495, tolerance - 1e-05\n",
      "Epoch 9/500: delta of gamma - 0.0003668157248927767, tolerance - 1e-05\n",
      "Epoch 10/500: delta of gamma - 0.00021119349029406873, tolerance - 1e-05\n",
      "Epoch 11/500: delta of gamma - 0.00019034440776355337, tolerance - 1e-05\n",
      "Epoch 12/500: delta of gamma - 0.0001814466133019971, tolerance - 1e-05\n",
      "Epoch 13/500: delta of gamma - 0.00010550073981531767, tolerance - 1e-05\n",
      "Epoch 14/500: delta of gamma - 4.6970261276072276e-05, tolerance - 1e-05\n",
      "Epoch 15/500: delta of gamma - 8.621744300415058e-05, tolerance - 1e-05\n",
      "Epoch 16/500: delta of gamma - 9.106673822710085e-05, tolerance - 1e-05\n",
      "Epoch 17/500: delta of gamma - 9.109784427614438e-05, tolerance - 1e-05\n",
      "Epoch 18/500: delta of gamma - 2.1207788379621245e-05, tolerance - 1e-05\n",
      "Epoch 19/500: delta of gamma - 9.873348332341065e-06, tolerance - 1e-05\n",
      "Missclassification rate for class 2: 0.1482040953340047\n",
      "Missclassification rate for class 3: 0.1239602022508563\n",
      "Missclassification rate for class 4: 0.013009243409791168\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_samples = None\n",
    "max_iter = 500\n",
    "\n",
    "latent_size = 3\n",
    "\n",
    "labels, _, bin_samples, sampled_sizes =  sample_data(start_digit, stop_digit, num_samples, binary = True)\n",
    "_, _, gamma = EM(bin_samples, latent_size, max_iter = max_iter, plot = False)\n",
    "inferred_labels = find_inferred_labels(gamma)\n",
    "\n",
    "for i in range(start_digit, stop_digit + 1):\n",
    "    starting_index = np.sum(sampled_sizes[:i - start_digit]).astype(int)\n",
    "    sample_size = sampled_sizes[i - start_digit]\n",
    "    labels_per_class = inferred_labels[starting_index : starting_index + sample_size]\n",
    "    true_labels = labels[starting_index : starting_index + sample_size]\n",
    "    sample_per_class = bin_samples[starting_index : starting_index + sample_size]\n",
    "    \n",
    "    idxs = np.where(labels_per_class - true_labels != 0)[0]\n",
    "    print(f'Missclassification rate for class {i}: {idxs.shape[0]/sample_size}')\n",
    "    \n",
    "    K = 5\n",
    "    fig, axes = plt.subplots(1, K)\n",
    "    \n",
    "    for j, idx in enumerate(idxs[:5]):\n",
    "        sample = sample_per_class[idx]\n",
    "        sample = sample.reshape(28, 28)\n",
    "        \n",
    "        axes[j].axis('off')\n",
    "        axes[j].imshow(sample, cmap='Greys')\n",
    "        axes[j].set_title(f'p:{labels_per_class[idx]} t:{true_labels[idx]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "baf43434481c13d76ad51e3ba07e2bf5",
     "grade": true,
     "grade_id": "cell-329245c02df7850d",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "To get predicted label of all datapoints we first find $$label_n = argmax_k (\\boldsymbol{\\gamma_n}) \\forall x_n$$\n",
    "We assume, that this value corresponds to some label from original data. However, because predicted labels can be in any position, we add +1 for each correspondence between specific position in $\\boldsymbol{\\gamma_n}$ and label in original data. We use this for further mapping between predicted label and original label.. \n",
    "\n",
    "Imagine, we get following results: \n",
    "- original labels are $\\{ 3, 2, 3, 3, 4, 2, 2, 4, 4 \\}$\n",
    "- predicted labels are $\\{ 0, 1, 0, 0, 1, 1, 0, 2, 2 \\}$.\n",
    "\n",
    "This gives us following correspondences (note that number after \":\" stands for number of occurrences): $\\{ (0, 3):3 ; (0, 2): 1 ; (1, 2) : 2 ; (1, 4) : 1 ; (2, 4) : 2 \\}$. We choose correspondences with highest number of occurences for the same inferred label. Thus, we will have following correspondences between position in $\\boldsymbol{\\gamma_n}$ and true labels: $\\{(0,3); (1,2); (2,4)\\}$. \n",
    "\n",
    "**Note**, that to account for the fact that latent space can have higher dimensionality than number of classes, we allow multiple true labels to be corresponding to the same predicted label.\n",
    "\n",
    "Afterwards, we compare these inferred labels with true labels and find number of misclassification. We have also visualized some of the misclassification in order to diagnose potential reasons for faulty performance. As we can see it, numbers which were classified incorrectly, are often not written properly and can be easily misclassified even by humans. However, some of the misclassifications are not as bad as others so this might point to the fact that EM algorithm is not advanced enough to generalize well to all the data. This might be due to the fact that that it underfits the data, as it doesn't have enough learnable parameters to account for all the data. Also, it might be due to the fact that we are only using subsamples of data and those can have internal biases so that EM fits these biases, or that it has not seen enough examples and does not generalize well.\n",
    "\n",
    "- - - - \n",
    "\n",
    "Another simpler approach is to compare the euclidean distance between the $\\mu$ parameters and the elements of the dataset, and registering the class for latent space $k$ as the class which has lowest average euclidean distance to $\\mu_k$ over the dataset.\n",
    "\n",
    "- - - -\n",
    "From the examples above, it seems like that 2s can get mistaken as 4s when the lower horizontal bar is around the center of the image.\n",
    "Regarding the digit 3 we can see that from the examples above, they get mistaken as 2s when they are a bit rotated to the right, and as 4s when the opposite happens.\n",
    "\n",
    "In total, 4s get mistaken much less than other digits, and most of the misclassifications are between class 2 and 3.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "640bc57a2d08c3becf534bb5e4b35971",
     "grade": false,
     "grade_id": "cell-67ce1222e8a7837b",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "#### 1.4.3 Initialize with true values (5 points)\n",
    "Initialize the three classes with the true values of the parameters and see what happens. Report your results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def init_mu_with_true(start, stop, num_samples):\n",
    "    first = True\n",
    "    for i in range(start, stop+1):\n",
    "        _, _, bin_samples, _ =  sample_data(i, i, num_samples, binary = True)\n",
    "        if first:\n",
    "            mu = np.zeros((stop - start + 1, bin_samples.shape[1]))\n",
    "            first = False\n",
    "\n",
    "        avg_values = np.mean(bin_samples, axis = 0)\n",
    "        mu[i - start] = avg_values\n",
    "    return mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "a48f788e286458ef0f776865a3bcd58b",
     "grade": true,
     "grade_id": "cell-aa5d6b9f941d985d",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/500: delta of gamma - 0.00744747981816786, tolerance - 1e-05\n",
      "Epoch 1/500: delta of gamma - 0.001131502075929914, tolerance - 1e-05\n",
      "Epoch 2/500: delta of gamma - 0.0006773936819290769, tolerance - 1e-05\n",
      "Epoch 3/500: delta of gamma - 0.00038465966816704885, tolerance - 1e-05\n",
      "Epoch 4/500: delta of gamma - 0.00022098457428914906, tolerance - 1e-05\n",
      "Epoch 5/500: delta of gamma - 0.00011794313203321668, tolerance - 1e-05\n",
      "Epoch 6/500: delta of gamma - 6.419858536832716e-05, tolerance - 1e-05\n",
      "Epoch 7/500: delta of gamma - 3.667927162971629e-05, tolerance - 1e-05\n",
      "Epoch 8/500: delta of gamma - 1.7811709826930317e-05, tolerance - 1e-05\n",
      "Epoch 9/500: delta of gamma - 9.18115014533511e-06, tolerance - 1e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_digit = 2\n",
    "stop_digit = 4\n",
    "range_digits = stop_digit - start_digit + 1\n",
    "im_size = bin_samples.shape[1]\n",
    "\n",
    "num_samples = None\n",
    "max_iter = 500\n",
    "latent_size = range_digits\n",
    "\n",
    "mu = init_mu_with_true(start_digit, stop_digit, num_samples)\n",
    "    \n",
    "_, _, bin_samples, _ = sample_data(start_digit, stop_digit, num_samples, binary = True)\n",
    "mu, _, _ = EM(bin_samples, latent_size, max_iter = max_iter, plot = False, mu = mu)\n",
    "plot_MNIST_latent_representation(mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "1dc4adf3081f3bec93f94c3b12b87db9",
     "grade": true,
     "grade_id": "cell-981e44f35a3764b0",
     "locked": false,
     "points": 3,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "The results show the visualization of the $\\mu_k$ after the EM algorithm when their values are initialized as the average digits for every class. We can see that the algorithm converges in much less number of iterations, and that the delta (average difference of elements of $\\gamma_{nk}$ from the last iteration) monotonically decreases.The reason for that might be that we initialize $\\mu$ with values close to a local minima in a parameter space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "bd613f41e5d2b7d22b0d5b1e7644a48a",
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     "grade_id": "cell-19bfd7cf4017ed84",
     "locked": true,
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    }
   },
   "source": [
    "## Part 2: Variational Auto-Encoder\n",
    "\n",
    "A Variational Auto-Encoder (VAE) is a probabilistic model $p(\\bx, \\bz)$ over observed variables $\\bx$ and latent variables and/or parameters $\\bz$. Here we distinguish the decoder part, $p(\\bx | \\bz) p(\\bz)$ and an encoder part $p(\\bz | \\bx)$ that are both specified with a neural network. A lower bound on the log marginal likelihood $\\log p(\\bx)$ can be obtained by approximately inferring the latent variables z from the observed data x using an encoder distribution $q(\\bz| \\bx)$ that is also specified as a neural network. This lower bound is then optimized to fit the model to the data. \n",
    "\n",
    "The model was introduced by Diederik Kingma (during his PhD at the UVA) and Max Welling in 2013, https://arxiv.org/abs/1312.6114. \n",
    "\n",
    "Since it is such an important model there are plenty of well written tutorials that should help you with the assignment. E.g: https://jaan.io/what-is-variational-autoencoder-vae-tutorial/.\n",
    "\n",
    "In the following, we will make heavily use of the torch module, https://pytorch.org/docs/stable/index.html. Most of the time replacing `np.` with `torch.` will do the trick, e.g. `np.sum` becomes `torch.sum` and `np.log` becomes `torch.log`. In addition, we will use `torch.FloatTensor()` as an equivalent to `np.array()`. In order to train our VAE efficiently we will make use of batching. The number of data points in a batch will become the first dimension of our data tensor, e.g. A batch of 128 MNIST images has the dimensions [128, 1, 28, 28]. To check check the dimensions of a tensor you can call `.size()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "92bd337f41c3f94777f47376c7149ca7",
     "grade": false,
     "grade_id": "cell-bcbe35b20c1007d3",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.1 Loss function\n",
    "The objective function (variational lower bound), that we will use to train the VAE, consists of two terms: a log Bernoulli loss (reconstruction loss) and a Kullback–Leibler divergence. We implement the two terms separately and combine them in the end.\n",
    "As seen in Part 1: Expectation Maximization, we can use a multivariate Bernoulli distribution to model the likelihood $p(\\bx | \\bz)$ of black and white images. Formally, the variational lower bound is maximized but in PyTorch we are always minimizing therefore we need to calculate the negative log Bernoulli loss and Kullback–Leibler divergence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "3fb5f70b132e1233983ef89d19998374",
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     "grade_id": "cell-389d81024af846e5",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.1.1 Negative Log Bernoulli loss (5 points)\n",
    "The negative log Bernoulli loss is defined as,\n",
    "\n",
    "\\begin{align}\n",
    "loss = - (\\sum_i^D \\bx_i \\log \\hat{\\bx_i} + (1 − \\bx_i) \\log(1 − \\hat{\\bx_i})).\n",
    "\\end{align}\n",
    "\n",
    "Write a function `log_bernoulli_loss` that takes a D dimensional vector `x`, its reconstruction `x_hat` and returns the negative log Bernoulli loss. Make sure that your function works for batches of arbitrary size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "952435ca03f47ab67a7e88b8306fc9a0",
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     "grade_id": "cell-1d504606d6f99145",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def log_bernoulli_loss(x_hat, x):\n",
    "    loss = -torch.sum(x * torch.log(x_hat) + (1 - x) * torch.log(1 - x_hat))\n",
    "    return loss\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "bd2a490aa694507bd032e86d77fc0087",
     "grade": true,
     "grade_id": "cell-9666dad0b2a9f483",
     "locked": true,
     "points": 5,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Test test test\n",
    "x_test = torch.FloatTensor([[0.1, 0.2, 0.3, 0.4], [0.5, 0.6, 0.7, 0.8], [0.9, 0.9, 0.9, 0.9]])\n",
    "x_hat_test = torch.FloatTensor([[0.11, 0.22, 0.33, 0.44], [0.55, 0.66, 0.77, 0.88], [0.99, 0.99, 0.99, 0.99]])\n",
    "\n",
    "assert log_bernoulli_loss(x_hat_test, x_test) > 0.0\n",
    "assert log_bernoulli_loss(x_hat_test, x_test) < 10.0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "6b75b7a531ecc87bce57925c4da464ee",
     "grade": false,
     "grade_id": "cell-b3a7c02dee7aa505",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.1.2 Negative Kullback–Leibler divergence (10 Points)\n",
    "The variational lower bound (the objective to be maximized) contains a KL term $D_{KL}(q(\\bz)||p(\\bz))$ that can often be calculated analytically. In the VAE we assume $q = N(\\bz, \\mu, \\sigma^2I)$ and $p = N(\\bz, 0, I)$. Solve analytically!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "d01a7e7fe2dcf5f1c5fb955b85c8a04a",
     "grade": true,
     "grade_id": "cell-4cab10fd1a636858",
     "locked": false,
     "points": 5,
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    }
   },
   "source": [
    "\n",
    "We can express the KL divergence as\n",
    "\\begin{align*}\n",
    "\tKL(q || p) &= - \\int q(\\mathbf{z}) \\ln \\big( \\frac{p(\\mathbf{z})}{q(\\mathbf{z})} \\big) d\\mathbf{z} = -\\int q(\\mathbf{z}) \\big( \\ln p(\\mathbf{z}) - q(\\mathbf{z}) \\big) d\\mathbf{z} \\\\\n",
    "\t&= -\\int q(\\mathbf{z}) \\ln p(\\mathbf{z}) d\\mathbf{z} - \\big[ - \\int q(\\mathbf{z}) \\ln q(\\mathbf{z}) d\\mathbf{z}  \\big] \\end{align*}\n",
    "\n",
    "so that we can divide the problem in two similar integrals. This kind of integral with normals as functions $p$ and $q$ is known.\n",
    "As derived in homework 2, if $p(\\mathbf{z}) = \\mathcal{N}(\\mathbf{z} | \\mathbf{m}, \\mathbf{L})$ and $q=\\mathcal{N}(\\mathbf{z} | \\boldsymbol{\\mu}, \\boldsymbol{\\Sigma})$, then\n",
    "\\begin{align*}\n",
    "\t-\\int q(\\mathbf{z}) \\ln p(\\mathbf{z}) d\\mathbf{z} = \\frac{D}{2} \\ln 2 \\pi +\\frac{1}{2} \\ln |\\mathbf{L}| +\\frac{1}{2} Tr(\\mathbf{L}^{-1} \\boldsymbol{\\Sigma})  +\\frac{1}{2} (\\boldsymbol{\\mu} - \\mathbf{m})^T L^{-1} (\\boldsymbol{\\mu} - \\mathbf{m})\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "For the variational autoencoder case, we have then \n",
    "\\begin{align*}\n",
    "\t-\\int q(\\mathbf{z}) \\ln p(\\mathbf{z}) d\\mathbf{z}  &= \\frac{D}{2} \\ln 2 \\pi +\\frac{1}{2} \\ln |\\mathbf{L}| +\\frac{1}{2} Tr(\\mathbf{L}^{-1} \\boldsymbol{\\Sigma})  +\\frac{1}{2} (\\boldsymbol{\\mu} - \\mathbf{m})^T \\mathbf{L}^{-1} (\\boldsymbol{\\mu} - \\mathbf{m}) \\\\\n",
    "\t&=  \\frac{D}{2} \\ln 2 \\pi   +\\frac{1}{2} Tr( \\boldsymbol{\\sigma}^2 \\mathbf{I})  +\\frac{1}{2} \\boldsymbol{\\mu} ^T  \\boldsymbol{\\mu} = \\frac{D}{2} \\ln 2 \\pi   +\\frac{1}{2} \\sum_{d=1}^{D} (\\sigma_d^2  + \\mu_d^2)\\\\\n",
    "\t-\\int q(\\mathbf{z}) \\ln q(\\mathbf{z}) d\\mathbf{z}  &= \\frac{D}{2} \\ln 2 \\pi +\\frac{1}{2} \\ln |\\boldsymbol{\\Sigma}| +\\frac{D}{2} = \\frac{D}{2} \\ln 2 \\pi +\\frac{1}{2} \\sum_{d=1}^{D} \\log \\sigma_d^2 +\\frac{D}{2} \n",
    "\\end{align*}\n",
    "\n",
    "From those expressions, and the KL expression above, it follows that\n",
    "\n",
    "\\begin{align*}\n",
    "\tKL(q || p) &= - \\frac{1}{2} \\sum_{d=1}^{D} (1 + \\log \\sigma_d^2  - \\sigma_d^2  - \\mu_d^2)\n",
    "\\end{align*}\n",
    "\n",
    "------------------------\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "328115c94a66e8aba0a62896e647c3ba",
     "grade": false,
     "grade_id": "cell-c49899cbf2a49362",
     "locked": true,
     "schema_version": 1,
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    }
   },
   "source": [
    "Write a function `KL_loss` that takes two J dimensional vectors `mu` and `logvar` and returns the negative Kullback–Leibler divergence. Where `logvar` is $\\log(\\sigma^2)$. Make sure that your function works for batches of arbitrary size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "33b14b79372dd0235d67bb66921cd3e0",
     "grade": false,
     "grade_id": "cell-125b41878005206b",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def KL_loss(mu, logvar):\n",
    "    loss = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())\n",
    "    return loss\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "cf72e196d2b60827e8e940681ac50a07",
     "grade": true,
     "grade_id": "cell-ba714bbe270a3f39",
     "locked": true,
     "points": 5,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Test test test\n",
    "mu_test = torch.FloatTensor([[0.1, 0.2], [0.3, 0.4], [0.5, 0.6]])\n",
    "logvar_test = torch.FloatTensor([[0.01, 0.02], [0.03, 0.04], [0.05, 0.06]])\n",
    "\n",
    "assert KL_loss(mu_test, logvar_test) > 0.0\n",
    "assert KL_loss(mu_test, logvar_test) < 10.0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "65335a588baac26bc48dd6c4d275fdca",
     "grade": false,
     "grade_id": "cell-18cb3f8031edec23",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.1.3 Putting the losses together (5 points)\n",
    "Write a function `loss_function` that takes a D dimensional vector `x`, its reconstruction `x_hat`, two J dimensional vectors `mu` and `logvar` and returns the final loss. Make sure that your function works for batches of arbitrary size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "f6ecb5b60b2c8d7b90070ed59320ee70",
     "grade": false,
     "grade_id": "cell-d2d18781683f1302",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def loss_function(x_hat, x, mu, logvar):\n",
    "    loss = log_bernoulli_loss(x_hat, x) + KL_loss(mu, logvar)\n",
    "    return loss\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "816e9508408bfcb2c7332b508d505081",
     "grade": true,
     "grade_id": "cell-57747988d29bbb5d",
     "locked": true,
     "points": 5,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "x_test = torch.FloatTensor([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6], [0.7, 0.8, 0.9]])\n",
    "x_hat_test = torch.FloatTensor([[0.11, 0.22, 0.33], [0.44, 0.55, 0.66], [0.77, 0.88, 0.99]])\n",
    "mu_test = torch.FloatTensor([[0.1, 0.2], [0.3, 0.4], [0.5, 0.6]])\n",
    "logvar_test = torch.FloatTensor([[0.01, 0.02], [0.03, 0.04], [0.05, 0.06]])\n",
    "\n",
    "assert loss_function(x_hat_test, x_test, mu_test, logvar_test) > 0.0\n",
    "assert loss_function(x_hat_test, x_test, mu_test, logvar_test) < 10.0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "4506e06ed44a0535140582277a528ba4",
     "grade": false,
     "grade_id": "cell-9e3ba708967fe918",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.2 The model\n",
    "Below you see a data structure for the VAE. The modell itself consists of two main parts the encoder (images $\\bx$ to latent variables $\\bz$) and the decoder (latent variables $\\bz$ to images $\\bx$). The encoder is using 3 fully-connected layers, whereas the decoder is using fully-connected layers. Right now the data structure is quite empty, step by step will update its functionality. For test purposes we will initialize a VAE for you. After the data structure is completed you will do the hyperparameter search.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "31eccf2f6600764e28eb4bc6c5634e49",
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     "grade_id": "cell-e7d9dafee18f28a1",
     "locked": true,
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    }
   },
   "outputs": [],
   "source": [
    "from torch import nn\n",
    "from torch.nn import functional as F \n",
    "\n",
    "class VAE(nn.Module):\n",
    "    def __init__(self, fc1_dims, fc21_dims, fc22_dims, fc3_dims, fc4_dims):\n",
    "        super(VAE, self).__init__()\n",
    "\n",
    "        self.fc1 = nn.Linear(*fc1_dims)\n",
    "        self.fc21 = nn.Linear(*fc21_dims)\n",
    "        self.fc22 = nn.Linear(*fc22_dims)\n",
    "        self.fc3 = nn.Linear(*fc3_dims)\n",
    "        self.fc4 = nn.Linear(*fc4_dims)\n",
    "\n",
    "    def encode(self, x):\n",
    "        # To be implemented\n",
    "        raise Exception('Method not implemented')\n",
    "\n",
    "    def reparameterize(self, mu, logvar):\n",
    "        # To be implemented\n",
    "        raise Exception('Method not implemented')\n",
    "\n",
    "    def decode(self, z):\n",
    "        # To be implemented\n",
    "        raise Exception('Method not implemented')\n",
    "\n",
    "    def forward(self, x):\n",
    "        # To be implemented\n",
    "        raise Exception('Method not implemented')\n",
    "\n",
    "VAE_test = VAE(fc1_dims=(784, 4), fc21_dims=(4, 2), fc22_dims=(4, 2), fc3_dims=(2, 4), fc4_dims=(4, 784))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "1a2243397998b4f55c25dfd734f3e7e0",
     "grade": false,
     "grade_id": "cell-c4f9e841b8972a43",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.3 Encoding (10 points)\n",
    "Write a function `encode` that gets a vector `x` with 784 elements (flattened MNIST image) and returns `mu` and `logvar`. Your function should use three fully-connected layers (`self.fc1()`, `self.fc21()`, `self.fc22()`). First, you should use `self.fc1()` to embed `x`. Second, you should use `self.fc21()` and `self.fc22()` on the embedding of `x` to compute `mu` and `logvar` respectively. PyTorch comes with a variety of activation functions, the most common calls are `F.relu()`, `F.sigmoid()`, `F.tanh()`. Make sure that your function works for batches of arbitrary size.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "628bcd88c611cf01e70f77854600199b",
     "grade": false,
     "grade_id": "cell-93cb75b98ae76569",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def encode(self, x):\n",
    "    h1 = F.relu(self.fc1(x))\n",
    "    mu = self.fc21(h1)\n",
    "    logvar = self.fc22(h1)\n",
    "    return mu, logvar\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "370d930fa9f10f1d3a451f3805c04d88",
     "grade": true,
     "grade_id": "cell-9648960b73337a70",
     "locked": true,
     "points": 10,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Test, test, test\n",
    "VAE.encode = encode\n",
    "\n",
    "x_test = torch.ones((5,784))\n",
    "mu_test, logvar_test = VAE_test.encode(x_test)\n",
    "\n",
    "assert np.allclose(mu_test.size(), [5, 2])\n",
    "assert np.allclose(logvar_test.size(), [5, 2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "6f597cc2b5ef941af282d7162297f865",
     "grade": false,
     "grade_id": "cell-581b4ed1996be868",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.4 Reparameterization (10 points)\n",
    "One of the major question that the VAE is answering, is 'how to take derivatives with respect to the parameters of a stochastic variable?', i.e. if we are given $\\bz$ that is drawn from a distribution $q(\\bz|\\bx)$, and we want to take derivatives. This step is necessary to be able to use gradient-based optimization algorithms like SGD.\n",
    "For some distributions, it is possible to reparameterize samples in a clever way, such that the stochasticity is independent of the parameters. We want our samples to deterministically depend on the parameters of the distribution. For example, in a normally-distributed variable with mean $\\mu$ and standard deviation $\\sigma$, we can sample from it like this:\n",
    "\n",
    "\\begin{align}\n",
    "\\bz = \\mu + \\sigma \\odot \\epsilon,\n",
    "\\end{align}\n",
    "\n",
    "where $\\odot$ is the element-wise multiplication and $\\epsilon$ is sampled from $N(0, I)$.\n",
    "\n",
    "\n",
    "Write a function `reparameterize` that takes two J dimensional vectors `mu` and `logvar`. It should return $\\bz = \\mu + \\sigma \\odot \\epsilon$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "6331cb5dd23aaacbcf1a52cfecb1afaa",
     "grade": false,
     "grade_id": "cell-679aea8b2adf7ec4",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def reparameterize(self, mu, logvar):\n",
    "    std = torch.exp(1/2 * logvar)\n",
    "    eps = torch.randn_like(std)\n",
    "    z = mu + std * eps \n",
    "    return z\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "38d4e047717ab334b262c8c177f0a420",
     "grade": true,
     "grade_id": "cell-fdd7b27a3d17f84e",
     "locked": true,
     "points": 10,
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    }
   },
   "outputs": [],
   "source": [
    "### Test, test, test\n",
    "VAE.reparameterize = reparameterize\n",
    "VAE_test.train()\n",
    "\n",
    "mu_test = torch.FloatTensor([[0.1, 0.2], [0.3, 0.4], [0.5, 0.6]])\n",
    "logvar_test = torch.FloatTensor([[0.01, 0.02], [0.03, 0.04], [0.05, 0.06]])\n",
    "\n",
    "z_test = VAE_test.reparameterize(mu_test, logvar_test)\n",
    "\n",
    "assert np.allclose(z_test.size(), [3, 2])\n",
    "assert z_test[0][0] < 5.0\n",
    "assert z_test[0][0] > -5.0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "9241ab0eaf8366c37ad57072ce66f095",
     "grade": false,
     "grade_id": "cell-0be851f9f7f0a93e",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.5 Decoding (10 points)\n",
    "Write a function `decode` that gets a vector `z` with J elements and returns a vector `x_hat` with 784 elements (flattened MNIST image). Your function should use two fully-connected layers (`self.fc3()`, `self.fc4()`). PyTorch comes with a variety of activation functions, the most common calls are `F.relu()`, `F.sigmoid()`, `F.tanh()`. Make sure that your function works for batches of arbitrary size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "e8e833cfd7c54a9b67a38056d5d6cab8",
     "grade": false,
     "grade_id": "cell-bf92bb3878275a41",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def decode(self, z):\n",
    "    x_hat = F.relu(self.fc3(z))\n",
    "    x_hat = F.sigmoid(self.fc4(x_hat))\n",
    "    return x_hat\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "7732293fd7d971fcf255496e8c68638d",
     "grade": true,
     "grade_id": "cell-4abb91cb9e80af5d",
     "locked": true,
     "points": 10,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# test test test\n",
    "VAE.decode = decode\n",
    "\n",
    "z_test = torch.ones((5,2))\n",
    "x_hat_test = VAE_test.decode(z_test)\n",
    "\n",
    "assert np.allclose(x_hat_test.size(), [5, 784])\n",
    "assert (x_hat_test <= 1).all()\n",
    "assert (x_hat_test >= 0).all()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "e2e113d1f45398b2a1399c336526e755",
     "grade": false,
     "grade_id": "cell-97511fbc4f5b469b",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.6 Forward pass (10)\n",
    "To complete the data structure you have to define a forward pass through the VAE. A single forward pass consists of the encoding of an MNIST image $\\bx$ into latent space $\\bz$, the reparameterization of $\\bz$ and the decoding of $\\bz$ into an image $\\bx$.\n",
    "\n",
    "Write a function `forward` that gets a a vector `x` with 784 elements (flattened MNIST image) and returns a vector `x_hat` with 784 elements (flattened MNIST image), `mu` and `logvar`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "8b7433c4631dd01c07a5fe287e55ae13",
     "grade": false,
     "grade_id": "cell-26bb463b9f98ebd5",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def forward(self, x):\n",
    "    x = x.view(-1, 784)\n",
    "    mu, logvar = self.encode(x)\n",
    "    z = self.reparameterize(mu, logvar)\n",
    "    x_hat = self.decode(z)\n",
    "    return x_hat, mu, logvar\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "8e7e495f40465c162512e9873c360b25",
     "grade": true,
     "grade_id": "cell-347e5fba3d02754b",
     "locked": true,
     "points": 10,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# test test test \n",
    "VAE.forward = forward\n",
    "\n",
    "x_test = torch.ones((5,784))\n",
    "x_hat_test, mu_test, logvar_test = VAE_test.forward(x_test)\n",
    "\n",
    "assert np.allclose(x_hat_test.size(), [5, 784])\n",
    "assert np.allclose(mu_test.size(), [5, 2])\n",
    "assert np.allclose(logvar_test.size(), [5, 2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "a114a6fd781fb949b887e6a028e07946",
     "grade": false,
     "grade_id": "cell-62c89e4d3b253671",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.7 Training (15)\n",
    "We will now train the VAE using an optimizer called Adam, https://arxiv.org/abs/1412.6980. The code to train a model in PyTorch is given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "f3b6bb965fb48229c63cacda48baea65",
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     "grade_id": "cell-be75f61b09f3b9b6",
     "locked": true,
     "schema_version": 1,
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    }
   },
   "outputs": [],
   "source": [
    "from torch.autograd import Variable\n",
    "\n",
    "def train(epoch, train_loader, model, optimizer):\n",
    "    model.train()\n",
    "    train_loss = 0\n",
    "    for batch_idx, (data, _) in enumerate(train_loader):\n",
    "        data = Variable(data)\n",
    "        optimizer.zero_grad()\n",
    "        recon_batch, mu, logvar = model(data)\n",
    "        loss = loss_function(recon_batch, data.view(-1, 784), mu, logvar)\n",
    "        loss.backward()\n",
    "        train_loss += loss.data\n",
    "        optimizer.step()\n",
    "        if batch_idx % 100 == 0:\n",
    "            print('Train Epoch: {} [{}/{} ({:.0f}%)]\\tLoss: {:.6f}'.format(\n",
    "                epoch, batch_idx * len(data), len(train_loader.dataset),\n",
    "                100. * batch_idx / len(train_loader),\n",
    "                loss.data / len(data)))\n",
    "\n",
    "    print('====> Epoch: {} Average loss: {:.4f}'.format(\n",
    "          epoch, train_loss / len(train_loader.dataset)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "48ca730dbef06a668f4dfdb24888f265",
     "grade": false,
     "grade_id": "cell-da1b063b7de850b9",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Let's train. You have to choose the hyperparameters. Make sure your loss is going down in a reasonable amount of epochs (around 10)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "846430258fb80f50b161135448726520",
     "grade": false,
     "grade_id": "cell-d4d4408d397f6967",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "# Hyperparameters\n",
    "fc1_dims = (784, 400)\n",
    "fc21_dims = (400, 20)\n",
    "fc22_dims = (400, 20)\n",
    "fc3_dims = (20, 400)\n",
    "fc4_dims = (400, 784)\n",
    "lr = 0.001\n",
    "batch_size = 128\n",
    "epochs = 10\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "b93390f399b743276bc25e67493344f2",
     "grade": true,
     "grade_id": "cell-ca352d8389c1809a",
     "locked": true,
     "points": 15,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# This cell contains a hidden test, please don't delete it, thx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "20719070ed85964de9722acc3456a515",
     "grade": false,
     "grade_id": "cell-5c77370db7cec9f2",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Run the box below to train the model using the hyperparameters you entered above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "38306be3638e85812bd5b2a052fcc0a4",
     "grade": false,
     "grade_id": "cell-5712d42de1068398",
     "locked": true,
     "schema_version": 1,
     "solution": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Epoch: 1 [0/60000 (0%)]\tLoss: 549.080933\n",
      "Train Epoch: 1 [12800/60000 (21%)]\tLoss: 174.812973\n",
      "Train Epoch: 1 [25600/60000 (43%)]\tLoss: 155.863464\n",
      "Train Epoch: 1 [38400/60000 (64%)]\tLoss: 140.523712\n",
      "Train Epoch: 1 [51200/60000 (85%)]\tLoss: 136.123383\n",
      "====> Epoch: 1 Average loss: 164.1155\n",
      "Train Epoch: 2 [0/60000 (0%)]\tLoss: 130.457916\n",
      "Train Epoch: 2 [12800/60000 (21%)]\tLoss: 124.440216\n",
      "Train Epoch: 2 [25600/60000 (43%)]\tLoss: 121.119637\n",
      "Train Epoch: 2 [38400/60000 (64%)]\tLoss: 117.109848\n",
      "Train Epoch: 2 [51200/60000 (85%)]\tLoss: 118.635345\n",
      "====> Epoch: 2 Average loss: 121.3830\n",
      "Train Epoch: 3 [0/60000 (0%)]\tLoss: 116.411163\n",
      "Train Epoch: 3 [12800/60000 (21%)]\tLoss: 107.948074\n",
      "Train Epoch: 3 [25600/60000 (43%)]\tLoss: 113.194458\n",
      "Train Epoch: 3 [38400/60000 (64%)]\tLoss: 111.878311\n",
      "Train Epoch: 3 [51200/60000 (85%)]\tLoss: 116.621796\n",
      "====> Epoch: 3 Average loss: 114.3433\n",
      "Train Epoch: 4 [0/60000 (0%)]\tLoss: 112.258392\n",
      "Train Epoch: 4 [12800/60000 (21%)]\tLoss: 112.560303\n",
      "Train Epoch: 4 [25600/60000 (43%)]\tLoss: 113.737000\n",
      "Train Epoch: 4 [38400/60000 (64%)]\tLoss: 109.284439\n",
      "Train Epoch: 4 [51200/60000 (85%)]\tLoss: 114.106560\n",
      "====> Epoch: 4 Average loss: 111.3866\n",
      "Train Epoch: 5 [0/60000 (0%)]\tLoss: 109.086349\n",
      "Train Epoch: 5 [12800/60000 (21%)]\tLoss: 111.400459\n",
      "Train Epoch: 5 [25600/60000 (43%)]\tLoss: 111.344154\n",
      "Train Epoch: 5 [38400/60000 (64%)]\tLoss: 106.616562\n",
      "Train Epoch: 5 [51200/60000 (85%)]\tLoss: 105.224358\n",
      "====> Epoch: 5 Average loss: 109.7272\n",
      "Train Epoch: 6 [0/60000 (0%)]\tLoss: 110.069893\n",
      "Train Epoch: 6 [12800/60000 (21%)]\tLoss: 110.312950\n",
      "Train Epoch: 6 [25600/60000 (43%)]\tLoss: 108.667816\n",
      "Train Epoch: 6 [38400/60000 (64%)]\tLoss: 109.934998\n",
      "Train Epoch: 6 [51200/60000 (85%)]\tLoss: 109.397537\n",
      "====> Epoch: 6 Average loss: 108.5957\n",
      "Train Epoch: 7 [0/60000 (0%)]\tLoss: 109.919960\n",
      "Train Epoch: 7 [12800/60000 (21%)]\tLoss: 106.549416\n",
      "Train Epoch: 7 [25600/60000 (43%)]\tLoss: 106.700226\n",
      "Train Epoch: 7 [38400/60000 (64%)]\tLoss: 106.950630\n",
      "Train Epoch: 7 [51200/60000 (85%)]\tLoss: 106.321609\n",
      "====> Epoch: 7 Average loss: 107.7511\n",
      "Train Epoch: 8 [0/60000 (0%)]\tLoss: 110.561966\n",
      "Train Epoch: 8 [12800/60000 (21%)]\tLoss: 108.605164\n",
      "Train Epoch: 8 [25600/60000 (43%)]\tLoss: 102.262032\n",
      "Train Epoch: 8 [38400/60000 (64%)]\tLoss: 104.754669\n",
      "Train Epoch: 8 [51200/60000 (85%)]\tLoss: 102.156967\n",
      "====> Epoch: 8 Average loss: 107.1659\n",
      "Train Epoch: 9 [0/60000 (0%)]\tLoss: 106.334747\n",
      "Train Epoch: 9 [12800/60000 (21%)]\tLoss: 106.522491\n",
      "Train Epoch: 9 [25600/60000 (43%)]\tLoss: 108.042160\n",
      "Train Epoch: 9 [38400/60000 (64%)]\tLoss: 104.794006\n",
      "Train Epoch: 9 [51200/60000 (85%)]\tLoss: 104.753616\n",
      "====> Epoch: 9 Average loss: 106.6718\n",
      "Train Epoch: 10 [0/60000 (0%)]\tLoss: 102.435097\n",
      "Train Epoch: 10 [12800/60000 (21%)]\tLoss: 111.231087\n",
      "Train Epoch: 10 [25600/60000 (43%)]\tLoss: 106.948837\n",
      "Train Epoch: 10 [38400/60000 (64%)]\tLoss: 104.716637\n",
      "Train Epoch: 10 [51200/60000 (85%)]\tLoss: 106.205627\n",
      "====> Epoch: 10 Average loss: 106.2514\n"
     ]
    }
   ],
   "source": [
    "from torchvision import datasets, transforms\n",
    "from torch import nn, optim\n",
    "\n",
    "# Load data\n",
    "train_data = datasets.MNIST('../data', train=True, download=True,\n",
    "                   transform=transforms.ToTensor())\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(train_data,\n",
    "                                           batch_size=batch_size, shuffle=True, **{})\n",
    "\n",
    "# Init model\n",
    "VAE_MNIST = VAE(fc1_dims=fc1_dims, fc21_dims=fc21_dims, fc22_dims=fc22_dims, fc3_dims=fc3_dims, fc4_dims=fc4_dims)\n",
    "\n",
    "# Init optimizer\n",
    "optimizer = optim.Adam(VAE_MNIST.parameters(), lr=lr)\n",
    "\n",
    "# Train\n",
    "for epoch in range(1, epochs + 1):\n",
    "    train(epoch, train_loader, VAE_MNIST, optimizer)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "e2f8fcc9384e30cb154cf931f223898b",
     "grade": false,
     "grade_id": "cell-bd07c058c661b9c6",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Run the box below to check if the model you trained above is able to correctly reconstruct images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "80d198e03b1287741d761a12e38dcf73",
     "grade": false,
     "grade_id": "cell-df03d717307a6863",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdgAAAHiCAYAAABLON1SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAE/1JREFUeJzt3X/I5nW95/HX21Fbp1EZOZuJujvniEaxsOMyylbL0iKdPP2h9ceRI+zBlRPTH0dIEFqLE8c/TiCLdhZiiSYaMuh0OFJtUofdIxV0DizRGJOZ5halnslJKaPGsKPOfPaPuWQHzz0zt9/v/fa6r9vHA+S+7u99ffx8/HoNz/leP+5PjTECAGysM5a9AADYigQWABoILAA0EFgAaCCwANBAYAGggcACQAOBhS2gqm6pqgNV9U9V9ZllrwdIzlz2AoAN8WSSv0jyriTnLHktQAQWtoQxxheTpKr2JLlkycsB4iliAGghsADQQGABoIHAAkADb3KCLaCqzszxP8/bkmyrqn+R5MUxxovLXRm8drmCha3hz5I8l+T2JP95cfvPlroieI0rG64DwMZzBQsADQQWABoILAA0EFgAaCCwANDgVf0cbFV5yzIAq+7nY4x/ebo7uYIFgFfm8fXcSWABoIHAAkCDWYGtqmur6tGq+lFV3b5RiwKAVTc5sFW1Lcn/SPIHSd6S5MaqestGLQwAVtmcK9irk/xojPHjMcbzSf46yfUbsywAWG1zAntxkn884ftDi2MA8Jo353Owtcaxf/Y516ram2TvjHkAYOXMCeyhJJee8P0lSZ58+Z3GGPuS7Ev8ogkAXjvmPEX87SSXV9XvVtXZSf4oyX0bsywAWG2Tr2DHGC9W1S1J/neSbUn2jzG+v2ErA4AVVmO8es/aeooYgC3ggTHGntPdyW9yAoAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGZy57AQAboaqWNvcYY2lzs3m5ggWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIH9YNmS5u4NOmd/z2XuSzrX3LWfc845k8e++c1vnjX3ddddN3nsww8/PGvur3zlK5PHPvvss7PmZvNyBQsADQQWABoILAA0mPUabFU9luRIkqNJXhxj7NmIRQHAqtuINzn9pzHGzzfg3wMAW4aniAGgwdzAjiR/V1UPVNXete5QVXur6kBVHZg5FwCsjLlPEb99jPFkVb0hyf1V9YMxxjdPvMMYY1+SfUlSVdM/XAgAK2TWFewY48nF16eTfCnJ1RuxKABYdZMDW1Wvr6pzX7qd5PeTPLRRCwOAVTbnKeILk3xp8avVzkzyV2OM/7UhqwKAFTc5sGOMHyf5txu4FgDYMnxMBwAaCCwANLBdHW22bdu27CUsxdwt3+aMX+Z2c0nyrne9a/LYO+64Y9bcl1566eSxjz766Ky5Dx48OHnsD37wg1lzs3m5ggWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIH9YGlz9OjRWeOXuS/qqpr7371jx45Z46+99trJY6+44opZc59xxvTrhQsvvHDW3Oeff/7ksXP/n40xZo2njytYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA1sV8emNWcbrrlbeC1zu7s5a5+zZVuS7Ny5c9b4PXv2TB67bdu2WXMfO3Zs8tjDhw/PmvuJJ56YNZ6tyRUsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwAN7AcLm8ycPV0vuOCCWXNff/31s8Zfdtllk8fO3cP3yJEjk8fed999s+Z+5plnJo+d+9/N5uUKFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkAD29XBGqpq8tizzjpr1txzti9705veNGvum2++edb47du3Tx579OjRWXM/+OCDk8fu379/1tzPP//8rPFsTa5gAaCBwAJAA4EFgAanDWxV7a+qp6vqoROOXVBV91fVDxdfd/YuEwBWy3quYD+T5NqXHbs9ydfGGJcn+driewBg4bSBHWN8M8kzLzt8fZJ7FrfvSfKeDV4XAKy0qa/BXjjGOJwki69v2LglAcDqa/8cbFXtTbK3ex4A2EymXsE+VVUXJcni69Mnu+MYY98YY88YY8/EuQBg5UwN7H1JblrcvinJlzdmOQCwNaznYzqfT/J/krypqg5V1Z8kuTPJO6vqh0neufgeAFg47WuwY4wbT/KjazZ4LQCwZfhNTgDQQGABoIHAAkAD+8HCGubsBzvXjh07Jo+97rrrZs19ySWXzBo/x29+85tZ4z/+8Y9PHvuzn/1s1txz9vBl63IFCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCB7epgDXO2H5u71d2VV145eewNN9wwa+7Xve51s8bPOW9f//rXZ8391a9+dfLYY8eOzZob1uIKFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABvaDhQ123nnnzRr/kY98ZPLYN77xjbPmnrOfa5IcPnx48tjbbrtt1tzPPffcrPGw0VzBAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGhguzpYwxlnTP+75zXXXDNr7quuumry2DPPnPdHeu6Wb3fdddfksY8//visuedutQcbzRUsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwAN7AcLa7jgggsmj/3gBz84a+7t27dPHjt3T9Sf/OQns8Z/9rOfnTz26NGjs+aGzcYVLAA0EFgAaCCwANDgtIGtqv1V9XRVPXTCsTuq6qdVdXDxz7t7lwkAq2U9V7CfSXLtGsf/coyxe/HP327ssgBgtZ02sGOMbyZ55lVYCwBsGXNeg72lqh5cPIW8c8NWBABbwNTAfiLJZUl2Jzmc5O6T3bGq9lbVgao6MHEuAFg5kwI7xnhqjHF0jHEsyaeSXH2K++4bY+wZY+yZukgAWDWTAltVF53w7XuTPHSy+wLAa9Fpf1ViVX0+yTuS/E5VHUry50neUVW7k4wkjyV5f+MaAWDlnDawY4wb1zj86Ya1AMCW4Tc5AUADgQWABgILAA3sB8uWtG3btlnjb7jhhsljd+3aNWvuOXu6vvDCC7PmvvPOO2eNf+YZv/QNXuIKFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkAD29WxJe3cuXPW+Pe9732Tx5577rmz5p6zXd2jjz46a+5777131vg5a4etxhUsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwAN7AfLplVVk8deddVVs+a+4oorJo8944x5f2/91a9+NXnszTffPGvu3/72t7PGA/+fK1gAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADWxXx6Z11llnTR77oQ99aNbc55xzzuSxY4xZc997772Tx373u9+dNTewcVzBAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQQGABoIHAAkADgQWABgILAA0EFgAaCCwANBBYAGggsADQwH6wtKmqWePf9ra3TR67e/fuWXPP8eyzz84a/9GPfnTy2BdffHHW3MDGcQULAA0EFgAaCCwANDhtYKvq0qr6RlU9UlXfr6oPLI5fUFX3V9UPF1939i8XAFbDeq5gX0xy2xjjzUn+fZI/raq3JLk9ydfGGJcn+driewAg6wjsGOPwGOM7i9tHkjyS5OIk1ye5Z3G3e5K8p2uRALBqXtHHdKpqV5Irk3wryYVjjMPJ8QhX1RtOMmZvkr3zlgkAq2Xdga2qHUm+kOTWMcav1/sZxzHGviT7Fv+OMWWRALBq1vUu4qo6K8fj+rkxxhcXh5+qqosWP78oydM9SwSA1bOedxFXkk8neWSM8bETfnRfkpsWt29K8uWNXx4ArKb1PEX89iR/nOR7VXVwcezDSe5M8jdV9SdJnkjyhz1LBIDVc9rAjjH+IcnJXnC9ZmOXAwBbg9/kBAANBBYAGtiujjZnn332rPG33nrr5LHbt2+fNfcLL7wweezdd989a+5Dhw7NGg9sDq5gAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoYD9Y2lx++eWzxr/1rW+dPPaMM+b93fEXv/jF5LGf/OQnZ8199OjRWeOBzcEVLAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGtqujzTXXXDNr/Pnnn79BK3nlfvnLX04ea7s5IHEFCwAtBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA/vBckpVNXns9u3bZ8393HPPTR577NixWXM//PDDS5sb2BpcwQJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0EBgAaCBwAJAA4EFgAYCCwANBBYAGggsADQQWABoUGOMV2+yqldvMpbuvPPOmzV+165dk8c+/vjjs+Y+cuTI5LG2q4Mt74Exxp7T3ckVLAA0EFgAaCCwANDgtIGtqkur6htV9UhVfb+qPrA4fkdV/bSqDi7+eXf/cgFgNZy5jvu8mOS2McZ3qurcJA9U1f2Ln/3lGOOuvuUBwGo6bWDHGIeTHF7cPlJVjyS5uHthALDKXtFrsFW1K8mVSb61OHRLVT1YVfuraucGrw0AVta6A1tVO5J8IcmtY4xfJ/lEksuS7M7xK9y7TzJub1UdqKoDG7BeAFgJ6wpsVZ2V43H93Bjji0kyxnhqjHF0jHEsyaeSXL3W2DHGvjHGnvV8KBcAtor1vIu4knw6ySNjjI+dcPyiE+723iQPbfzyAGA1reddxG9P8sdJvldVBxfHPpzkxqranWQkeSzJ+1tWCAAraD3vIv6HJLXGj/5245cDAFuD3+QEAA0EFgAaCCwANLAfLAC8MvaDBYBlEVgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGAgsADQQWABoILAA0EFgAaCCwANBAYAGggcACQAOBBYAGZ77K8/08yeOn+PnvLO7D+jln0zhv0zhvr5xzNs1mPm//ej13qjFG90LWraoOjDH2LHsdq8Q5m8Z5m8Z5e+Wcs2m2wnnzFDEANBBYAGiw2QK7b9kLWEHO2TTO2zTO2yvnnE2z8udtU70GCwBbxWa7ggWALWFTBLaqrq2qR6vqR1V1+7LXsyqq6rGq+l5VHayqA8tez2ZVVfur6umqeuiEYxdU1f1V9cPF153LXONmc5JzdkdV/XTxeDtYVe9e5ho3o6q6tKq+UVWPVNX3q+oDi+MebydxinO28o+3pT9FXFXbkvzfJO9McijJt5PcOMZ4eKkLWwFV9ViSPWOMzfpZsU2hqv5jkmeTfHaM8W8Wx/5bkmfGGHcu/lK3c4zxX5e5zs3kJOfsjiTPjjHuWubaNrOquijJRWOM71TVuUkeSPKeJP8lHm9rOsU5uyEr/njbDFewVyf50Rjjx2OM55P8dZLrl7wmtpAxxjeTPPOyw9cnuWdx+54c/wPNwknOGacxxjg8xvjO4vaRJI8kuTgebyd1inO28jZDYC9O8o8nfH8oW+TkvgpGkr+rqgeqau+yF7NiLhxjHE6O/wFP8oYlr2dV3FJVDy6eQvY05ylU1a4kVyb5Vjze1uVl5yxZ8cfbZghsrXHMW5vX5+1jjH+X5A+S/OniaT3o8okklyXZneRwkruXu5zNq6p2JPlCklvHGL9e9npWwRrnbOUfb5shsIeSXHrC95ckeXJJa1kpY4wnF1+fTvKlHH+6nfV5avHaz0uvAT295PVsemOMp8YYR8cYx5J8Kh5va6qqs3I8FJ8bY3xxcdjj7RTWOmdb4fG2GQL77SSXV9XvVtXZSf4oyX1LXtOmV1WvX7whIFX1+iS/n+ShU4/iBPcluWlx+6YkX17iWlbCS4FYeG883v6Zqqokn07yyBjjYyf8yOPtJE52zrbC423p7yJOksXbr/97km1J9o8xPrrkJW16VfV7OX7VmhzfFemvnLe1VdXnk7wjx3fneCrJnyf5n0n+Jsm/SvJEkj8cY3hTz8JJztk7cvzpupHksSTvf+l1RY6rqv+Q5O+TfC/JscXhD+f4a4oeb2s4xTm7MSv+eNsUgQWArWYzPEUMAFuOwAJAA4EFgAYCCwANBBYAGggsADQQWABoILAA0OD/Af2l7GE3ja6JAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Let's check if the reconstructions make sense\n",
    "# Set model to test mode\n",
    "VAE_MNIST.eval()\n",
    "    \n",
    "# Reconstructed\n",
    "train_data_plot = datasets.MNIST('../data', train=True, download=True,\n",
    "                   transform=transforms.ToTensor())\n",
    "\n",
    "train_loader_plot = torch.utils.data.DataLoader(train_data_plot,\n",
    "                                           batch_size=1, shuffle=False, **{})\n",
    "\n",
    "for batch_idx, (data, _) in enumerate(train_loader_plot):\n",
    "    x_hat, mu, logvar = VAE_MNIST(data)\n",
    "    plt.imshow(x_hat.view(1,28,28).squeeze().data.numpy(), cmap='gray')\n",
    "    plt.title('%i' % train_data.train_labels[batch_idx])\n",
    "    plt.show()\n",
    "    if batch_idx == 3:\n",
    "        break\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "7f559122b150f5f1228d6b66b62f462c",
     "grade": false,
     "grade_id": "cell-76649d51fdf133dc",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 2.8 Visualize latent space (20 points)\n",
    "Now, implement the auto-encoder now with a 2-dimensional latent space, and train again over the MNIST data. Make a visualization of the learned manifold by using a linearly spaced coordinate grid as input for the latent space, as seen in  https://arxiv.org/abs/1312.6114 Figure 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Epoch: 1 [0/60000 (0%)]\tLoss: 554.592590\n",
      "Train Epoch: 1 [12800/60000 (21%)]\tLoss: 209.523148\n",
      "Train Epoch: 1 [25600/60000 (43%)]\tLoss: 191.917328\n",
      "Train Epoch: 1 [38400/60000 (64%)]\tLoss: 182.557785\n",
      "Train Epoch: 1 [51200/60000 (85%)]\tLoss: 172.512238\n",
      "====> Epoch: 1 Average loss: 204.5454\n",
      "Train Epoch: 2 [0/60000 (0%)]\tLoss: 175.624649\n",
      "Train Epoch: 2 [12800/60000 (21%)]\tLoss: 175.830200\n",
      "Train Epoch: 2 [25600/60000 (43%)]\tLoss: 173.224213\n",
      "Train Epoch: 2 [38400/60000 (64%)]\tLoss: 179.612778\n",
      "Train Epoch: 2 [51200/60000 (85%)]\tLoss: 163.673264\n",
      "====> Epoch: 2 Average loss: 174.6481\n",
      "Train Epoch: 3 [0/60000 (0%)]\tLoss: 173.196152\n",
      "Train Epoch: 3 [12800/60000 (21%)]\tLoss: 170.953735\n",
      "Train Epoch: 3 [25600/60000 (43%)]\tLoss: 168.407883\n",
      "Train Epoch: 3 [38400/60000 (64%)]\tLoss: 172.898041\n",
      "Train Epoch: 3 [51200/60000 (85%)]\tLoss: 162.724609\n",
      "====> Epoch: 3 Average loss: 169.6187\n",
      "Train Epoch: 4 [0/60000 (0%)]\tLoss: 170.613419\n",
      "Train Epoch: 4 [12800/60000 (21%)]\tLoss: 171.693802\n",
      "Train Epoch: 4 [25600/60000 (43%)]\tLoss: 161.662735\n",
      "Train Epoch: 4 [38400/60000 (64%)]\tLoss: 173.998764\n",
      "Train Epoch: 4 [51200/60000 (85%)]\tLoss: 171.696518\n",
      "====> Epoch: 4 Average loss: 167.0996\n",
      "Train Epoch: 5 [0/60000 (0%)]\tLoss: 173.357925\n",
      "Train Epoch: 5 [12800/60000 (21%)]\tLoss: 166.839691\n",
      "Train Epoch: 5 [25600/60000 (43%)]\tLoss: 165.224075\n",
      "Train Epoch: 5 [38400/60000 (64%)]\tLoss: 164.336548\n",
      "Train Epoch: 5 [51200/60000 (85%)]\tLoss: 162.352249\n",
      "====> Epoch: 5 Average loss: 165.2963\n",
      "Train Epoch: 6 [0/60000 (0%)]\tLoss: 165.943710\n",
      "Train Epoch: 6 [12800/60000 (21%)]\tLoss: 159.297073\n",
      "Train Epoch: 6 [25600/60000 (43%)]\tLoss: 173.495605\n",
      "Train Epoch: 6 [38400/60000 (64%)]\tLoss: 166.114929\n",
      "Train Epoch: 6 [51200/60000 (85%)]\tLoss: 165.138397\n",
      "====> Epoch: 6 Average loss: 163.8681\n",
      "Train Epoch: 7 [0/60000 (0%)]\tLoss: 162.566574\n",
      "Train Epoch: 7 [12800/60000 (21%)]\tLoss: 157.133743\n",
      "Train Epoch: 7 [25600/60000 (43%)]\tLoss: 153.186249\n",
      "Train Epoch: 7 [38400/60000 (64%)]\tLoss: 163.335892\n",
      "Train Epoch: 7 [51200/60000 (85%)]\tLoss: 155.955399\n",
      "====> Epoch: 7 Average loss: 162.7057\n",
      "Train Epoch: 8 [0/60000 (0%)]\tLoss: 165.971115\n",
      "Train Epoch: 8 [12800/60000 (21%)]\tLoss: 159.792908\n",
      "Train Epoch: 8 [25600/60000 (43%)]\tLoss: 166.989883\n",
      "Train Epoch: 8 [38400/60000 (64%)]\tLoss: 154.912811\n",
      "Train Epoch: 8 [51200/60000 (85%)]\tLoss: 152.962387\n",
      "====> Epoch: 8 Average loss: 161.8131\n",
      "Train Epoch: 9 [0/60000 (0%)]\tLoss: 162.158325\n",
      "Train Epoch: 9 [12800/60000 (21%)]\tLoss: 163.304291\n",
      "Train Epoch: 9 [25600/60000 (43%)]\tLoss: 155.977036\n",
      "Train Epoch: 9 [38400/60000 (64%)]\tLoss: 165.142883\n",
      "Train Epoch: 9 [51200/60000 (85%)]\tLoss: 163.008133\n",
      "====> Epoch: 9 Average loss: 160.9316\n",
      "Train Epoch: 10 [0/60000 (0%)]\tLoss: 167.036621\n",
      "Train Epoch: 10 [12800/60000 (21%)]\tLoss: 160.614624\n",
      "Train Epoch: 10 [25600/60000 (43%)]\tLoss: 153.307800\n",
      "Train Epoch: 10 [38400/60000 (64%)]\tLoss: 156.478821\n",
      "Train Epoch: 10 [51200/60000 (85%)]\tLoss: 156.564377\n",
      "====> Epoch: 10 Average loss: 160.3051\n"
     ]
    }
   ],
   "source": [
    "fc1_dims = (784, 128)\n",
    "fc21_dims = (128, 2)\n",
    "fc22_dims = (128, 2)\n",
    "fc3_dims = (2, 128)\n",
    "fc4_dims = (128, 784)\n",
    "lr = 0.001\n",
    "batch_size = 128\n",
    "epochs = 10\n",
    "\n",
    "# Load data\n",
    "train_data = datasets.MNIST('../data', train=True, download=True,\n",
    "                   transform=transforms.ToTensor())\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(train_data,\n",
    "                                           batch_size=batch_size, shuffle=True, **{})\n",
    "\n",
    "# Init model\n",
    "VAE_MNIST = VAE(fc1_dims=fc1_dims, fc21_dims=fc21_dims, fc22_dims=fc22_dims, fc3_dims=fc3_dims, fc4_dims=fc4_dims)\n",
    "\n",
    "# Init optimizer\n",
    "optimizer = optim.Adam(VAE_MNIST.parameters(), lr=lr)\n",
    "\n",
    "# Train\n",
    "for epoch in range(1, epochs + 1):\n",
    "    train(epoch, train_loader, VAE_MNIST, optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "c879ffdb0d355349d7144a33d16ca93a",
     "grade": true,
     "grade_id": "cell-4a0af6d08d055bee",
     "locked": false,
     "points": 20,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# Display a 2D manifold of the digits\n",
    "grid_size = 20  # figure with 20x20 digits\n",
    "digit_size = 28\n",
    "figure = np.zeros((digit_size * grid_size, digit_size * grid_size))\n",
    "\n",
    "# Construct grid of latent variable values\n",
    "grid_x = norm.ppf(np.linspace(0, 1, grid_size))\n",
    "grid_y = norm.ppf(np.linspace(0, 1, grid_size))\n",
    "\n",
    "# # decode for each square in the grid\n",
    "for i, yi in enumerate(grid_x):\n",
    "    for j, xi in enumerate(grid_y):\n",
    "        z_sample = np.array([[xi, yi]])\n",
    "        z_sample = np.tile(z_sample, batch_size).reshape(batch_size, 2)\n",
    "        x_decoded = VAE_MNIST.decode(torch.FloatTensor(z_sample))\n",
    "        digit = x_decoded[0].reshape(digit_size, digit_size)\n",
    "        figure[i * digit_size: (i + 1) * digit_size,\n",
    "               j * digit_size: (j + 1) * digit_size] = digit.data.numpy()\n",
    "\n",
    "plt.figure(figsize=(10, 10))\n",
    "plt.axis('off')\n",
    "plt.imshow(figure, cmap='Greys')\n",
    "plt.show()  "
   ]
  },
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   "source": [
    "### 2.8 Amortized inference (10 points)\n",
    "What is amortized inference? Where in the code of Part 2 is it used? What is the benefit of using it?\n"
   ]
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    "Amortized inference refers to using past inferences as a base for future computations. In our case, we have that instead of approximating separate variables for each datapoint, we assume that latent variables can be predicted by a parametrized function of the data. This function is estimated using neural networks, so that latent variables can be obtained by passing new data points through the network.\n",
    "\n",
    "In our code, it is used in the encoder $q_{\\phi}(z | x)$, because the modeled distribution does not depend on local parameters, but is conditioned on the data and parametrized by global parameters $\\phi$. This has the advantage of allowing the generation (sampling) of new datapoints starting from the latent variables."
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