{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST Demo\n",
    "In this demo, we will show how to train and transform MNIST data. First, we start with imports and some utility functions that will be needed later in the demo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys, urllib, warnings, errno, logging, time\n",
    "import zipfile\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import fetch_mldata\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.utils import check_random_state\n",
    "\n",
    "# Add relative directories so that we have access to ddl library\n",
    "sys.path.append('.')\n",
    "sys.path.append('..')\n",
    "from ddl.base import CompositeDestructor\n",
    "from ddl.deep import DeepDestructorCV\n",
    "from ddl.independent import IndependentDensity, IndependentDestructor, IndependentInverseCdf\n",
    "from ddl.linear import BestLinearReconstructionDestructor\n",
    "from ddl.univariate import HistogramUnivariateDensity, ScipyUnivariateDensity\n",
    "\n",
    "# Setup logger for ddl so we can see debug output\n",
    "logging.basicConfig(stream=sys.stdout)\n",
    "logging.getLogger('ddl').setLevel(logging.DEBUG)\n",
    "\n",
    "_DOWNLOAD_DIR = 'data'  # Directory where MNIST data and MAF samples will be downloaded\n",
    "\n",
    "# Function to load (and download if necessary) the MNIST dataset\n",
    "def get_mnist_raw():\n",
    "    def _download_from_other_source():\n",
    "        # Attempt to download mnist data from another source\n",
    "        url = 'http://www.cs.cmu.edu/~dinouye/data/mnist-original.mat'\n",
    "        warnings.warn('Could not download from mldata.org, attempting '\n",
    "                      'to download from <%s>.' % url)\n",
    "        file_name = os.path.join(_DOWNLOAD_DIR, 'mldata/mnist-original.mat')\n",
    "        urllib.request.urlretrieve(url, file_name)\n",
    "    # Make directory if needed\n",
    "    try:\n",
    "        os.makedirs(_DOWNLOAD_DIR)\n",
    "    except OSError as exc:\n",
    "        if exc.errno == errno.EEXIST and os.path.isdir(_DOWNLOAD_DIR):\n",
    "            pass\n",
    "        else:\n",
    "            raise\n",
    "    try:\n",
    "        data_obj = fetch_mldata('MNIST original', data_home=_DOWNLOAD_DIR)\n",
    "    except (ConnectionResetError, urllib.error.HTTPError):\n",
    "        # Retry by downloading data from another source and then loading\n",
    "        _download_from_other_source()\n",
    "        data_obj = fetch_mldata('MNIST original', data_home=_DOWNLOAD_DIR)\n",
    "    return data_obj.data, data_obj.target\n",
    "        \n",
    "# Utility functions to transform between uniform and Gaussian supports\n",
    "def gaussian_to_uniform(Z):\n",
    "    return scipy.stats.norm.cdf(Z)\n",
    "\n",
    "def uniform_to_gaussian(U):\n",
    "    return scipy.stats.norm.ppf(U)\n",
    "\n",
    "# Image plotting function\n",
    "def plot_images(X, fig_height=4, title=None):\n",
    "    n_images = X.shape[0]\n",
    "    fig, axes = plt.subplots(1, n_images, figsize=(fig_height * n_images, fig_height))\n",
    "    for x, ax in zip(X, axes):\n",
    "        ax.imshow(-x.reshape(28, 28), cmap='gray')\n",
    "        ax.axis('off')\n",
    "    if title is not None:\n",
    "        fig.suptitle(title, fontsize=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and preprocess MNIST\n",
    "First, we will load and preprocess the MNIST dataset. Note that we will have to dequantize the MNIST dataset by adding uniform noise and then rescaling so that the values fall on the unit hypercube (or canonical domain)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. Attempting to load/fetch MNIST data via sklearn.datasets.fetch_mldata.\n",
      "  Done! MNIST data shape = (70000, 784), max value = 255\n",
      "2. Dequantizing and normalizing values between 0 and 1.\n",
      "  Done! After dequantization and normalization: min=4.04763e-11, max=1\n",
      "3. Setting up train, validation and test sizes.\n",
      "  Done! train = 56700, validation = 6300, test = 7000\n"
     ]
    }
   ],
   "source": [
    "# Load dataset\n",
    "print('1. Attempting to load/fetch MNIST data via sklearn.datasets.fetch_mldata.')\n",
    "X_raw, y = get_mnist_raw()\n",
    "print('  Done! MNIST data shape = %s, max value = %g' % (str(X_raw.shape), np.max(X_raw)))\n",
    "\n",
    "# Add uniform noise to dequantize the images\n",
    "print('2. Dequantizing and normalizing values between 0 and 1.')\n",
    "random_state = 0\n",
    "rng = check_random_state(random_state)\n",
    "X = (X_raw + rng.rand(*X_raw.shape)) / 256.0\n",
    "print('  Done! After dequantization and normalization: min=%g, max=%g' % (np.min(X), np.max(X)))\n",
    "\n",
    "# Create train and test splits of the data\n",
    "print('3. Setting up train, validation and test sizes.')\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1)\n",
    "n_test = X_test.shape[0]\n",
    "n_validation = int(X_train.shape[0] * 0.1)\n",
    "n_train = X_train.shape[0] - n_validation\n",
    "print('  Done! train = %d, validation = %d, test = %d' % (n_train, n_validation, n_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train deep copula model\n",
    "We will now define and train a deep copula model on the MNIST train dataset. First, we will define the deep copula destructor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DeepDestructorCV(canonical_destructor=CompositeDestructor(destructors=[IndependentDestructor(independent_density=IndependentDensity(univariate_estimators=HistogramUnivariateDensity(alpha=100, bins=40, bounds=[0, 1]))), IndependentInverseCdf(), BestLinearReconstructionDestructor(destructor=IndependentDestructor(indep...None, random_state=None,\n",
      "  svd_solver='auto', tol=0.0, whiten=False))],\n",
      "          random_state=None),\n",
      "         cv=[(array([    0,     1, ..., 56698, 56699]), array([56700, 56701, ..., 62998, 62999]))],\n",
      "         init_destructor=CompositeDestructor(destructors=[IndependentDestructor(independent_density=IndependentDensity(univariate_estimators=HistogramUnivariateDensity(alpha=1, bins=256, bounds=[0, 1])))],\n",
      "          random_state=None),\n",
      "         log_prefix='', max_canonical_destructors=None, n_extend=1,\n",
      "         random_state=0, refit=False, silent=False, stop_tol=0.001)\n"
     ]
    }
   ],
   "source": [
    "# Create deep copula destructor\n",
    "deep_copula_destructor = DeepDestructorCV(\n",
    "    init_destructor=CompositeDestructor([\n",
    "        IndependentDestructor(IndependentDensity(HistogramUnivariateDensity(\n",
    "            bins=256, bounds=[0, 1], alpha=1\n",
    "        )))\n",
    "    ]),\n",
    "    canonical_destructor=CompositeDestructor([\n",
    "        IndependentDestructor(IndependentDensity(HistogramUnivariateDensity(\n",
    "            bins=40, bounds=[0, 1], alpha=100\n",
    "        ))),\n",
    "        IndependentInverseCdf(),\n",
    "        BestLinearReconstructionDestructor(\n",
    "            linear_estimator=PCA(), destructor=IndependentDestructor(),\n",
    "            linear_projector_kwargs=dict(fit_bias=False),\n",
    "        )\n",
    "    ]),\n",
    "    # Setup copula destructor to just use a single train/validation split and do not refit\n",
    "    cv=[(np.arange(n_train), n_train + np.arange(n_validation))], refit=False,\n",
    "    stop_tol=0.001, random_state=random_state,\n",
    ")\n",
    "print(deep_copula_destructor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will actually train the deep copula destructor.  Note that this may take some time (on MacBook Pro, this took about 5 minutes or about 300 seconds)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DEBUG:ddl.deep:(CV sp=1, L=1) Scores: train=3429.15 val=3427.61\n",
      "DEBUG:ddl.deep:(CV sp=1, L=2) Scores: train=135.41 val=129.448\n",
      "DEBUG:ddl.deep:(CV sp=1, L=2) Relative diff=0.0377663\n",
      "DEBUG:ddl.deep:(CV sp=1, L=3) Scores: train=29.5752 val=29.1621\n",
      "DEBUG:ddl.deep:(CV sp=1, L=3) Relative diff=0.00819837\n",
      "DEBUG:ddl.deep:(CV sp=1, L=4) Scores: train=2.31424 val=2.09258\n",
      "DEBUG:ddl.deep:(CV sp=1, L=4) Relative diff=0.000583507\n",
      "DEBUG:ddl.deep:Fitting extra needed layers\n",
      "DEBUG:ddl.deep:Already done fitting cv=0 deep destructor\n",
      "Wall-clock time for training: 254.082 s\n"
     ]
    }
   ],
   "source": [
    "# Train and transform destructor\n",
    "start_time = time.time()\n",
    "deep_copula_destructor.fit(X_train)\n",
    "print('Wall-clock time for training: %g s' % (time.time() - start_time))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing MNIST samples to other methods\n",
    "In this part, we will compare MNIST samples from the models in the Masked Autoregressive Flow (MAF) paper and samples from our destructor.\n",
    "We have precomputed and saved samples from the MAF models so we just load them directly.\n",
    "\n",
    "Note that none of these models use the structure of images to learn their models (e.g. smoothness of images).\n",
    "Thus, all these models will not be state-of-the-art for image generation.\n",
    "In addition, these models optimize for test log-likelihood (i.e. the density task) rather sample generation as is the case for GANs or similar models.\n",
    "\n",
    "First we will download the MAF data samples if not already downloaded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAF data already downloaded\n"
     ]
    }
   ],
   "source": [
    "# Show samples from models in MAF paper\n",
    "# Attempt to download mnist data from another source\n",
    "maf_folder = os.path.join(_DOWNLOAD_DIR, 'model_samples')\n",
    "if not os.path.isdir(maf_folder):\n",
    "    url = 'http://www.cs.cmu.edu/~dinouye/data/maf_paper_model_samples.zip'\n",
    "    filename = os.path.join(_DOWNLOAD_DIR, 'maf_paper_model_samples.zip')\n",
    "    print('Downloading MAF data to %s' % os.path.abspath(filename))\n",
    "    urllib.request.urlretrieve(url, filename)\n",
    "\n",
    "    print('Extracting MAF data')\n",
    "    zip_ref = zipfile.ZipFile(filename, 'r')\n",
    "    zip_ref.extractall(_DOWNLOAD_DIR)\n",
    "    zip_ref.close()\n",
    "else:\n",
    "    print('MAF data already downloaded')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will train a transformation that will invert the logit preprocessing transformation that was applied to the pixel values in the MAF paper.\n",
    "We will use this transformation to project samples from the MAF models back to pixel space so that we can visualize the samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CompositeDestructor(destructors=[IndependentDestructor(independent_density=IndependentDensity(univariate_estimators=ScipyUnivariateDensity(scipy_fit_kwargs={'floc': 0, 'fscale': 1},\n",
       "            scipy_rv=<scipy.stats._continuous_distns.logistic_gen object at 0x180edf6b00>))), IndependentDestructor(independent_density=In...99998},\n",
       "            scipy_rv=<scipy.stats._continuous_distns.uniform_gen object at 0x180ee2f9b0>)))],\n",
       "          random_state=None)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define inverse logit destructor (copied from scripts/icml_2018_experiment.py)\n",
    "#  to invert samples from MAF paper where the samples are in logit space\n",
    "alpha = 1.0e-6\n",
    "mnist_inverse_logit = CompositeDestructor([\n",
    "    IndependentDestructor(IndependentDensity(ScipyUnivariateDensity(\n",
    "        scipy_rv=scipy.stats.logistic, scipy_fit_kwargs=dict(floc=0, fscale=1)\n",
    "    ))),\n",
    "    IndependentDestructor(IndependentDensity(ScipyUnivariateDensity(\n",
    "        scipy_rv=scipy.stats.uniform, scipy_fit_kwargs=dict(floc=alpha, fscale=1 - 2 * alpha)\n",
    "    )))\n",
    "])\n",
    "mnist_inverse_logit.fit(X_train[:1, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we show samples from the MAF models and from our trained destructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a101e3cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a59e46208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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rrZH9YovSmwcgXN/GiUjbXDKKyGAAvUNJi1V1u7V8JO8gAM8ieyqOVwCcrqqV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\n6NFmbOvWrWbMV8Y0qqurzVhJSUmqdVr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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a5a1e2630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a754b70f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a756fb198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a7592cb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a75b708d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a59fc7160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_images = 10\n",
    "for filename in os.listdir(maf_folder):\n",
    "    filepath = os.path.join(maf_folder, filename)\n",
    "    X_sample_logit = np.load(filepath)\n",
    "    with warnings.catch_warnings():\n",
    "        # Ignore data conversion warnings near boundary\n",
    "        warnings.simplefilter('ignore')\n",
    "        X_sample = mnist_inverse_logit.transform(X_sample_logit)\n",
    "    plot_images(X_sample[:n_images, :], title=filename)\n",
    "    \n",
    "# Show our samples\n",
    "with warnings.catch_warnings():\n",
    "    # Ignore n_features_ warning\n",
    "    warnings.simplefilter('ignore')\n",
    "    X_sample = deep_copula_destructor.sample(n_samples=n_images, random_state=0)\n",
    "plot_images(X_sample, title='Deep Copula Destructor')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploring the discovered MNIST latent space\n",
    "Now we will explore the discovered MNIST latent space.\n",
    "First, we project the data into the latent space.\n",
    "Because destructors project onto the unit hypercube, we label the transformed data U_train and U_test.\n",
    "We also project onto the unbounded space by applying the standard normal inverse CDF independently to each coordinate. \n",
    "This unbounded latent space is likely more suited for linear interpolation than the bounded unit hypercube latent space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Transform data into uniform latent space on unit hypercube\n",
    "U_train = deep_copula_destructor.transform(X_train)\n",
    "U_test = deep_copula_destructor.transform(X_test)\n",
    "\n",
    "# Project uniform data onto unbounded space via Gaussian inverse cdf\n",
    "Z_train = uniform_to_gaussian(U_train)\n",
    "Z_test = uniform_to_gaussian(U_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will interpolate between two random images.\n",
    "We compare linear interpolation in the raw pixel space and linear interpolation in the latent space.\n",
    "Notice that the latent space is more intuitive and generally includes darker pixels at all times rather than a mixed gray color as is the case for linear interpolation in the pixel space.\n",
    "Also, note that previous methods such as MADE or MAF do not have an explicit latent space representation so it is not possible to directly compare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a6832e2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a72ee2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a67c7ce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a59e2e0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show interpolations between two images in raw pixel space and latent space\n",
    "rng = check_random_state(1)\n",
    "perm = rng.permutation(U_train.shape[0])\n",
    "for i in range(2):\n",
    "    rand_ind = [perm[i*2], perm[i*2 + 1]]\n",
    "    weights = np.linspace(0, 1, n_images)\n",
    "    \n",
    "    # Linear interpolation in pixel space\n",
    "    X_interp_linear = np.outer(weights, X_train[rand_ind[0], :]) + np.outer(1 - weights, X_train[rand_ind[1], :])\n",
    "    \n",
    "    # Interpolation in latent Gaussian unbounded space\n",
    "    Z_interp = np.outer(weights, Z_train[rand_ind[0], :]) + np.outer(1 - weights, Z_train[rand_ind[1], :])\n",
    "    U_interp = gaussian_to_uniform(Z_interp)  # Transform back onto unit hypercube\n",
    "    X_interp = deep_copula_destructor.inverse_transform(U_interp)  # Transform to pixel space\n",
    "    \n",
    "    plot_images(X_interp_linear, title='Linear interpolation for set %d' % i)\n",
    "    plot_images(X_interp, title='Latent interpolation for set %d' % i)\n",
    "plt.show()"
   ]
  }
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