VAE_gaussian_mixture_prior.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "VAE_gaussian_mixture_prior.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "machine_shape": "hm",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/dauparas/tensorflow_examples/blob/master/VAE_gaussian_mixture_prior.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1acwEv77mZc3",
        "colab_type": "text"
      },
      "source": [
        "https://arxiv.org/abs/1606.05908\n",
        "\n",
        "http://ruishu.io/2016/12/25/gmvae/"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wQCl1jWjmszg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5749c7fc-cf4e-48db-8fe5-e5d4effc5039"
      },
      "source": [
        "from sklearn.cluster import KMeans\n",
        "from sklearn import metrics\n",
        "\n",
        "#Step 1: import dependencies\n",
        "from tensorflow.keras import layers\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import tensorflow as tf\n",
        "from keras import regularizers\n",
        "import time\n",
        "from __future__ import division\n",
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "tfd = tfp.distributions\n",
        "\n",
        "%matplotlib inline\n",
        "plt.style.use('dark_background')\n",
        "\n",
        "import pandas as pd"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2S5e8M9xptjP",
        "colab_type": "code",
        "outputId": "c0d79ec9-1d3f-4fe2-9cbb-d5f0086ac34a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "from sklearn.datasets.samples_generator import make_blobs\n",
        "X, Y = make_blobs(n_samples=500, centers=5, n_features=50,\n",
        "                  random_state=0)\n",
        "print(X.shape)"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(500, 50)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IrnFT_QLUmhM",
        "colab_type": "code",
        "outputId": "d2af0cca-7ea0-4e31-f1dc-280669c7f2a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "plt.scatter(X[:,0], X[:,1], c=Y, s=5.0, cmap='tab10');"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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F6AE/ti79QZIo/PRveA/UlEARHJ2GzJtiC+gMIDc3l9WrV+PxeIiMjKRNmzb1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\nIEmSNE79/7O9HNa5mYNIAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sg27qMUgtExD",
        "colab_type": "text"
      },
      "source": [
        "# Gaussian Mixture Prior parameters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xFZhcaW7nAHW",
        "colab_type": "text"
      },
      "source": [
        "Mixture prior with free parameters to be learnt:\n",
        "\n",
        "https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/vae.py"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zUr3rjGyM0RO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def z_given(latent_size, mixture_components):\n",
        "  if mixture_components == 1:\n",
        "    return tfd.MultivariateNormalDiag(\n",
        "        loc=tf.zeros([latent_size]),\n",
        "        scale_identity_multiplier=1.0)\n",
        "\n",
        "  loc = tf.compat.v1.get_variable(\n",
        "      name=\"loc\", shape=[mixture_components, latent_size])\n",
        "  raw_scale_diag = tf.compat.v1.get_variable(\n",
        "      name=\"raw_scale_diag\", shape=[mixture_components, latent_size])\n",
        "  mixture_logits = tf.compat.v1.get_variable(\n",
        "      name=\"mixture_logits\", shape=[mixture_components])\n",
        "\n",
        "  return tfd.MixtureSameFamily(\n",
        "      components_distribution=tfd.MultivariateNormalDiag(\n",
        "          loc=loc,\n",
        "          scale_diag=tf.nn.softplus(raw_scale_diag)),\n",
        "      mixture_distribution=tfd.Categorical(logits=mixture_logits),\n",
        "      name=\"prior\"), loc, mixture_logits\n",
        "\n",
        "def z_given_x(x, latent_size, reg):\n",
        "    act = tf.nn.leaky_relu\n",
        "    h = x\n",
        "    h = tf.layers.dense(h, 64, act, kernel_regularizer=reg)\n",
        "    h = tf.layers.dense(h, 32, act, kernel_regularizer=reg)\n",
        "    loc = tf.layers.dense(h,latent_size)\n",
        "    log_variance = tf.layers.dense(h, latent_size)\n",
        "    scale = tf.nn.softplus(log_variance)\n",
        "    #scale = 1.0*tf.ones(tf.shape(loc))\n",
        "    return tfd.MultivariateNormalDiag(loc, scale)\n",
        "\n",
        "\n",
        "def x_given_z(z, output_size, reg):\n",
        "    act = tf.nn.leaky_relu\n",
        "    h = z\n",
        "    h = tf.layers.dense(h, 32, act, kernel_regularizer=reg)\n",
        "    h = tf.layers.dense(h, 64, act, kernel_regularizer=reg)\n",
        "    loc = tf.layers.dense(h, output_size)\n",
        "    log_variance = tf.layers.dense(h, output_size)\n",
        "    #scale = tf.nn.softplus(log_variance)\n",
        "    scale = 0.01*tf.ones(tf.shape(loc))\n",
        "    return tfd.MultivariateNormalDiag(loc, scale)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T15BhYWqO8OH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Connect encoder and decoder and define the loss function\n",
        "tf.reset_default_graph()\n",
        "\n",
        "x = tf.placeholder(tf.float32, shape=[None, X.shape[1]], name='x')\n",
        "reg = regularizers.l1_l2(l1=0.0, l2=1e-7)\n",
        "latent_size = 2\n",
        "k = 5\n",
        "\n",
        "latent_prior, loc, mixture_logits = z_given(latent_size=latent_size, mixture_components=k)\n",
        "latent_posterior = z_given_x(x, latent_size, reg)\n",
        "\n",
        "latent_sampled = latent_posterior.sample()\n",
        "latent_mean = latent_posterior.mean()\n",
        "\n",
        "posterior = x_given_z(latent_sampled, X.shape[1], reg)\n",
        "\n",
        "posterior_sampled = posterior.sample()\n",
        "posterior_mean = posterior.mean()\n",
        "\n",
        "rec_loss = tf.losses.mean_squared_error(x, posterior_mean)\n",
        "kl = tf.reduce_mean(latent_posterior.log_prob(latent_sampled)- latent_prior.log_prob(latent_sampled)) #approximate KL\n",
        "beta=1.0\n",
        "kl_loss = beta*kl\n",
        "reg_loss = tf.losses.get_regularization_loss()\n",
        "loss = rec_loss + kl_loss + reg_loss\n",
        "\n",
        "optimizer = tf.train.AdamOptimizer(0.001)\n",
        "train_op = optimizer.minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mlBKHx70PVVH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Helper function\n",
        "def batch_generator(features, batch_size):\n",
        "  \"\"\"Function to create python generator to shuffle and split features into batches along the first dimension.\"\"\"\n",
        "  idx = np.arange(features.shape[0])\n",
        "  np.random.shuffle(idx)\n",
        "  for start_idx in range(0, features.shape[0], batch_size):\n",
        "    end_idx = min(start_idx + batch_size, features.shape[0])\n",
        "    part = idx[start_idx:end_idx]\n",
        "    yield features[part,:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-xaWqhUSPXph",
        "colab_type": "code",
        "outputId": "a6902c92-311c-4354-f175-d416a581ed67",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "n_epochs = 500\n",
        "batch_size = 32\n",
        "with tf.Session() as sess:\n",
        "  sess.run(tf.global_variables_initializer())\n",
        "  for i in range(n_epochs):\n",
        "    gen = batch_generator(X, batch_size) #create batch generator\n",
        "    for j in range(np.int(X.shape[0]/batch_size)):\n",
        "      x_batch = gen.__next__()\n",
        "      _ = sess.run(train_op, feed_dict={x: x_batch})\n",
        "    if (i+1)% 100 == 0 or i == 0:\n",
        "      latent_mean_, posterior_mean_, rec_loss_, kl_loss_, reg_loss_, loc_= sess.run([latent_mean, posterior_mean, rec_loss, kl_loss, reg_loss, loc], feed_dict ={x:X})\n",
        "      \n",
        "      plt.figure(1);\n",
        "      plt.figure(figsize=(4,2));\n",
        "      plt.scatter(latent_mean_[:,0],latent_mean_[:,1], c=Y, s=6.0, cmap='tab10');\n",
        "      plt.scatter(loc_[:,0], loc_[:,1], s=30.0, c='red')\n",
        "      plt.xlabel('z1');\n",
        "      plt.ylabel('z2');\n",
        "      plt.show();\n",
        "      \n",
        "      print('epoch: {0}, rec_loss: {1:.4f}, kl_loss: {2:.4f}, reg_loss: {3:.4f}'.format((i+1), rec_loss_, kl_loss_, reg_loss_) )"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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aQm7JDpSAHyEEqqbR5vEyID2F+vhYhM+DLgSKJEDXsRUM5LM2J4HdO7DfeCcW\nxYCSP4DG267BEGUgelw03govbXtlEh/6F5ZlbyPrGl5/gDi77biCkpOTg2m4KWgZBkhKC4f+OLQA\nK1sPW0pKBgkhC1z7XJQ/X46tj43GZY2ggTHWiDAIJJOE5tVxjL4AAglEDJmGt3wV9vxmvBVeWjcG\n0/jdxesx9+iPkGW0U1jvMGcORvO5qHzuFpDkczZkDCeY8ng8HjweD5mZmdxzzz388Y9/DD03ZMiQ\n07pwampqJ4Od8vLyTuY7h7jllltYv34969evJy4u7ojnf2oYJCkUgTlV6oxWah0xHWsuYDUZSXTY\nOx1TMsbPZxfVUj7Wg73tLSSTGSkyGmGxAuD99hu8K5ZSYo3Cr4PXH6CquRWH2US83ca0L97kYHQi\nZfFpBITE1tzBOC0R4PcF25ElhGxAigxOZzJ/l0nC9ATSbk4j6vrZqJnZbBgwhoAkU+9sp6KphV7x\nsRjkI+99+PDhzLliDv18/RB6cLRRv6iE+k+foG3rF9S8+TuEpAZHL5LA3+yn/MVyNG9w0bZ1fStV\nr1WF8k485R7a97Sj6zquEi+a+9CPpyB1XjQJMxJIuzUNe0HwNXNuXoToWPswJffG0mt4l9+LqAuu\nJ37m70mYcz+W3qPOaTGBLuahNDc3M2HCBP75z3/y0UcfMXfu3B+6XyHmz5/P/PnzgaAN3U+Z3olx\n3HjeUABeWrmB6pY25o0dRoTZxFvrtrK35sTJYHJqOjHPvkWpqxX9/ScR6ARUFbvJyKHlzRibheme\nTOzrjWzNamHYnjJs3gdYMfwi1j/2As7nHsdfuJnWv/2RLcBBmwWHxUy83cZlg/PRNA1nQwMNv5zH\nM9WVCKMJe6+R6F9+gnP+P0EIlH4DkROTaH0kmA2rRCkELDm0xP0SJU0gdJ1VQy9kZ3Y+0xc8yt2T\nz0cIQYOznUe/XNnpnnr06IEiK+S25pJVo5C38RNyljWxVvua5xybKcsCS08Htr42JGNwZNKytgVz\n1hCix92Er6aYhkX/DNXkoEPlKyDZBd4D+zD1+Au2vufj2rOarHt9CFlCV3WUuOD6inBE0ilWfxLx\nCnPPQUjG4HqOpecgnJs+7frJZyFdEhQhBKqqcscdd3D99dezcuVKoqOjT+vCFRUV9OjRI/R3Wlpa\nl7ex/KlyYd9eKB3720zom83BxmaSIiPQjCZSfvsnats8tD3zKFr10TfcAlDyB4AAd1wSX4+YxOBl\nH7KrqoaSusObZd0xfjQOjwnhFSRsMiMQCLxMWP0Z2+b9CeUvjxCor6XhhtmgBnD7A2SkWMnLSuLb\nijJkn2DZ7mICruDwX2930vrp+eg5AAAgAElEQVTX/+7UD+/ab8iddQ23JyYzYOc2tvxpH/MfvBGX\nr4iAIR25rIoksQlH6xeMLq1iyB4PNTHRrO2diVkx4PEHEMZgtfKqVavI6ZNDTHs7tz37FiZvAKMG\nAyW4rrCNWX/OYa/WG01pRtIaUdtVUCF+xu+RjGYMUYl4Dm7F0mMrphQTbdtSiDzvd6BrOAuX0rTk\nGbxl2wGofCWKpKuS8FR4aFnTghSfSOwL7+FrA3lPI85VC3Hv67qxU8vqd4i/9LfouoazcAnmjAF4\nK3ahB3xdbuNsokuC8swzz4T+/corr1BYWMgdd9xxWhdev349OTk59OzZk4qKCq666iquueaa02rz\nXCM12oHb56exvWv1HHtq6unREfHYXVOH2+dH1TTWDBjLnn4jMMkSckIyjbd3HkEKIDsxDo/fT8X6\n1egeN7psYFWzi88+WXrEdaxGQygtQOjBBjTAY7KgSRIYzMjxSchx8dzaN4OUpEgUJAyaRCBa4y+f\nLsXrDTC0Zxour4+dVUdueZE74wqW3XYNVrcbo6oysEblyrt+x6wH8qiONVK5ZQAxGStZ+IcSFH8A\nRYP45lZ6HyjnwYBKc4Gd9J+ngwiGih968CGeipQxuVUOxR+NGuDVuOnzOu6/ZSRN3v9AXv46zcuD\nIxzd70Y3GEEHa04L8ZMTEIogYqCGuyzou2LNHkbTksOf/+ZVzTSvOmzQZBo1EGG0oCcbCCTZ8b5z\nYnf97+Leu4ayx69EssWQcsPjIEkEmqupeukuziH/+BBdEpTnnnuu09+bNm1i3rx5p3VhVVW58847\n+eKLL5BlmRdffPGkqkrPdab278Po7AwEgpdXbWBPF6YrX+0qpqyxBQhGawQQUDVcOSNQ9Y5v/vc2\n6Zo1uB8jsoIjQVXTeG9DIZuvmoIUFY1WV8PReGvtVi4f1h9ZEqzaV8qY7AwwmSlLSMXubMVli0A1\nGMiYcik9Wg7QblUxuIJrG0IX9PlbLqqiM25NAtHNCh9u3sG6/cHtM5SBQ4m890HueG1+h5gEpxlG\nAK/KvM8q+OvcTCj8itu/acPoD2DoyE9TtGDG6W+Bf1wSh2QMXjNuShxtW9sY3HJYTA5hVKGgxI3B\neRDLXh9Kno3o0ck0LtGoefs+HCNm46vehxJVAiKpI1vWg+b3IGQjuqYRMXQmktmGc/NnqO2d9+nx\nb9kQFF1VQzR6MUan4+Hb476PhshEhMmGvzYoPjGTf441dzRCkhCyghKXjmSyonmP3BWxu5DtMThG\nXkGgtY629QtBP7JE4VQ4o7U8ixYtCkWOfmoM7JHckUEKBWlJXRIUoNM6iQ6sP1COeOIRImQzUnQM\nbf98iJ5x0eQlJ3CwoZlhmWmhxVdZkuiTFM/mg5VodTUIYzAsyve8gLZVVLOtopq4Xg6uye1Pi9vD\neyvWYzSsJqq6EjE1AiE8eGZfgf+1FzC2eChJbyepycT29BZ81uAv66Z8CxWZv6T9egXl/t8SKNmL\n41f3IcclMGT3ppCYHMKoQr8SN6oSjbVfPJmffB0Sk9AxwHCgbWsb1l5W0KFtW7BIbx0wqOOYQ/hk\nKMyyoHsiQWj462aiufKIHv8SjV/toeHTfwTbTcnEvd+ObG+h6rVyrHlbsPQahiEqkejxN4KuY80Z\nRdVLd3bqj9bUgOuBh4mcfAN6XRPtO74OPWfOGkzs5J8jDEYaFj1OoLUec3o/os6/HtBp2/gJQjJg\nyx93OHQd8OMp3dpZTGQl+IXvRtOm+Fn3YUzoha4FIOCjbdPxjau6Srg48AyxpuQgE/Ny0HXYVHp6\na0e6q53Wv94LQKzdym2TL8AgS/gCAVRNQxICSQj8qsrq4mBKfuK4WDJmp9Jm8FPyYAneci9DMlK5\nfFh/2j0+XmvdzvihOaSVO4h0eXgrwkZMbT0rC5fy+qAEqmMNCM3Fi5ffSez8fzB1nwEtQkOVdOSA\nQJV19uVMwmuLASER8/enEJqO2VmEpeJXFKW10X+vQP7Ofjw+g4H1/S6hKeq3xA65he27rfSt8KB8\n53vkA3YV2EmcnYhzh5P6z+tx7Q6mwT8MXAvYCYqKTwa3SeKlKXEg/KArgEB1ZaL7YoNrKQRHDIlX\n/R01oKC2SMReCqqzETQNJAkQCFlGic/AkjMS997gCESyRRE5+mo0VzPl/zMH/B4OTVOUuAziZ/0B\nIQWnj3HT/gskKfi3HPza2fqODWUmA6Cp1Lz5O3xVu0P3a8u/kNhL7kIP+Kh+83ehUc3pIlkcCFkG\nNCTr0beQPRXCgnKG+GpXMVsOVuINqLR7u28B7qphA5A7CtskIfHyqvWkRDkobWiivKkFv6qR6LDz\ni6ThyKsEO9NbaR7XTNXrVcwclI9BknBYTIyKT8eARITLzXVffIMhoGLQdTIK3Vz2hyZm/yWbshSB\ny2KjyRvAHmFCDkgM3SrjrK+idgjI/krQ/YACQkI3CEzut5HVel6YGsu01Y1YvRqyruOXwGUy8NSl\nN4AnKBAvXhLH1DXNWFxaUCCAdglevToJyShhz7d3qrkpB8YOvZT/8roZ0raKwl5mXpoSR3WsmUBV\nNVrAC0gI4af08a1EjY3Cmm2lbWcKwmRGaEE5EIDsiMFdsR21tgJr7hhkS9BNLnL0VSFBib/0Hkyp\nfYOFf5pG65p3Qn0xRCXBd/Yl0nUNWQmG3HVdQ1cDtG39AiEkIkddAUKi6asXOokJQOSYq4MCJElE\nDJ5K4+dPdMvnpOGTR4i5+OeobfXBKU83ERaUM4DJYGBozzSaXW52VB59HeNkMMoyqh5Mm09w2EMf\n4oONzeypqT9iOlWQloRBE0gIcssiWLg3OLw2KYc/DmpNgF5uGyOKdqIE1NBIQtHA6tG4a0Ezz83q\nz6ryrbQuX8rqAX0ZmZvFqvxR7DV4sYulWFo/Q1ZdOKMvR5cjQNPQpUh0ZKpjFX51xwhu/3c5CU3N\nfNPfwFNzJlKVruBoK2T4zig2ZTYyMsvCz4vdjI4ysK2Hmb+pOsQYIdBRBChB1NgojPFGoi/IpL3i\nRv4sFITxCoyxK/E7UjGxAhiDZGqiZe23tG1ahDVDJXFmCpJZwt6/nbZ6gdQSvEcdQAjMWQNwO9to\nWfM2Uef9DNA71eJIlojQaEO2RHR6jd37N+Gt2IUpNQ9vZRFtmz4mburdiI7pi+Zx4tz8GZrHiWv3\nKjSfBz3gJWLwNHz1pXgPBjNkPQe3IduiQIjQY92Bt2IXVS/c3m3tHSIsKGeAm84bSnpMFDo676zf\nxtayU7cCHNYzjdlDCwioGk8vW8MXO/YwY2AeLp+ft9d958MvBD1jo2n2eEiLcoAOPl2lqLGe1g2t\npEY50HQdAWi6jqvcjZajk9TQ3GlaAkFRGbbby+4NG9jcpHHpyEG4/X7mx/XGM3YquiTQq/IYuvpp\n4gJVvDdbIUCAAVtX46hNZGhpCy1mwdOfLmX15clIw3t0DA22E1/2G2asTCbCFUGsU+GRHTt45L+z\neKpXMFdDqFD5aiWSVcJV4mL0bT24eVkj/Te3sq1lL88MWUYZk9B9yXiq5qDLdRgpJdAyAnQjjqGz\nMN12M9raR9HZEWwTDV+KhLlNDVUxo4Pk0bBkDcVbth3njqXI9rhOdTwNnz5KzCV3oblaaVnzbuc3\nRvVT+3bnUHll7QFS5z0VTOhTzJjS8nDvW4e/IZjgmTzvqY6RjUbte/fjLdtO4xdP4t63Ds3dhrfi\n7A9ahAXlDJDgsKMYZFRNOyJDtcsIgeO39zO5bjcGZwsGSWJkr3QWbNzOt8UH0b4nAjePHUZGbHSw\norhjnq+rGpJbJ8Zm4bLB/TB0VBtLQnB+70x2VtZwMD6W+JY2DNrh1VFVCCpjonBqMNPfSM/UJDRd\no7pXL/bKErokI1viKGiMRhPtzHvjLxh1E25XGzahIBtkIpwBBvZMpWZg0B5B13RUt8rg8ljs7uDH\n0lvrC9oQ+LWOWxboQkcYBfZ+dgZOiGXBn/Zh9WooKvQ56GHamn8x9XYD5coIdF8r7Tu/xtzb3LF+\nAgKBaVMTngm/pvnt2VizrdS8W4Mc8xbmEZeH1jMO7QmErmErmIQxPugHZErsRcXTNwDgqymm+uVf\ndPktUxwJQZOmDm8UX1WwENIx8nIsmYNRYlIRkozm96LE9gjmvuga7n2nZ6z9/5PTy+EOc0p8uHkH\nHn+ABqeLb0sOnlIbhpy+mM6fyMG0bHwGBZ+qsa82WK7fSUwkCfvt/8Xa/7yPqsxchAiOVgRgNBjI\nS0nkmhGDaPAFaDB50AWh7S3yUpK4d9Z1tFss+DqG9gEh8Coy/5wwnmeVOCQhhTJD0xZ/QGJdJdHN\n9Vy0YiFSR0qcECrbsmppT9JwqX78gWBBnuQHXdXRvBqaT6OubCzfDLuIl6epvH1eGq/vCE7Vyp8t\nx1PqQdd0vLVeXPtc2HJt3PR5fUhMABQVLF6Nm3d8i6n38zjX/xbfji20x88GyRX871BuR/EKokdF\nY0oyYc224t69Gj3gDdX66H4f7j1raVn1Fkpsaug1kU9jATN26q8QBgV0nbZNwRC0Ob0/kaOuxJxe\nEBSbgI9AUyWuXStO3OBZSHiEcgbYUlbFltOY5gBojfUIAV+MmcaelCwaPlrAgagk+E67s4f0Y2RW\nOq62A7xhuhihaQghWJuYhdVqJdLThsPZytrxl3Mwtz+yt4bLP36StIZDkQedicVreX3CaPJLK+ld\nVkFVtIMPR4/hi8uux970Jsu36Yxa10C708vWskquffdJTIoBFZ1mo582xc/q4Y24LRpFPQXy+21M\nNfTCblSY0KsXr/xrK7WJXtqL3MS98AC2ur8idB9eRy2mhx+G2bMINAcovv+wIZFQguHughJXpwgQ\nBEPP/UuaabLdS9OKaUTefy/C0YA95x+AwNuQT/VyGdv+xUgXxwAQMz6G2oVFVDxzM/YBk4gYeimB\n5mrqP3sU3efGMWwmurXDQkEIzFlD8ZRsOPn3zNWMbo1C1wKorUdZO9M1yh6/6pzNkoWwoJxT9IqP\n4dqRg/H4/Tz/zToaf30LpqGj2dVvAMY7fkeUELT+7Y94ly/BZJAZmRXcM9jqdXPZ568T3dqIJAQD\nWqp5asY9SLoe/FUUEggJ1ZTEwmm/4bJFjxHf5MHkk1CEhMdsZMWAPNb3yUTSdXQDxNbcx6hCmcQm\nO+tH17PkgS3cfP5wjAaZFpufb/s2ULS3hppFteScl4NAoAqNvftquWTEUFRNRXjdxPnM7F4WjNSo\nDc0QGl0JsEYQ9/qHtD3xMN7Vh7fB0P065c+Ws62nhT4HvxdWliU29y1AV4ODb3/xXox9qxCSHwCD\ncT3OT4rQ+9iIHR/VUQBoI27G73Fu+Qx7vwkYrFHIJhuO4Zfh2rUCYbQcDu3KBiJHzsFTsgH74GlY\ns0fQtuFD3N8RGEN0CglX/BnJaKHuw7+FFlNr3/8LjhGzCDRV49y6GAguurasfhtz5mBa175/TosJ\nhKc85xSXDe6Hw2Iizm7jwr7ZBIp20P76fCw9MoKO80YTSr9BAPhUNWQHCR1p8yLott4QGYsuG1AN\nCqosI2tq8IssBF5LJF+NvADVp1Lb5sSvqgQEfDtwNE2OGFwmC4bWJjIr/GRX2IhpMzJxdzKz5swk\nLSURIQTLB9ZRFe/FMSaWtDtz0ZDRMaAKG8qU63n+Z7/lqevuocgYwabS8tD9NTz8JK2O6/CYB9ES\nfTtINuTEFCL/8NfQMZZeFhzDHTi3O3kYcJkk/MHyJnwytCsKjxUMpvmPvwbA9cbzNH5QiBYQaH6N\nxq+DNUvtRe3svW8v5c/70OX/xtZnDAlz7kfze0NhYM3bTqCtHt3vQw/4OzxTPLj3b8KY3JvocTdg\nyRxE/GX3IozWUB8jR12BITIR2RpFzIRbQ4+rzgaals7vSCI7PC1tXfs+tW/fe4QL3LlIeIRyDlHv\nbCfWbkXXob4tGOrNT03iZx8/hy4k3p9yHfsHDcNxz19offRBnv56DVcOG0B773w+mnwNfXZvxl1d\nxd6JlwWFRlWR/D5mLnqdwr5D2JuVx4Ad67E421h23iy2lZTieOM5brxgJGlV5TicLciqiiTLJNcd\n3mM4YDCy9rp72OLzcP17jweDJAJAxZIEoKMLhebkP2OKt4Ki4NM03rcm4PYfzpaNvPsPeCN74hPj\ngpmhug90GUkP+qDYC+yk35keHFXscVH0RhWX3ZfFvMUN9NvnYlWDn/91eyl/4Dvuf5pGyztf0vax\nhGyV0f0xRJ1/Pb6afbh2r8KYkhMM5QLIBlrWvIc1a3AwJX3jxygxqdS+fz9KdAqaFkB3t+Ep3Yop\ntU/nUpvvVBv76suw+n3oQuBvKOenRFhQziHeXLuFkVnpuH1+NhwIflAn9OvdEYHRGL5lJTE9+9DL\n38hnl86i9P23qGxuJd7rJqWmjMq6eqoy81BkAwLwFm6m5b5f8oLqR4tcwNTcTIalJYIQFPYZws4p\nsxiweyNWCXJLizr1JbPUyuIduxmQm83yK2/Gbwz6yH4zyI7foKFJkUhay+FKfl3H4ClFYEXVchAq\n+DZ2jl7o7e0dh+rgbsfmfAfVmI7zjeBGYZYsS9D4SJawZFnw1fgodWv89Zpk0KH4gWK85V6sfS8g\ndsov0Fwt1Lz5OwItNWguDc2lkXr7w8i2KHTVj+ZtR3d33ltHKAoNix4HIPqi24gYeBGGyK20fvsJ\n9Z9uDh3nrSjCtX8Ttt4jQchYeg7EtXsVAG3rPkBrb0IyWXFuO3f8YLuDsKCcQ/gC6hF+sXsqqkmK\njgJJoiw5g9EbvsLudnIVgoeBOLuN1KZaZi96jc2lFezvNRhDehZIgkDxbnSfD33cRCJ/8yeSP38D\nQ2UwtTu+di0RTeXs87gZYZWD2aOyhKbp7KysYdnuYKHiqtIKUq/5BbLfQ3RDKe3GvThtKm3mK1Ck\nGqzOTwENVY5CajZj8z6CFtEb4WuiZssG5IigE72/3k/zH36F476/IkxmWh68lyZfDVJCEqbL/hP7\nHU00L3ya2Akqsk2m7sOgEZEl04KQBFoAbDk2vOVeosffhGQwIiJiiZpwC4GmSkzJvWnbuhjZ6kBI\nMnrAjxwRR/v2r/DXHUCJ70mgtTZk32iITCRi0BTMqR+gOLZivkwFNY76zzuSBCUZW/ZwhJBABseo\nK0KCAjrtO746rfdaskWReOWDGBxxNHz+L1xF35xWe/+/CAvKOc7n2/dQUt+EHh1LWmk1lrS4YI5Y\ne3CasHDzdn42ajDegMriHXtxrduK1tKM4+f3YJlyGeaCLOSYGDCaWD76EqI/fhFZtLEptxZT+0Gq\nRAWPL/ERY7WQHhuFJAQufwBzR2Gjz+Ol7qGfMXHmKEYUaUAMq7M1VjQWMix7AEb1BhojjUxd9gWv\nNT6LNMuPaNmOv8nPmFv6kuvoxa7svuzZsJaGF1bQ/OvDaw4aEP2nB1D69INAAL3dSdEvng56vQZ0\nLL2G46pJwppcCoqZQO5MWPYigcYKZHsMQkhYs0eApiJkA6a0fDwHtqDEZ+CvKQmGZnWNqpd+TjD2\nfXgOY4hORtdUZHNFcEFXgDnz8G4CwmAEEVyC1HUdX/W+475PwmjFmjsaf/1BfFV7jnssQMSAi4N5\nKbKBmIm3hQXlp0rP2GgsRoWi6lq+l1t2TISAPkkJuP1+DtQ3HfM4ySyRdE0SBruBqjer8NcHIxd7\nquuguo79skTcoHyibVY+2hzMAi1taOZ/Pun8aylFRoMsI5lMkDMIa9MCXFovaqPiedSYRGreNhS7\nAkLBPOMaqja/wfj0FAb0SA4lvwU0jee/WU9JXSPGaMiu8GDQgl+4pBWCEY3fMK6+GoGgxJbJwgnX\n0RBhp+3uGdjz7fS6JJXpbWkYWnRyKvfw3FV/pGnhVWjNTRiHjkSrqyGwfx/CaKQjeQZhNoNOUEyy\nRxA3/TeozUbaNDfeERnI+UXAizQueZbkGx4HOViYp0tyx+ssUOIzqHjyuqO8up3fLM/B7XgrdmKI\nmIwl9TU0t5f6Tw6XMCjRKajtTci2KLxVe2lcfPxN0hOv/l+UmFQQUPvOH0+Y9epvLA863+sa/qZj\nG2adbYQFpRsZlJ7C5UML0HXYfLCC9zdu79J5lw3KZ0hGGkIEN8DacODo1cfxl8YTNSoKIQtkh8z+\n/+k8/QmoQb+TE+H9Zgn2624BWWBuWYLRvwcXOsKgYJt9DaV3vEbq7y9Ei80jkHIp9nkxxBR+jSLL\nwUxaSQJNJz7CRkldI9qEe9ghryR2qwqqzprig/TvkYwBHYGOw99KlR6H7m5ETxmKuPYX+P070UXQ\n2UwABq+L6PExGEfMJtD3WoSs0PK//03LX+/D8ct70ZobaX9tPkgyjmEzMWcOAUlGIKG32jCubKJ5\n8StAcKe/5tVvEXXetcEpia6h6wJdU/Ec2IwS2wN/QxnCYiXqoX9h6NmLtucex/PpB4dfJC1wROr8\nd4md+msMEbHoagBv+Y7D9pHHwBifgZANaH4vxsSsEwqKq2gluhrAEJmIs/DUtnY9E4QFpRvJTojF\n2DEVyE7ouqF2dkJcqDAvOyHumILyXa/Sk9poTTYQ8Yvfo+Tm4XzuMdTamo4fZBXFtw9/qxE9WkWY\nAFlGyAbMhlJEWzGaiMQXF8/y639N4uevY/W40YEGycDWsmpM4ydjHDWRjWISRfkt6AE/9T1XUvX0\n/5GRnoUiyyyPH4vmUHC98z5Rf/4/hMlMpT+Nbek7yK7wszV3GL4D/yJxkgFM62nTC/CaRhP5x4dp\nfegPNP3q5tCtOEZfReTIy4PrIKofXe8YhbQ4EdXBBVZDbh6m/74LX0MAsbGEtm8+wLVzGbFT78ba\nezTW3DHUvv9npIIclJy+CLMZx133dBaUE6B529FVFV1T0TzH394DoHnlm0SNnYvqbKS9i9OXQ1XN\n5xJhQelGVheXMqBHCoos8eXOvSc+oYMvd+zlyhEDUFWNVXsPHPO4ug/rMDgMwSnP6yfOtJVTemC+\n8GKExYJ5wiVIFguRf36EhpuvCIqTMNIa9Z/U3zUT65yemEacR/vbLxM1XEEILwKBtf4dWo3/QX1y\nBkY1gBAQkGR2DrsQ4TGhtx/+MjltjmAi3QWjUXxpvNy6Fm/UbRjOy4NoM7Y516J7vaAY0QPwwTd1\neFd/DfybrD9mISVY0XUfqpISFExZxnr5XDxLDxfkybbo4M56siE4yjBaQ5W+/trgiC14r1b0NAhY\nUnE+HjQPMqX2QTIGtzyNn/l76tfOD9Y1BQKoR3GvUxKyELLhqGse9R8+ROSYa1Dbm2hdd+Ly/9Zv\n36V17fvd5ox2thIWlG6koqmVP/57MbIk8Ktd/+BsLquksLIaXddRtWMvvGgejYr5XTRjkmRinnwV\nYY8ANdBRlKaBz4tWXUnLg/divmgqnsUfo9XV4Hz6EZxPPwKAa6iDmHEx6AYFr9oD78qvMOYV0OCI\nJbalHoSgPjYJKSYO9ycL8F4wEeOQEQijCR1wtLyMsb8BNAdtBz7Bq12AYXs9hgo37ds+RhuSgb9o\nO97VXyOnpWMafQG1qwpJi/cgHLFosqMjTyaAZ0Xn9Z/WNe9gTMxCNkfQsOhx/E1VmHv0w1dTjOoM\n1jL51q7EOm0Ouq7hXfV16Ny2DR8Sed61wbocxYISsNPywO8wZGbjWdzZsczWfxIxFwUXiFtWv0Pr\nt+9951mBMFppWvbCcbcePYIfuZhAWFC6HU3X0VQdRDBvItAcwN/gP+F5gZMQoK4gjEaEzR7cfMrn\nxbtiCcJoov2NFwHwrlyGd+X/a+/uo6Mq7wSOf+/ceU1m8k6IJBB5U6GARgXRbKtLVZZW1LbaVdot\nCxblbNEVjy8Q21V2PW7E3UPp6rJWV4u7FrDiC9qSmhZ2EWMQJGBgE0hiQhI0hCQkmWTe7sx99o+B\nYAyBvNzhmuH5nPM7ZzL3zs3vDic/7n2e5z7P9jN+tnNPJ8d/8F2c35hI0JmHPe9DWu+5k/+wWrli\n/Fi6b19A3YlOfG9tAKDjyYcBsE64BPvV15BwyT4cEyzRhtSuTpy7WsBiRVGceKbciHfnH1CORdsw\n0ta9huJwga5TtfhOPPffhS3DBZEg3etfwLfxN71yi3S1cey/H+n13lefxg19sovWe/8aS3Iq2sH9\nPe93lGwk4dJ8rKljAEGouY5QQzmhj/o+iJdwybVYbM6e118uKKO+/zjOi/MQ4SBfvHI/EW9rn88r\ndheKakP3d57xO45XsqDESPZPs0m6KnoLULu6Fn/NIP4nO4fc9FR+OHMGnf4A//XRXnyhvgVLBPx0\nvfzvJC5YRKi8LLr+TfjsDYdfFuxMQXFcGe1VCQWJfN5IF7Czvg7+98xtAOHPDhP+7DBHM2xk/202\nuqbTuT+PpKuV07Poq3aSrpqPEBHa976OYneiWFUIK6R8dylt//QwOYV340z1ogQ+wDeULwiINNYT\naez9JLfqTqf57adxjbsc9+VzGX330/gqd9Ky5Zk+n/fu/T2u3MsB6Nz9zukNFhXXpGt6FpB35l5B\n94HeKwc4xk4j885VKIqF1uJ1dH/6/hDPYuSRBSVGkvKSUJ0qQhe4v+E2tKDcfc3lZLgTSU9M4PpL\nJ7C1/NAZ9/NtfAXfxlcGdEx13HgUlwsRDKA4nHifewYRCoKi0PXrXw4qP61Fo+5f6gCwZgiSrluC\niIBwgGjvjrZ56BZU3FB5BKZOwNISQPVG8Ex14LbvQo2ojJo/iuN/OI4InbwNtFoHVRS/zDPze6Te\nsAiAjtLfYUvPQVEUXJNmYU0dQ/grXbOBz/bQ+PxPQLH0vsrQIwQbDmDPmgRC9KzX0+t3XTEPiy36\naELSzNtlQZGG78QHJ0j7yzSELujca+xlb3cwRGqCC10IvIHgkI5hn5VP8s//Gd3biW/Tq3iWLkdY\nLNFlJLQwXZvW4/3Xfxx2rsIOgfw0FNWOHg7gX/tbUqbMR/e14/1kC8q+rWTe+SSqO41gx3FCzdF1\nknVNJ9IdQWgCxZ3EqDJwWh8AAAsPSURBVFe2oKQlEfqwlBP/MPipC1Py70I5Ofu/e8ZNAOhaABHR\n+iyNcUp/vTfHNv0ce9Zkwu1foPs6+mz3Ve/CNfkaEGJETY5kBFlQYqRpQxOtf2ol0h1B9xnbPvKb\nDz9hzmUT6fAHKKk+gi3NRu5DuahulcYXGumuOPd6Lp6fPYLF7UFJSCDhBz9CcTpP90pbbTivvxHf\nqy8MO9dI01G0qgpsl01Db2mm64M36Sr+ba99LC4PFruLxMu+SbC+nLpnS3FNdNHxcQcI8Mz/CUqy\nBxQFe/5slEQPotsLTidJDz+BelEO3n8rJFx5sN88wp3HsWVEnwjWWhpoe/95nOOm46/dO7iGVQA9\nQujzyn43+yp2oLU2YLEnRMeoXEBMKSirV69m/vz5hEIhampqWLRoER0dfSv9SKcdP3dj7FB4A0He\n2Xd6YNTo72TguMiBoiqMWTiGqhXn7rKONH6GmpUFuk5w907UzO9Hl4xQFNAFvs0bjElW1zmx/KdY\n0keht7WeeW2Zr4yp8VX78FWfbj3RqitxAYR1COl4ps+ls/QNEm6/C+dfzEGx20n5xTO0/OiWrx4Y\n18SZ6CE/xzYUkPZXyxBaiLb3n0eE/HSdZQSqxZVExq2PorqSaN26ltCxml7b7aMngkXtdxj9qS7s\nC40pBaW4uJiVK1cSiUQoLCxk5cqVrFixwoxU4kKwOYgIC4QuCDX3naDHPtqO53IP3ZXdBOqj6w2n\nKy8h2o+ghL10vb+R46/+GsVmR2ghFKsNva3/hccsriTUxFS0liMDS1AI9Ja+y5ECOK67Ae3aHKjz\nEagoo/v//qfPPv7df8L5n6+TMPvbqK1hHN/8Gzo/fhsRDERHweqR6OuvSP32kpO3Nwon/vwiLW89\n3Wef/iRfdxfOsdNQVCvp31nea4Ev94y5pN64BAS0l2zAu2vzgI8b70wrKKeUlpZyxx13mJFG3Ggr\nbkMEBKpHpW1bW69tFqeFiU9MRLFFFyiuWlmF1qbhzFRQ/H9GD+o4s534Drf1PM1ytkeQbKMuJuvH\nz4Ki0F2xg7atvxpW7q7b7oRMN1qmm4gnF9brpNywmIRJM+nYtZnuk8POu3e8hTt7JlhUIr5O0MP4\nt7yBbfqVOGZeS6SpiZQ59xBqrMB3uAQAZ+4MLHZXz+uuT/844Lwi/k7EyaspPdC7Dcx16eku5cRL\n82VB+RLT21AWL17Mpk2bzr2j1D8BJ3acuWFR9ajROURsFiKBCLZ0G1qbRtMbTWTdkUXoeCjaVjFA\nrglXoag2FNVK4mXfGnZBCWx/H/v0vJOv/4hj7HQ8efOw2F2kz/0Z/sMfoQe7CX1xmOY3VuHImkx3\nxcnpIPUIzuu+hWJ34Lh6NlbXZXjq24n4Ogg2HqTjww1kzH8YEQnTueeds2TRV2fpG0B0UuqOko29\ntnV98h6ucTOi++1+e1jnH29iVlCKi4vJysrq8/7jjz/Oli1bACgoKCAcDvPaa6/1e5wlS5Zw773R\nEYsZGQN/PkaK0o5rtJe0k5KfQndFN76aaNtEa1ErrUV9B2Sdi792L8nX3YXQwz1XAsMRKHoHrfIA\niqoSrjkcbZs4tZSFrvdcJQAE68t7L3YlBCIQAKstOrt+OLqgjupJB8B36EPqqz8e2rrAepjOkjO3\nI/n761KWgF5LG52/WLhwoSgpKREul2vAn9m9e7cpucroHZbEFGHLnCBAGfpxVJuwpo4RKJY+2xKm\nXC8ybnlYOLKnnvM41vGTRNJjq0Ty0l+IMX+3XmR873GBxWr6dxRvMYi/vfOf3Ny5c8XBgwdFRkZG\nrE5Kxtc4FHuCyF76shj70GYx+sfPimEVJhnnJQb6t2fKrPfPPfccHo+H4uJiysrKWLfu7JPTDIaa\nMw77rHyw2Qw7pmQsx5hLsTjdWGwOHKMnoXrkrWy8MKVRdvLkyTE5rvWSqaT98iWErqNVHKD9kaUx\n+T3S8ISO1SAiYfSQn4i3pecpYWnkM72Xx0j26VeARcXidGGfkWd2OlI/dH8nn794H7ZRudH1fS+A\nx/ovFHG10Fdg53aE34fQNHxvv252OtJZ6AEvwYYDiPDQnkUCSJhyPWP/fhMXLfoVFleSgdlJQxVX\nVyj6sS84/sObURLciI7+J3uW4kPaTUuxOBOx2cbinnFzdEY0yVRxdYUCgKbJYnKBCLd/gR4OISKR\nPtMPnI1ycvSsZLy4ukKRLizNrz+Be8aNaCea8Fd9dO4PqFayFjyDPWsygboymn/3JNHeTskosqBI\ng3dyXhF0cxtT9YB3QBNEn+LImowtYxyKxYJj7DSsaWMItw1wjl5pQOLvlkeKKfvV15L5+xJGvfsB\ntmlXmJ3OoGhtR0GPoIf8iJNd1pKx5BWKNCiJC5eiOBwoQOKCe2gvuN/slAZM93fy+cvLcGRPIVBf\njtCG3sMknZm8QpEGRSsvQ/f70P0+QuV7zU5n0CLeFnyVH6D72s1OJS7JKxRpULpeXIt2cB8iHCa0\na6fZ6UhfM7KgSIMjRK/FsyTpy+QtjyRJhpEFRZIkwyiMoJE9zc3NHDnSe2LkjIwMWloujO4/ea7x\naSSca25uLpmZmQPa1/TJW4YTF9KkS/Jc4zPi6VzlLY8kSYaRBUWSJMOowJNmJzFce/eOvAFWQyXP\nNT7Fy7mOqEZZSZK+3uQtjyRJhombgvLQQw8hhCA9Pd3sVGJq9erVVFRUsH//ft58802Sk5PNTslw\nc+fOpbKykqqqKh577DGz04mZnJwctm3bxsGDBzlw4AAPPPCA2SkZwvSupuFGTk6OKCoqEnV1dSI9\nPd30fGIZN910k1BVVQCisLBQFBYWmp6TkWGxWER1dbUYP368sNlsYt++fWLKlCmm5xWLyMrKEnl5\neQIQbrdbHDp0aMSfa1xcoaxZs4ZHH30UIYTZqcRccXExkUh0Wc3S0lJycnJMzshYs2bNorq6mtra\nWjRNY+PGjdx2221mpxUTTU1NlJWVAdDV1UVFRQXZ2dkmZzU8I76g3HrrrRw9epRPP/3U7FTOu8WL\nF7N161az0zBUdnY2DQ0NPT83NjaO+D+ygcjNzSUvL49du3aZncqwjIinjc+28HpBQQE333yzCVnF\njlELzUsjQ2JiIps3b+bBBx/E6/Wanc6wmX7fNdSYNm2aOHbsmKitrRW1tbVC0zRx5MgRMXr0aNNz\ni2UMZaH5kRKzZ88WRUVFPT+vWLFCrFixwvS8YhVWq1UUFRWJ5cuXm56LQWF6AoZFbW1t3DfKDnWh\n+ZESqqqKmpoacfHFF/c0yk6dOtX0vGIV69evF2vWrDE9DwPD9AQMiwuhoFRVVYn6+npRVlYmysrK\nxLp160zPyeiYN2+eOHTokKiurhYFBQWm5xOryM/PF0IIsX///p5/z3nz5pme13BCjpSVJMkwI76X\nR5Kkrw9ZUCRJMowsKJIkGUYWFEmSDCMLiiRJhpEFRTovnnrqKerr6+NiJKjUP1lQpPPi3XffZdas\nWWanIcXYiHiWRxpZ7rvvPpYuXQpAcnIydXV1zJkzx+SspPPF9NF1MuIzrFar2LFjh7jlllt63vN6\nvabnJSN2IW95pJhZu3Yt27Zt47333jM7Fek8kbc8UkwsXLiQ3Nxcli1bZnYq0nlm+mWSjPiKK6+8\nUpSXl4uUlJQ+2+QtT3yHvEKRDLds2TLS0tLYvn07AHv27KGtrY0FCxaQkJBAQ0MDL730EqtWrTI5\nU8lo8mljSZIMIxtlJUkyjCwokiQZRhYUSZIMIwuKJEmGkQVFkiTDyIIiSZJhZEGRJMkwsqBIkmSY\n/wddoJtmyL91wQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 1, rec_loss: 32.6216, kl_loss: 2.2470, reg_loss: 0.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 100, rec_loss: 1.6437, kl_loss: 2.6001, reg_loss: 0.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 200, rec_loss: 1.2575, kl_loss: 2.2104, reg_loss: 0.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 300, rec_loss: 1.1194, kl_loss: 2.0126, reg_loss: 0.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 400, rec_loss: 1.0680, kl_loss: 1.9895, reg_loss: 0.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SDQvlJ9i6dSuqq6tRXl6O/fv3w2KxSMnxzDPPoLKyEqqqIjk5WUqG9PR01NTUoK6uDhs3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\nc5F9AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 500, rec_loss: 1.2048, kl_loss: 1.9375, reg_loss: 0.0000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EVweieEJp-3M",
        "colab_type": "text"
      },
      "source": [
        "# Gaussian Mixture Prior full model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4RO5nsI2qCzS",
        "colab_type": "text"
      },
      "source": [
        "ELBO = sum_x sum_y sum_z [log p(x, y, z) -log q(z|x,y)]\n",
        "     \n",
        "     = sum_x sum_y sum_z [log p(y)p(z|y)p(x|y,z) -log q(y|x)q(z|x,y)]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gUKtgihyUtWk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def y_given(k):\n",
        "  probs = tf.nn.softmax(tf.ones(k))\n",
        "  return tfd.Categorical(probs=probs)\n",
        "\n",
        "def y_given_x(x, k, reg): #+\n",
        "    act = tf.nn.leaky_relu\n",
        "    h = x\n",
        "    \n",
        "    h = tf.layers.dense(h, 32, act, kernel_regularizer=reg)\n",
        "    h = tf.layers.dense(h, 32, act, kernel_regularizer=reg)\n",
        "    h = tf.layers.dense(h, 32, act, kernel_regularizer=reg)\n",
        "    h = tf.layers.dense(h, 32, act, kernel_regularizer=reg)\n",
        "    \n",
        "    loc = tf.layers.dense(h, k)\n",
        "    probs = tf.nn.softmax(loc, axis=-1)\n",
        "    return tfd.Categorical(probs=probs), probs\n",
        "  \n",
        "def z_given_x_y(x, y, latent_size, reg, reuse):\n",
        "  with tf.variable_scope('z_given_x_y', reuse=reuse):\n",
        "      act = tf.nn.leaky_relu\n",
        "\n",
        "      h = tf.concat((x,y), axis=-1)\n",
        "      h = tf.layers.dense(h, 256, act, kernel_regularizer=reg)\n",
        "      h = tf.layers.dense(h, 256, act, kernel_regularizer=reg)\n",
        "      h = tf.layers.dense(h, 256, act, kernel_regularizer=reg)\n",
        "\n",
        "      loc = tf.layers.dense(h,latent_size)\n",
        "      log_variance = tf.layers.dense(h, latent_size)\n",
        "      scale = tf.nn.softplus(log_variance)\n",
        "      #scale = 1.0*tf.ones(tf.shape(loc))\n",
        "      return tfd.MultivariateNormalDiag(loc, scale)\n",
        "\n",
        "#KL term for w\n",
        "def z_given_y(y, latent_size, reg, reuse):\n",
        "  with tf.variable_scope('z_given_y', reuse=reuse):\n",
        "      act = tf.nn.leaky_relu\n",
        "      h = y\n",
        "\n",
        "      loc = tf.layers.dense(h,latent_size)\n",
        "      log_variance = tf.layers.dense(h, latent_size)\n",
        "      #scale = tf.nn.softplus(log_variance)\n",
        "      scale = 0.1*tf.ones(tf.shape(loc))\n",
        "      return tfd.MultivariateNormalDiag(loc, scale)\n",
        "\n",
        "\n",
        "def x_given_y_z(y, z, output_size, reg, reuse):\n",
        "  with tf.variable_scope('x_given_z', reuse=reuse):\n",
        "      act = tf.nn.leaky_relu\n",
        "\n",
        "      h = tf.concat((y,z), axis=-1)\n",
        "\n",
        "      h = tf.layers.dense(h, 256, act, kernel_regularizer=reg)\n",
        "      h = tf.layers.dense(h, 256, act, kernel_regularizer=reg)\n",
        "\n",
        "      loc = tf.layers.dense(h, output_size)\n",
        "      log_variance = tf.layers.dense(h, output_size)\n",
        "      #scale = tf.nn.softplus(log_variance)\n",
        "      scale = 0.01*tf.ones(tf.shape(loc))\n",
        "      return tfd.MultivariateNormalDiag(loc, scale)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yWCSW-nUWpMl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Connect encoder and decoder and define the loss function\n",
        "tf.reset_default_graph()\n",
        "\n",
        "x = tf.placeholder(tf.float32, shape=[None, X.shape[1]], name='x')\n",
        "reg = regularizers.l1_l2(l1=0.0, l2=1e-8)\n",
        "latent_size = 2\n",
        "k = 5\n",
        "reuse = tf.AUTO_REUSE\n",
        "\n",
        "y_x, y_probs = y_given_x(x, k, reg)\n",
        "y_prior = y_given(k)\n",
        "\n",
        "\n",
        "with tf.name_scope('y_'):\n",
        "    y_ = tf.fill(tf.stack([tf.shape(x)[0], k]), 0.0)\n",
        "\n",
        "# for each proposed y, infer z and reconstruct x\n",
        "z_y, z_x_y, x_z = [[None] * k for i in range(3)]\n",
        "for i in range(k):\n",
        "    with tf.name_scope('graphs/hot_at{:d}'.format(i)):\n",
        "        y = tf.add(y_, tf.constant(np.eye(k)[i], name='hot_at_{:d}'.format(i), dtype=tf.float32))\n",
        "        z_x_y[i] = z_given_x_y(x, y, latent_size, reg, reuse)\n",
        "        z_y[i] = z_given_y(y, latent_size, reg, reuse)\n",
        "        x_z[i] = x_given_y_z(y, z_y[i].sample(), X.shape[1], reg, reuse)\n",
        "        \n",
        "# Aggressive name scoping for pretty graph visualization :P\n",
        "with tf.name_scope('loss'):\n",
        "    losses = [None] * k\n",
        "    for i in range(k):\n",
        "        with tf.name_scope('loss_at{:d}'.format(i)):\n",
        "            losses[i] = 1.0*tfd.kl_divergence(z_x_y[i], z_y[i]) + 1.0*tf.reduce_sum(tf.math.square(x_z[i].mean()-x), axis=-1)\n",
        "    with tf.name_scope('final_loss'):\n",
        "        loss1 = tf.add_n([y_probs[:, i] * losses[i] for i in range(k)])\n",
        "\n",
        "entropy = -1.0*tf.reduce_mean(y_x.entropy())\n",
        "reg_loss = tf.losses.get_regularization_loss()\n",
        "kl_y = 200.0*tf.reduce_mean(tfd.kl_divergence(y_x, y_prior))\n",
        "loss = tf.reduce_mean(loss1)+entropy+kl_y+reg_loss\n",
        "\n",
        "y_sampled = y_x.sample()\n",
        "z_mean = z_given_x_y(x, tf.one_hot(y_sampled, k, axis=-1), latent_size, reg, reuse).mean()\n",
        "\n",
        "optimizer = tf.train.AdamOptimizer(0.001)\n",
        "train_op = optimizer.minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kJR_LJn2Wwml",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Helper function\n",
        "def batch_generator(features, batch_size):\n",
        "  \"\"\"Function to create python generator to shuffle and split features into batches along the first dimension.\"\"\"\n",
        "  idx = np.arange(features.shape[0])\n",
        "  np.random.shuffle(idx)\n",
        "  for start_idx in range(0, features.shape[0], batch_size):\n",
        "    end_idx = min(start_idx + batch_size, features.shape[0])\n",
        "    part = idx[start_idx:end_idx]\n",
        "    yield features[part,:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vBZzUAyNW4lL",
        "colab_type": "code",
        "outputId": "aba1fc33-e4e5-40ce-9446-c95cb703f4d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "n_epochs = 50\n",
        "batch_size = 32\n",
        "with tf.Session() as sess:\n",
        "  sess.run(tf.global_variables_initializer())\n",
        "  for i in range(n_epochs):\n",
        "    gen = batch_generator(X, batch_size) #create batch generator\n",
        "    for j in range(np.int(X.shape[0]/batch_size)):\n",
        "      x_batch = gen.__next__()\n",
        "      _ = sess.run(train_op, feed_dict={x: x_batch})\n",
        "    if (i+1)% 10 == 0 or i == 0:\n",
        "      loss_, y_probs_, z_mean_= sess.run([loss, y_probs, z_mean], feed_dict ={x:X})\n",
        "      \n",
        "      plt.figure(1);\n",
        "      plt.figure(figsize=(4,2));\n",
        "      plt.scatter(z_mean_[:,0],z_mean_[:,1], c=Y, s=6.0, cmap='tab10');\n",
        "      plt.xlabel('z1');\n",
        "      plt.ylabel('z2');\n",
        "      plt.show();\n",
        "\n",
        "      print('epoch: {0}, loss: {1:.4f}, rand_score: {2:.4f}'.format((i+1), loss_, metrics.adjusted_rand_score(Y, np.argmax(y_probs_, axis=-1))))"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5i06YbN1ms+HxeNA0jV4pScRH2RBCcG5BLgu37qa4uJjExETi4uJYuPDk/658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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 1, loss: 1595.8430, rand_score: 0.0749\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qamdbV6DY6jo/SlGYOSqPF7fuQlEU0hPc3DpjUvgUEik6kqGMFJ6z4E+7PiVg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\nI3YAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 10, loss: 379.9305, rand_score: 1.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DUqwBkihCJYp4cfFczJ2Q7DE/b0x4GJ7/3myoxKB9SxkbtKBs8UiigJ8v/i7CdVqP7e6z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\n",
            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 20, loss: 372.4672, rand_score: 1.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 30, loss: 371.6561, rand_score: 1.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 40, loss: 371.1739, rand_score: 1.0000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x144 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "epoch: 50, loss: 370.9378, rand_score: 1.0000\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}