VAE_Hyperbolic.ipynb

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  "metadata": {
    "colab": {
      "name": "VAE_Hyperbolic.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "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_Hyperbolic.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q6iVkwPQZKas",
        "colab_type": "text"
      },
      "source": [
        "# VAE with the Hyperbolic Wrapped distribution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pXQG7VtQVk6Z",
        "colab_type": "text"
      },
      "source": [
        "Variational Autoencoder Model (VAE) (https://arxiv.org/pdf/1312.6114.pdf) with the Hyperbolic Wrapped distribution \n",
        "\n",
        "https://github.com/pfnet-research/hyperbolic_wrapped_distribution\n",
        "\n",
        "https://arxiv.org/abs/1902.02992."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bL6BBloIUobY",
        "colab_type": "code",
        "outputId": "46f0b6b2-97ff-4f37-e41e-d8c0b6c3b2d6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "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('ggplot')"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "joYfPqOiQ7OP",
        "colab_type": "text"
      },
      "source": [
        "# Generate binary tree"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JgsinjLTQ9YJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def hasone(node_index, dim_index):\n",
        "    bin_i, bin_j = np.binary_repr(node_index), np.binary_repr(dim_index)\n",
        "    length = len(bin_j)\n",
        "    return (bin_i[:length] == bin_j) * 1\n",
        "\n",
        "def hamming_distance(x, y):\n",
        "    return (x.astype(np.int32) ^ y.astype(np.int32)).sum()\n",
        "\n",
        "def euclid_distance(x, y):\n",
        "    return np.sqrt(((x - y)**2).sum(axis=-1))\n",
        "\n",
        "def get_data(depth, dtype=np.float32):\n",
        "    n = 2**depth - 1\n",
        "    x = np.fromfunction(lambda i, j: np.vectorize(hasone)(i + 1, j + 1),\n",
        "                        (n, n), dtype=np.int32).astype(dtype)\n",
        "    return x\n",
        "\n",
        "def get_example(data, i, eps):\n",
        "  filter_ = np.random.random(size=data.shape[-1]) < eps\n",
        "  return (data[i,:].astype(bool) ^ filter_).astype(data.dtype)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hgt4lnOXUYQ6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "my_data = []\n",
        "labels = []\n",
        "true_data = get_data(4)\n",
        "for i in range(true_data.shape[0]*50):\n",
        "  one_example = get_example(true_data, i % true_data.shape[0], eps=0.001)\n",
        "  labels.append(i%true_data.shape[0])\n",
        "  my_data.append(one_example)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wYeoolA7U-Yh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = np.array(my_data)\n",
        "y = np.array(labels)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Esmvc6zmq9fb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_levels = np.copy(y)\n",
        "for i in range(y.shape[0]):\n",
        "  if y[i] == 0:\n",
        "    y_levels[i] = 0\n",
        "  elif 1<= y[i] <= 2:\n",
        "    y_levels[i] = 1\n",
        "  elif 3<= y[i] <= 6:\n",
        "    y_levels[i] = 2\n",
        "  elif 7<= y[i] <= 14:\n",
        "    y_levels[i] = 3\n",
        "  elif 15<=y[i] <= 30:\n",
        "    y_levels[i] = 4"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f2d0NAieIbdr",
        "colab_type": "code",
        "outputId": "55eafbbb-1c41-4804-95ba-d5341152311f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X.shape"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(750, 15)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JyFcj2aptGOC",
        "colab_type": "text"
      },
      "source": [
        "# Helper functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yR0_qjMzNHRQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def project_2D(z):\n",
        "  t = z[:,0][:,np.newaxis]\n",
        "  x = z[:,1:]\n",
        "  y = x/(1+t)\n",
        "  return y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FweczyF-s6D-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "eps=1e-12\n",
        "\n",
        "def clamp(a, a_min):\n",
        "    \"\"\"checked\"\"\"\n",
        "    return tf.nn.relu(a - a_min) + a_min\n",
        "\n",
        "def negate_first_index(x):\n",
        "    \"\"\"checked\"\"\"\n",
        "    x0, xrest = tf.split(x, num_or_size_splits=[1,tf.shape(x)[-1]-1], axis=-1)\n",
        "    return tf.concat((x0 * -1, xrest), axis=-1)\n",
        "  \n",
        "def lorentzian_product(u, v=None, keepdims=False):\n",
        "    \"\"\"checked\"\"\"\n",
        "    if v is None:\n",
        "        v = u\n",
        "    uv = u * v\n",
        "    return tf.reduce_sum(negate_first_index(uv), axis=-1, keepdims=keepdims)\n",
        "\n",
        "def lorentz_distance(u, v, keepdims=False):\n",
        "    \"\"\"checked\n",
        "    arccosh(x) = ln[x+sqrt(x^2-1)]\"\"\"\n",
        "    x = -lorentzian_product(u, v, keepdims=keepdims)\n",
        "    return tf.math.log(clamp(x + tf.math.sqrt(clamp(x**2 - 1, eps)), eps))\n",
        "\n",
        "def inv_exponential_map(x, z):\n",
        "    \"\"\"checked\n",
        "    Eq. (14)\"\"\"\n",
        "    alpha = -lorentzian_product(x, z, keepdims=True)\n",
        "    C = lorentz_distance(x, z, keepdims=True)/tf.math.sqrt(clamp(alpha ** 2 - 1, eps))\n",
        "    return C * (z - alpha * x)\n",
        "\n",
        "def exponential_map(x, v):\n",
        "    \"\"\"checked\"\"\"\n",
        "    vnorm = tf.math.sqrt(clamp(lorentzian_product(v, keepdims=True), eps))\n",
        "    return tf.math.cosh(vnorm) * x + tf.math.sinh(vnorm) * v / vnorm  \n",
        "  \n",
        "def parallel_transport(xi, x, y):\n",
        "    \"\"\"checked\n",
        "    Eq. (15)\n",
        "    \"\"\"\n",
        "    alpha = -lorentzian_product(x, y, keepdims=True)\n",
        "    coef = lorentzian_product(y - alpha * x, xi, keepdims=True) / (alpha + 1)\n",
        "    return xi + coef * (x + y)\n",
        "  \n",
        "def algo1(mu, epsilon):\n",
        "  \"\"\"checked\"\"\"\n",
        "  mu_0 = tf.concat((tf.ones(shape=[tf.shape(mu)[0], 1]), tf.zeros(shape=[tf.shape(mu)[0], tf.shape(mu)[1]-1])), axis=-1) #origin\n",
        "  v = tf.concat((tf.zeros(shape=[tf.shape(mu)[0], 1]), epsilon), axis=-1)\n",
        "  u = parallel_transport(v, mu_0, mu)\n",
        "  z = exponential_map(mu, u)\n",
        "  return z\n",
        "\n",
        "def algo2(z, mu):\n",
        "  \"\"\"Output:\n",
        "  v1 - point sampled from original distribution\n",
        "  r - the distance used for detlog.\"\"\"\n",
        "  mu_0 = tf.concat((tf.ones(shape=[tf.shape(mu)[0], 1]), tf.zeros(shape=[tf.shape(mu)[0], tf.shape(mu)[1]-1])), axis=-1) #origin\n",
        "  u = inv_exponential_map(mu, z)\n",
        "  v = parallel_transport(u, mu, mu_0) #move to the origin\n",
        "  v_tilde = v[:,1:] #omit the first coordinate which is zero\n",
        "  r = tf.math.sqrt(clamp(lorentzian_product(u, keepdims=True), eps))\n",
        "  return v_tilde, r"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "brAwd9DRIYNY",
        "colab_type": "text"
      },
      "source": [
        "# Hyperbolic VAE"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4E1cgAP9UtB_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def create_encoder(inpt, latent_size, activation, reg):\n",
        "  x = inpt\n",
        "  x = tf.layers.dense(x, 16, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 10, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 8, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 6, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 4, activation, kernel_regularizer=reg)\n",
        "  \n",
        "  h = tf.layers.dense(x,latent_size, kernel_regularizer=reg)\n",
        "  #h = tf.clip_by_norm(h, clip_norm = 500.0, axes=-1)\n",
        "  mu1 = tf.math.cosh(tf.norm(h, axis=-1, keep_dims=True))\n",
        "  mu2 = h*tf.math.sinh(tf.norm(h, axis=-1, keep_dims=True))/(tf.norm(h, axis=-1, keep_dims=True)+eps)\n",
        "  mu = tf.concat((mu1, mu2),axis=-1)\n",
        "  \n",
        "  sigma = tf.layers.dense(x,2, kernel_regularizer=reg)\n",
        "  sigma = tf.math.softplus(sigma)\n",
        "  return mu, sigma\n",
        "\n",
        "def create_prior(latent_size):\n",
        "  return tf.constant([1.0, 0.0, 0.0]), 1.0*tf.ones(latent_size)\n",
        "\n",
        "def create_decoder(inpt, output_size, activation, reg):\n",
        "  x = inpt\n",
        "  x = tf.layers.dense(x, 4, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 6, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 8, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 10, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 16, activation, kernel_regularizer=reg)\n",
        "  theta = tf.layers.dense(x, output_size, kernel_regularizer=reg)\n",
        "  return tfd.Independent(tfd.Bernoulli(theta), 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6cz7pGYjU6Mo",
        "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",
        "latent_size = 2\n",
        "\n",
        "mu, sigma = create_encoder(x, latent_size, tf.nn.elu, regularizers.l1_l2(l1=0.0, l2=0.001))\n",
        "\n",
        "sigma = 0.2*tf.ones(latent_size)\n",
        "\n",
        "\n",
        "mu_prior, sigma_prior = create_prior(latent_size)\n",
        "mu_prior = tf.reshape(mu_prior, shape=[1,-1])\n",
        "mu_prior = tf.ones(shape=[tf.shape(mu)[0], latent_size+1])*mu_prior\n",
        "\n",
        "zero_vec = tf.zeros(shape=[tf.shape(mu)[0], tf.shape(mu)[1]-1])\n",
        "dist_latent = tfd.MultivariateNormalDiag(loc=zero_vec, scale_diag=sigma)\n",
        "dist_prior = tfd.MultivariateNormalDiag(loc=zero_vec, scale_diag=sigma_prior)\n",
        "epsilon = dist_latent.sample()\n",
        "latent_sampled = algo1(mu, epsilon)\n",
        "\n",
        "v_latent, r_latent = algo2(latent_sampled, mu)\n",
        "v_prior, r_prior = algo2(latent_sampled, mu_prior)\n",
        "\n",
        "log_latent_posterior = dist_latent.log_prob(v_latent) - (latent_size-1)*tf.math.log(1e-12+tf.math.sinh(r_latent)/(r_latent+1e-12))\n",
        "log_prior = dist_prior.log_prob(v_prior) - (latent_size-1)*tf.math.log(1e-12+tf.math.sinh(r_prior)/(r_prior+1e-12))\n",
        "kl = tf.reduce_mean(log_latent_posterior-log_prior)\n",
        "\n",
        "beta = tf.placeholder(tf.float32, name='beta')\n",
        "kl_loss = beta*kl\n",
        "\n",
        "posterior = create_decoder(latent_sampled, X.shape[1], tf.nn.elu, regularizers.l1_l2(l1=0.0, l2=0.001))\n",
        "\n",
        "posterior_sampled = posterior.sample()\n",
        "posterior_mean = posterior.mean()\n",
        "\n",
        "rec_loss = -tf.reduce_mean(posterior.log_prob(x))\n",
        "reg_loss = tf.losses.get_regularization_loss()\n",
        "loss = rec_loss + kl_loss + reg_loss\n",
        "optimizer = tf.train.AdamOptimizer(0.001).minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oVaO0RxsY7Ht",
        "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": "Gm1vfi3hYzuK",
        "colab_type": "code",
        "outputId": "82df50aa-d9fa-44e1-f0ed-b7391bbe3cc7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "source": [
        "n_epochs = 200\n",
        "batch_size = 25\n",
        "start = time.time()\n",
        "with tf.Session() as sess:\n",
        "  sess.run(tf.global_variables_initializer())\n",
        "  for i in range(n_epochs):\n",
        "    if i < 100:\n",
        "      beta_0 = 0.15\n",
        "    else:\n",
        "      beta_0 = 0.15+0.7*(i+1)/n_epochs\n",
        "    gen = batch_generator(X, batch_size) #create batch generator\n",
        "    total_loss = 0\n",
        "    total_rec_loss = 0\n",
        "    for j in range(np.int(X.shape[0]/batch_size)):\n",
        "      x_batch = gen.__next__()\n",
        "      _, total_loss_, total_rec_loss_ = sess.run([optimizer, loss, rec_loss], feed_dict={x: x_batch, beta: beta_0})\n",
        "      total_loss += total_loss_\n",
        "      total_rec_loss += total_rec_loss_\n",
        "    if (i+1)% 10 == 0 or i == 0:\n",
        "      #latent_mean_, latent_sampled_, posterior_mean_, posterior_sampled_= sess.run([latent_mean, latent_sampled, posterior_mean, posterior_sampled], feed_dict ={x:X})\n",
        "      end = time.time()\n",
        "      print('epoch: {0}, total_loss: {1:.2f}, rec_loss: {2:.2f}, time: {3:.2f}'.format((i+1), \n",
        "                                       total_loss/(1+np.int(X.shape[0]/batch_size)), total_rec_loss/(1+np.int(X.shape[0]/batch_size)), end-start))\n",
        "      start = time.time()\n",
        "  latent_sampled_, mu_, posterior_mean_, posterior_sampled_= sess.run([latent_sampled, mu, posterior_mean, posterior_sampled], feed_dict ={x:X})"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch: 1, total_loss: 9.34, rec_loss: 8.86, time: 1.76\n",
            "epoch: 10, total_loss: 3.41, rec_loss: 2.80, time: 2.88\n",
            "epoch: 20, total_loss: 2.88, rec_loss: 2.27, time: 3.20\n",
            "epoch: 30, total_loss: 1.86, rec_loss: 1.05, time: 3.13\n",
            "epoch: 40, total_loss: 1.43, rec_loss: 0.63, time: 3.25\n",
            "epoch: 50, total_loss: 1.30, rec_loss: 0.51, time: 3.21\n",
            "epoch: 60, total_loss: 1.18, rec_loss: 0.38, time: 3.16\n",
            "epoch: 70, total_loss: 1.13, rec_loss: 0.32, time: 3.18\n",
            "epoch: 80, total_loss: 1.06, rec_loss: 0.23, time: 3.09\n",
            "epoch: 90, total_loss: 1.02, rec_loss: 0.21, time: 3.07\n",
            "epoch: 100, total_loss: 1.02, rec_loss: 0.22, time: 3.07\n",
            "epoch: 110, total_loss: 2.44, rec_loss: 0.45, time: 2.95\n",
            "epoch: 120, total_loss: 2.48, rec_loss: 0.42, time: 2.96\n",
            "epoch: 130, total_loss: 2.58, rec_loss: 0.46, time: 3.05\n",
            "epoch: 140, total_loss: 2.74, rec_loss: 0.52, time: 3.07\n",
            "epoch: 150, total_loss: 2.76, rec_loss: 0.45, time: 3.15\n",
            "epoch: 160, total_loss: 2.84, rec_loss: 0.46, time: 3.21\n",
            "epoch: 170, total_loss: 2.97, rec_loss: 0.46, time: 3.21\n",
            "epoch: 180, total_loss: 3.11, rec_loss: 0.54, time: 3.31\n",
            "epoch: 190, total_loss: 3.10, rec_loss: 0.44, time: 3.30\n",
            "epoch: 200, total_loss: 3.23, rec_loss: 0.49, time: 3.28\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dtr96SNQCVNt",
        "colab_type": "text"
      },
      "source": [
        "# Simple VAE"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MERQgSoXCU2s",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Multivariate diagional\n",
        "def create_encoder(inpt, latent_size, activation, reg):\n",
        "  x = inpt\n",
        "  x = tf.layers.dense(x, 16, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 10, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 8, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 6, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 4, activation, kernel_regularizer=reg)\n",
        "  loc = tf.layers.dense(x,latent_size)\n",
        "  log_variance = tf.layers.dense(x, latent_size)\n",
        "  #scale = tf.nn.softplus(log_variance)\n",
        "  scale = 0.2*tf.ones((tf.shape(x)[0],2))\n",
        "  return tfd.MultivariateNormalDiag(loc, scale)\n",
        "\n",
        "def create_prior(latent_size):\n",
        "  return tfd.MultivariateNormalDiag(loc=[0.0, 0.0], scale_diag=[1.0, 1.0])\n",
        "\n",
        "def create_decoder(inpt, output_size, activation, reg):\n",
        "  x = inpt\n",
        "  x = tf.layers.dense(x, 4, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 6, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 8, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 10, activation, kernel_regularizer=reg)\n",
        "  x = tf.layers.dense(x, 16, activation, kernel_regularizer=reg)\n",
        "  theta = tf.layers.dense(x, output_size, kernel_regularizer=reg)\n",
        "  return tfd.Independent(tfd.Bernoulli(theta), 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KB68WGbhCay0",
        "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",
        "latent_size = 2\n",
        "\n",
        "latent_prior = create_prior(latent_size=latent_size)\n",
        "latent_posterior = create_encoder(x, latent_size, tf.nn.elu, regularizers.l1_l2(l1=0.0, l2=0.001))\n",
        "\n",
        "latent_sampled = latent_posterior.sample()\n",
        "latent_mean = latent_posterior.mean()\n",
        "\n",
        "posterior = create_decoder(latent_sampled, X.shape[1], tf.nn.elu, regularizers.l1_l2(l1=0.0, l2=0.001))\n",
        "\n",
        "posterior_sampled = posterior.sample()\n",
        "posterior_mean = posterior.mean()\n",
        "\n",
        "rec_loss = -tf.reduce_mean(posterior.log_prob(x))\n",
        "#kl = tf.reduce_mean(tfd.kl_divergence(latent_posterior, latent_prior)) #analytical\n",
        "kl = tf.reduce_mean(latent_posterior.log_prob(latent_sampled)- latent_prior.log_prob(latent_sampled)) #approximate KL\n",
        "beta = tf.placeholder(tf.float32, name='beta')\n",
        "kl_loss = beta*kl\n",
        "loss = rec_loss + kl_loss\n",
        "optimizer = tf.train.AdamOptimizer(0.001).minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pyPYVR3LECFr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "outputId": "ad1a0c14-0660-41a0-bd82-a3bb3ab3f1ca"
      },
      "source": [
        "n_epochs = 200\n",
        "batch_size = 25\n",
        "start = time.time()\n",
        "with tf.Session() as sess:\n",
        "  sess.run(tf.global_variables_initializer())\n",
        "  for i in range(n_epochs):\n",
        "    if i < 100:\n",
        "      beta_0 = 0.15\n",
        "    else:\n",
        "      beta_0 = 0.15+0.7*(i+1)/n_epochs\n",
        "    gen = batch_generator(X, batch_size) #create batch generator\n",
        "    total_loss = 0\n",
        "    total_rec_loss = 0\n",
        "    for j in range(np.int(X.shape[0]/batch_size)):\n",
        "      x_batch = gen.__next__()\n",
        "      _, total_loss_, total_rec_loss_ = sess.run([optimizer, loss, rec_loss], feed_dict={x: x_batch, beta: beta_0})\n",
        "      total_loss += total_loss_\n",
        "      total_rec_loss += total_rec_loss_\n",
        "    if (i+1)% 10 == 0 or i == 0:\n",
        "      #latent_mean_, latent_sampled_, posterior_mean_, posterior_sampled_= sess.run([latent_mean, latent_sampled, posterior_mean, posterior_sampled], feed_dict ={x:X})\n",
        "      end = time.time()\n",
        "      print('epoch: {0}, total_loss: {1:.2f}, rec_loss: {2:.2f}, time: {3:.2f}'.format((i+1), \n",
        "                                       total_loss/(1+np.int(X.shape[0]/batch_size)), total_rec_loss/(1+np.int(X.shape[0]/batch_size)), end-start))\n",
        "      start = time.time()\n",
        "  latent_sampled_, mu_, posterior_mean_, posterior_sampled_= sess.run([latent_sampled, latent_mean, posterior_mean, posterior_sampled], feed_dict ={x:X})"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch: 1, total_loss: 9.69, rec_loss: 9.26, time: 0.58\n",
            "epoch: 10, total_loss: 3.32, rec_loss: 2.82, time: 1.05\n",
            "epoch: 20, total_loss: 2.40, rec_loss: 1.89, time: 1.09\n",
            "epoch: 30, total_loss: 1.81, rec_loss: 1.27, time: 1.03\n",
            "epoch: 40, total_loss: 1.38, rec_loss: 0.84, time: 1.07\n",
            "epoch: 50, total_loss: 1.18, rec_loss: 0.63, time: 1.03\n",
            "epoch: 60, total_loss: 1.01, rec_loss: 0.44, time: 1.01\n",
            "epoch: 70, total_loss: 0.91, rec_loss: 0.35, time: 1.04\n",
            "epoch: 80, total_loss: 0.82, rec_loss: 0.25, time: 1.02\n",
            "epoch: 90, total_loss: 0.76, rec_loss: 0.20, time: 1.02\n",
            "epoch: 100, total_loss: 0.74, rec_loss: 0.18, time: 1.03\n",
            "epoch: 110, total_loss: 2.02, rec_loss: 0.33, time: 1.01\n",
            "epoch: 120, total_loss: 2.16, rec_loss: 0.41, time: 1.03\n",
            "epoch: 130, total_loss: 2.21, rec_loss: 0.35, time: 1.03\n",
            "epoch: 140, total_loss: 2.27, rec_loss: 0.33, time: 1.05\n",
            "epoch: 150, total_loss: 2.42, rec_loss: 0.36, time: 1.04\n",
            "epoch: 160, total_loss: 2.50, rec_loss: 0.37, time: 1.05\n",
            "epoch: 170, total_loss: 2.52, rec_loss: 0.36, time: 1.04\n",
            "epoch: 180, total_loss: 2.68, rec_loss: 0.44, time: 1.04\n",
            "epoch: 190, total_loss: 2.74, rec_loss: 0.42, time: 1.02\n",
            "epoch: 200, total_loss: 2.83, rec_loss: 0.38, time: 1.04\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cMbeiHhDIdM8",
        "colab_type": "text"
      },
      "source": [
        "# Visualize"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "syErX-9KKEqC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "disk = project_2D(latent_sampled_)\n",
        "mu_d = project_2D(mu_)\n",
        "t = np.linspace(0,1,5000)\n",
        "x_c = np.cos(2*np.pi*t)\n",
        "y_c = np.sin(2*np.pi*t)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-gI38VgSI_jb",
        "colab_type": "code",
        "outputId": "26be334c-9c54-4d28-c5e0-e83fdc1dda00",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        }
      },
      "source": [
        "plt.style.use(['dark_background'])\n",
        "plt.figure(figsize=(9,9))\n",
        "#plt.scatter(disk[:,0], disk[:,1], c=y_levels, s=25.0, cmap='viridis');\n",
        "plt.scatter(mu_d[:,0], mu_d[:,1], c=y_levels, s=100.0, cmap='viridis');\n",
        "plt.scatter(x_c, y_c, s=1.0);\n",
        "plt.axis('equal');\n",
        "plt.xlabel('z1')\n",
        "plt.ylabel('z2')\n",
        "plt.savefig('latent_space.png')"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BswfeTtVyjkpSyzlKom8xMTFSZmam835qaqqUmpra7LGHDx+Wfvazn7X4vdatWydNnTq1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\n8CEiIiK3weBDREREbuP/AVQ6SLmxvSOjAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z5-XrWksLpEC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def map_to_zero(z, a):\n",
        "  return (z-a)/(1-np.conjugate(a)*z)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RAiooJTCP0AN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a = mu_d[0,0]+mu_d[0,1]*1.0j\n",
        "mu_c = mu_d[:,0]+mu_d[:,1]*1.0j\n",
        "disk_c = disk[:,0]+disk[:,1]*1.0j\n",
        "mu_r = map_to_zero(mu_c, a)\n",
        "disk_r = map_to_zero(disk_c, a)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X8VnIxqoQG56",
        "colab_type": "code",
        "outputId": "38e6a064-adf7-4144-d69d-e27ccc3b73e8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        }
      },
      "source": [
        "plt.figure(figsize=(9,9))\n",
        "#plt.scatter(disk_r.real, disk_r.imag, c=y_levels, s=25.0, cmap='viridis');\n",
        "plt.scatter(mu_r.real, mu_r.imag, c=y_levels, s=100.0, cmap='viridis');\n",
        "plt.scatter(x_c, y_c, s=1.0);\n",
        "plt.axis('equal');\n",
        "plt.xlabel('z1')\n",
        "plt.ylabel('z2')\n",
        "plt.savefig('latent_space_shifted.png')"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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poHMZ7Sx/3bZtW5wtCVGyXK9y7fIa+dSvBVejPgw+Pu6h5+bAYDSiPH8/1+wh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\ngg==\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "20QOHAE-_vMw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        },
        "outputId": "58cdcad1-fde2-4ba8-ef60-677a5c61e5bc"
      },
      "source": [
        "plt.style.use(['dark_background'])\n",
        "plt.figure(figsize=(9,9))\n",
        "plt.scatter(latent_sampled_[:,0], latent_sampled_[:,1], c=y_levels, s=25.0, cmap='viridis');\n",
        "#plt.scatter(mu_[:,0], mu_[:,1], c=y_levels, s=100.0, cmap='viridis');\n",
        "plt.axis('equal');\n",
        "plt.xlabel('z1')\n",
        "plt.ylabel('z2')\n",
        "plt.savefig('latent_euclidean.png')"
      ],
      "execution_count": 139,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SfNvU42OVfDs/juZJ3pyJfr10xEUreOyFvLM+92BqNeVqLD1b+ioj61vHsHvygiCPqm7d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Aqco4TiUi/vfGrlotlG0pJl7C3y8NzrtR3arriPWM1KdMrGcEtqkozbrolhzlWtTy89+2otbo/I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V3+bAETOTXkvng7d6cvr0YQ4dNfPIeM91QXbsMTFyj+PfbrxWS+sWrtafVs1VtG+t5tB/5Ztl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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LLMYo-oLEZOz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}