training_latent_ode.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# import\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import autograd_extended\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from keras.models import Model\n",
    "from keras.layers import LSTM, Input, Lambda, Dense, RepeatVector\n",
    "from keras import backend as K\n",
    "from keras import objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training the latent ODE model\n",
    "<strong>From appendix D</strong>\n",
    "\n",
    "To obtain the latent representation $z_{t_{0}}$, we traverse using RNN and obtain parameters of distribution $ q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}, \\theta_{enc})$. The algorithm is the following:\n",
    "\n",
    "\n",
    "## Step 1\n",
    "Run an RNN encoder through the time series and infer the parameters for the a posterior over $ \\textbf{z}_{t_{0}}$:\n",
    "$$ q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}, \\phi) = \\mathcal{N}(\\textbf{z}_{t_{0}} | \\mu_{\\textbf{z}_{t_{0}}}, \\sigma_{\\textbf{z}_{0}}) $$\n",
    "\n",
    "where $\\mu_{z_{0}}, \\sigma_{z_{0}}$ comes from hidden state of $ RNN(\\{ \\textbf{x}_{t_{i}} , t_{i} \\}_{i}, \\phi) $\n",
    "\n",
    "## Step 2\n",
    "Sample $ \\textbf{z}_{t_{0}} \\sim q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}) $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Process Data\n",
    "\n",
    "# obtain simple time series with sine function\n",
    "df = pd.read_csv('./data.csv')\n",
    "\n",
    "x, y = df[\"x\"], df[\"y\"]\n",
    "\n",
    "# split y into timesteps for training (-1, 100, 1) we use a sliding window\n",
    "timesteps = 5\n",
    "\n",
    "newY = []\n",
    "for i in range(0, len(y)-timesteps):\n",
    "    temp = y[i:i+timesteps]\n",
    "    \n",
    "    temp_ls = []\n",
    "    for j in temp:\n",
    "        temp_ls.append([j])\n",
    "    newY.append(temp_ls)\n",
    "    \n",
    "y = np.array(newY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define and run the autoencoder model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "encoder_input (InputLayer)   (None, 5, 1)              0         \n",
      "_________________________________________________________________\n",
      "lstm_1 (LSTM)                (None, 32)                4352      \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 100)               3300      \n",
      "=================================================================\n",
      "Total params: 7,652\n",
      "Trainable params: 7,652\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 100)               0         \n",
      "_________________________________________________________________\n",
      "repeat_vector_2 (RepeatVecto (None, 5, 100)            0         \n",
      "_________________________________________________________________\n",
      "lstm_2 (LSTM)                (None, 5, 32)             17024     \n",
      "_________________________________________________________________\n",
      "lstm_3 (LSTM)                (None, 5, 1)              136       \n",
      "=================================================================\n",
      "Total params: 17,160\n",
      "Trainable params: 17,160\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "encoder_input (InputLayer)      (None, 5, 1)         0                                            \n",
      "__________________________________________________________________________________________________\n",
      "lstm_1 (LSTM)                   (None, 32)           4352        encoder_input[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 100)          3300        lstm_1[0][0]                     \n",
      "__________________________________________________________________________________________________\n",
      "dense_2 (Dense)                 (None, 100)          3300        lstm_1[0][0]                     \n",
      "__________________________________________________________________________________________________\n",
      "lambda_1 (Lambda)               (None, 100)          0           dense_1[0][0]                    \n",
      "                                                                 dense_2[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "repeat_vector_1 (RepeatVector)  (None, 5, 100)       0           lambda_1[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "lstm_2 (LSTM)                   (None, 5, 32)        17024       repeat_vector_1[0][0]            \n",
      "__________________________________________________________________________________________________\n",
      "lstm_3 (LSTM)                   (None, 5, 1)         136         lstm_2[0][0]                     \n",
      "==================================================================================================\n",
      "Total params: 28,112\n",
      "Trainable params: 28,112\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Run an RNN encoder on the time series\n",
    "\n",
    "# Params\n",
    "timesteps = 5\n",
    "input_dim = 1\n",
    "lstm_dim = 32\n",
    "latent_dim = 100\n",
    "batch_size = 1\n",
    "\n",
    "# Encoder model\n",
    "def sample_z(args):\n",
    "    \"\"\"Reparameterization trick by sampling fr an isotropic unit Gaussian.\n",
    "    # Arguments:\n",
    "        args (tensor): mean and log of variance of Q(z|X)\n",
    "    # Returns:\n",
    "        z (tensor): sampled latent vector\n",
    "    \"\"\"\n",
    "\n",
    "    z_mean, z_log_var = args\n",
    "    batch = K.shape(z_mean)[0]\n",
    "    dim = K.int_shape(z_mean)[1]\n",
    "    # by default, random_normal has mean=0 and std=1.0\n",
    "    epsilon = K.random_normal(shape=(batch, dim))\n",
    "    return z_mean + K.exp(0.5 * z_log_var) * epsilon\n",
    "\n",
    "\n",
    "# Input\n",
    "inputs = Input(shape=(timesteps, input_dim,), name='encoder_input')\n",
    "\n",
    "# LSTM encoding\n",
    "h = LSTM(lstm_dim)(inputs)\n",
    "\n",
    "# VAE Z layer\n",
    "z_mean = Dense(latent_dim)(h)\n",
    "z_log_sigma = Dense(latent_dim)(h)\n",
    "\n",
    "# Obtain z\n",
    "z = Lambda(sample_z, output_shape=(latent_dim,))([z_mean, z_log_sigma])\n",
    "\n",
    "encoder = Model(inputs, z_mean, name=\"encoder\")\n",
    "\n",
    "# Decoder model\n",
    "decoder_h = LSTM(lstm_dim, return_sequences=True)\n",
    "decoder_mean = LSTM(input_dim, return_sequences=True)\n",
    "\n",
    "h_decoded = RepeatVector(timesteps)(z)\n",
    "h_decoded = decoder_h(h_decoded)\n",
    "\n",
    "# decoded layer\n",
    "outputs = decoder_mean(h_decoded)\n",
    "\n",
    "# decoder, from latent space to reconstructed inputs\n",
    "decoder_inputs = Input(shape=(latent_dim,))\n",
    "\n",
    "_h_decoded = RepeatVector(timesteps)(decoder_inputs)\n",
    "_h_decoded = decoder_h(_h_decoded)\n",
    "\n",
    "decoder_outputs = decoder_mean(_h_decoded)\n",
    "\n",
    "decoder = Model(decoder_inputs, decoder_outputs)\n",
    "\n",
    "# Build vae\n",
    "vae = Model(inputs, outputs, name='vae_lstm')\n",
    "def vae_loss(x, x_decoded_mean):\n",
    "    xent_loss = objectives.mse(x, x_decoded_mean)\n",
    "    kl_loss = - 0.5 * K.mean(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma))\n",
    "    loss = xent_loss + kl_loss\n",
    "    return loss\n",
    "\n",
    "vae.compile(optimizer='adam', loss=vae_loss)\n",
    "\n",
    "encoder.summary()\n",
    "decoder.summary()\n",
    "vae.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "1995/1995 [==============================] - 6s 3ms/step - loss: 0.5021\n",
      "Epoch 2/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.4749\n",
      "Epoch 3/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.4643\n",
      "Epoch 4/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.4568\n",
      "Epoch 5/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.4422\n",
      "Epoch 6/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.3795\n",
      "Epoch 7/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.2682\n",
      "Epoch 8/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.2233\n",
      "Epoch 9/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.2022\n",
      "Epoch 10/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1923\n",
      "Epoch 11/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1809\n",
      "Epoch 12/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1736\n",
      "Epoch 13/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1697\n",
      "Epoch 14/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1614\n",
      "Epoch 15/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1550\n",
      "Epoch 16/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1526\n",
      "Epoch 17/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1449\n",
      "Epoch 18/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1434\n",
      "Epoch 19/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1373\n",
      "Epoch 20/20\n",
      "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1364\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7fa94d0b75f8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the VAE to obtain z\n",
    "vae.fit(y, y, epochs=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: (1995, 5, 1), preds: (1995, 5, 1)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sanity check, we should get a sine graph\n",
    "prediction = vae.predict(y, batch_size=batch_size)\n",
    "\n",
    "# pick a column to plot.\n",
    "print(\"x: %s, preds: %s\" % (y.shape, prediction.shape))\n",
    "plt.plot(y[:100,0,0], label='data')\n",
    "plt.plot(prediction[:100,0,0], label='predict')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3\n",
    "Obtain $\\textbf{z}_{t_{1}}, \\textbf{z}_{t_{2}}, ..., \\textbf{z}_{t_{M}} $ by solving ODE $ ODESolve(\\textbf{z}_{t_{0}}, f, \\theta_{f}, t_{0},...,t_{M})$ where $f$ is the function defining the gradient $d\\textbf{z}/{dt}$ as a function of $\\textbf{z}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4\n",
    "Maximize ELBO (Evidence Lower Bound) \n",
    "$$ ELBO = \\sum^{M}_{i=1}\n",
    "        {\n",
    "             \\log p(\\textbf{x}_{t_{i}}) | \\textbf{z}_{t_{i}}, \\theta_{\\textbf{x}} ) \n",
    "             + \\log p(\\textbf{z}_{t_{0}})\n",
    "             - \\log q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}, \\phi)\n",
    "        }  \n",
    "$$\n",
    "\n",
    "Where $p(\\textbf{z}_{t_{0}}) = \\mathcal{N}(0,1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:catalyst]",
   "language": "python",
   "name": "conda-env-catalyst-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}