tybalt_vae.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational Autoencoder for pan-cancer gene expression\n",
    "\n",
    "**Alexander Titus 2018** -- extended from Gregory Way 2017\n",
    "\n",
    "This script trains and outputs results for a [variational autoencoder (VAE)](https://arxiv.org/abs/1312.6114)\n",
    "applied to breast cancer methylation data.\n",
    "\n",
    "A VAE aproximates the data generating function for the cancer data and learns the lower dimensional manifold a tumor occupies in methylation space. By compressing the methylation space into lower dimensional space, the VAE would, ideally, learn biological principles, such as cancer hallmark pathway activations, that help explain how tumors are similar and different. The VAE is also a generative model with a latent space that can be interpolated to observe transitions between cancer states.\n",
    "\n",
    "The particular model trained in this notebook consists of methylation input (100,000 most variably methylated CpGs by median absolute deviation) compressed down into two length 100 vectors (mean and variance encoded spaces) which are made deterministic through the reparameterization trick of sampling an epsilon vector from the uniform distribution. The encoded layer is then decoded back to original 100,000 dimensions through a single reconstruction layer. Included is a layer of batch normalization in the encoding step to prevent dead nodes. The encoding scheme also uses relu activation while the decoder uses a sigmoid activation to enforce positive activations. All weights are glorot uniform initialized. \n",
    "\n",
    "Another trick used here to encourage manifold learning is _warm start_ as discussed in [Sonderby et al. 2016](https://arxiv.org/abs/1602.02282). With warm starts, we add a parameter _beta_, which controls the contribution of the KL divergence loss in the total VAE loss (reconstruction + (beta * KL)). In this setting, the model begins training deterministically as a vanilla autoencoder (_beta_ = 0) and slowly ramps up after each epoch linearly until _beta_ = 1. After a parameter sweep, we observed that kappa has little influence in training, therefore, we set  _kappa_ = 1, which is a full VAE.\n",
    "\n",
    "Much of this script is inspired by the [keras variational_autoencoder.py example](https://github.com/fchollet/keras/blob/master/examples/variational_autoencoder.py)\n",
    "\n",
    "## conda version 4.4.10\n",
    "conda env create --force --file environment.yml\n",
    "\n",
    "## activate environment\n",
    "conda activate tybalt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "No module named seaborn",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-aedf36c5c6f8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mpandas\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mpd\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[1;32mimport\u001b[0m \u001b[0mseaborn\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0msns\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mtensorflow\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mtf\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mImportError\u001b[0m: No module named seaborn"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import tensorflow as tf\n",
    "from keras.layers import Input, Dense, Lambda, Layer, Activation\n",
    "from keras.layers.normalization import BatchNormalization\n",
    "from keras.models import Model\n",
    "from keras import backend as K\n",
    "from keras import metrics, optimizers\n",
    "from keras.callbacks import Callback\n",
    "import keras\n",
    "\n",
    "import pydot\n",
    "import graphviz\n",
    "from keras.utils import plot_model\n",
    "from keras_tqdm import TQDMNotebookCallback\n",
    "from IPython.display import SVG\n",
    "from keras.utils.vis_utils import model_to_dot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(keras.__version__)\n",
    "tf.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "plt.style.use('seaborn-notebook')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sns.set(style=\"white\", color_codes=True)\n",
    "sns.set_context(\"paper\", rc={\"font.size\":14,\"axes.titlesize\":15,\"axes.labelsize\":20,\n",
    "                             'xtick.labelsize':14, 'ytick.labelsize':14})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Functions and Classes\n",
    "\n",
    "This will facilitate connections between layers and also custom hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Function for reparameterization trick to make model differentiable\n",
    "def sampling(args):\n",
    "    \n",
    "    import tensorflow as tf\n",
    "    # Function with args required for Keras Lambda function\n",
    "    z_mean, z_log_var = args\n",
    "\n",
    "    # Draw epsilon of the same shape from a standard normal distribution\n",
    "    epsilon = K.random_normal(shape=tf.shape(z_mean), mean=0.,\n",
    "                              stddev=epsilon_std)\n",
    "    \n",
    "    # The latent vector is non-deterministic and differentiable\n",
    "    # in respect to z_mean and z_log_var\n",
    "    z = z_mean + K.exp(z_log_var / 2) * epsilon\n",
    "    return z\n",
    "\n",
    "\n",
    "class CustomVariationalLayer(Layer):\n",
    "    \"\"\"\n",
    "    Define a custom layer that learns and performs the training\n",
    "    This function is borrowed from:\n",
    "    https://github.com/fchollet/keras/blob/master/examples/variational_autoencoder.py\n",
    "    \"\"\"\n",
    "    def __init__(self, **kwargs):\n",
    "        # https://keras.io/layers/writing-your-own-keras-layers/\n",
    "        self.is_placeholder = True\n",
    "        super(CustomVariationalLayer, self).__init__(**kwargs)\n",
    "\n",
    "    def vae_loss(self, x_input, x_decoded):\n",
    "        reconstruction_loss = original_dim * metrics.binary_crossentropy(x_input, x_decoded)\n",
    "        kl_loss = - 0.5 * K.sum(1 + z_log_var_encoded - K.square(z_mean_encoded) - \n",
    "                                K.exp(z_log_var_encoded), axis=-1)\n",
    "        return K.mean(reconstruction_loss + (K.get_value(beta) * kl_loss))\n",
    "\n",
    "    def call(self, inputs):\n",
    "        x = inputs[0]\n",
    "        x_decoded = inputs[1]\n",
    "        loss = self.vae_loss(x, x_decoded)\n",
    "        self.add_loss(loss, inputs=inputs)\n",
    "        # We won't actually use the output.\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing Warm-up as described in Sonderby et al. LVAE\n",
    "\n",
    "This is modified code from https://github.com/fchollet/keras/issues/2595"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class WarmUpCallback(Callback):\n",
    "    def __init__(self, beta, kappa):\n",
    "        self.beta = beta\n",
    "        self.kappa = kappa\n",
    "    # Behavior on each epoch\n",
    "    def on_epoch_end(self, epoch, logs={}):\n",
    "        if K.get_value(self.beta) <= 1:\n",
    "            K.set_value(self.beta, K.get_value(self.beta) + self.kappa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Methylation Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1230, 100000)\n"
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       "                   cg01682111  cg18391209  cg27260772  cg27363327  cg17882374  \\\n",
       "CpG                                                                             \n",
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       "CpG                                                                             \n",
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       "CpG                                                                             \n",
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     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# BreastCancerMethylation_top100kMAD_cpg.csv file = https://app.box.com/s/xzh0vu2e85pxusflxt47434yfxqi4355\n",
    "methyl_file = os.path.join('data/raw', 'BreastCancerMethylation_top100kMAD_cpg.csv')\n",
    "methyl_df = pd.read_csv(methyl_file, index_col = 0, header  = 0)\n",
    "print(methyl_df.shape)\n",
    "methyl_df.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Split 10% test set randomly\n",
    "test_set_percent = 0.1\n",
    "methyl_test_df = methyl_df.sample(frac=test_set_percent)\n",
    "methyl_train_df = methyl_df.drop(methyl_test_df.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize variables and hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set hyper parameters\n",
    "original_dim = methyl_df.shape[1]\n",
    "latent_dim = 100\n",
    "\n",
    "batch_size = 50\n",
    "epochs = 50\n",
    "learning_rate = 0.0005\n",
    "\n",
    "epsilon_std = 1.0\n",
    "beta = K.variable(0)\n",
    "kappa = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Encoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Input place holder for methylation data with specific input size\n",
    "methyl_input = Input(shape=(original_dim, ))\n",
    "\n",
    "# Input layer is compressed into a mean and log variance vector of size `latent_dim`\n",
    "# Each layer is initialized with glorot uniform weights and each step (dense connections,\n",
    "# batch norm, and relu activation) are funneled separately\n",
    "# Each vector of length `latent_dim` are connected to the rnaseq input tensor\n",
    "z_mean_dense_linear = Dense(latent_dim, kernel_initializer='glorot_uniform')(methyl_input)\n",
    "z_mean_dense_batchnorm = BatchNormalization()(z_mean_dense_linear)\n",
    "z_mean_encoded = Activation('relu')(z_mean_dense_batchnorm)\n",
    "\n",
    "z_log_var_dense_linear = Dense(latent_dim, kernel_initializer='glorot_uniform')(methyl_input)\n",
    "z_log_var_dense_batchnorm = BatchNormalization()(z_log_var_dense_linear)\n",
    "z_log_var_encoded = Activation('relu')(z_log_var_dense_batchnorm)\n",
    "\n",
    "# return the encoded and randomly sampled z vector\n",
    "# Takes two keras layers as input to the custom sampling function layer with a `latent_dim` output\n",
    "z = Lambda(sampling, output_shape=(latent_dim, ))([z_mean_encoded, z_log_var_encoded])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# The decoding layer is much simpler with a single layer and sigmoid activation\n",
    "decoder_to_reconstruct = Dense(original_dim, kernel_initializer='glorot_uniform', activation='sigmoid')\n",
    "methyl_reconstruct = decoder_to_reconstruct(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Connect the encoder and decoder to make the VAE\n",
    "\n",
    "The `CustomVariationalLayer()` includes the VAE loss function (reconstruction + (beta * KL)), which is what will drive our model to learn an interpretable representation of gene expression space.\n",
    "\n",
    "The VAE is compiled with an Adam optimizer and built-in custom loss function. The `loss_weights` parameter ensures beta is updated at each epoch end callback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\atitus\\Anaconda3\\envs\\tybalt\\lib\\site-packages\\ipykernel\\__main__.py:4: UserWarning: Output \"custom_variational_layer_2\" missing from loss dictionary. We assume this was done on purpose, and we will not be expecting any data to be passed to \"custom_variational_layer_2\" during training.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_3 (InputLayer)            (None, 100000)       0                                            \n",
      "__________________________________________________________________________________________________\n",
      "dense_4 (Dense)                 (None, 100)          10000100    input_3[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_5 (Dense)                 (None, 100)          10000100    input_3[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_3 (BatchNor (None, 100)          400         dense_4[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_4 (BatchNor (None, 100)          400         dense_5[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "activation_3 (Activation)       (None, 100)          0           batch_normalization_3[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "activation_4 (Activation)       (None, 100)          0           batch_normalization_4[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "lambda_2 (Lambda)               (None, 100)          0           activation_3[0][0]               \n",
      "                                                                 activation_4[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "dense_6 (Dense)                 (None, 100000)       10100000    lambda_2[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "custom_variational_layer_2 (Cus [(None, 100000), (No 0           input_3[0][0]                    \n",
      "                                                                 dense_6[0][0]                    \n",
      "==================================================================================================\n",
      "Total params: 30,101,000\n",
      "Trainable params: 30,100,600\n",
      "Non-trainable params: 400\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "adam = optimizers.Adam(lr=learning_rate)\n",
    "vae_layer = CustomVariationalLayer()([methyl_input, methyl_reconstruct])\n",
    "vae = Model(methyl_input, vae_layer)\n",
    "vae.compile(optimizer=adam, loss=None, loss_weights=[beta])\n",
    "\n",
    "vae.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Visualize the connections of the custom VAE model\n",
    "#output_model_file = os.path.join('figures', 'onehidden_vae_architecture.png')\n",
    "#plot_model(vae, to_file=output_model_file)\n",
    "\n",
    "#SVG(model_to_dot(vae).create(prog='dot', format='svg'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train the model\n",
    "\n",
    "The training data is shuffled after every epoch and 10% of the data is heldout for calculating validation loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
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     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5c37ebb1b2164588b62654c7e69659a9"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Wall time: 22min 20s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "hist = vae.fit(np.array(methyl_train_df),\n",
    "               shuffle=True,\n",
    "               epochs=epochs,\n",
    "               verbose=0,\n",
    "               batch_size=batch_size,\n",
    "               validation_data=(np.array(methyl_test_df), None),\n",
    "               callbacks=[WarmUpCallback(beta, kappa),\n",
    "                          TQDMNotebookCallback(leave_inner=True, leave_outer=True)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25f05b86cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize training performance\n",
    "history_df = pd.DataFrame(hist.history)\n",
    "hist_plot_file = os.path.join('figures', 'onehidden_vae_training.pdf')\n",
    "ax = history_df.plot()\n",
    "ax.set_xlabel('Epochs')\n",
    "ax.set_ylabel('VAE Loss')\n",
    "fig = ax.get_figure()\n",
    "fig.savefig(hist_plot_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compile and output trained models\n",
    "\n",
    "We are interested in:\n",
    "\n",
    "1. The model to encode/compress the input methylation data\n",
    "  * Can be possibly used to compress other tumors\n",
    "2. The model to decode/decompress the latent space back into methylation space\n",
    "  * This is our generative model\n",
    "3. The latent space compression of all breast cancer samples\n",
    "  * Non-linear reduced dimension representation of tumors can be used as features for various tasks\n",
    "    * Supervised learning tasks predicting specific methylation events\n",
    "    * Interpolating across this space to observe how methylation changes between two cancer states\n",
    "4. The weights used to compress each latent node\n",
    "  * Potentially indicate learned biology differentially activating tumors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Encoder model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Model to compress input\n",
    "encoder = Model(methyl_input, z_mean_encoded)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Encode methylation into the hidden/latent representation - and save output\n",
    "encoded_methyl_df = encoder.predict_on_batch(methyl_df)\n",
    "encoded_methyl_df = pd.DataFrame(encoded_methyl_df, index=methyl_df.index)\n",
    "\n",
    "encoded_methyl_df.columns.name = 'sample_id'\n",
    "encoded_methyl_df.columns = encoded_methyl_df.columns + 1\n",
    "#encoded_file = os.path.join('data', 'encoded_methyl_onehidden_warmup_batchnorm_100k_2.tsv')\n",
    "#encoded_file = os.path.join('data', 'encoded_methyl_onehidden_warmup_batchnorm_100k_3.tsv')\n",
    "encoded_file = os.path.join('data', 'encoded_methyl_onehidden_warmup_batchnorm_100k_100.tsv')\n",
    "\n",
    "encoded_methyl_df.to_csv(encoded_file, sep='\\t')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decoder (generative) model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build a generator that can sample from the learned distribution\n",
    "decoder_input = Input(shape=(latent_dim, ))  # can generate from any sampled z vector\n",
    "_x_decoded_mean = decoder_to_reconstruct(decoder_input)\n",
    "decoder = Model(decoder_input, _x_decoded_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save the encoder/decoder models for future investigation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "encoder_model_file = os.path.join('models', 'encoder_onehidden_vae_100k_2.hdf5')\n",
    "decoder_model_file = os.path.join('models', 'decoder_onehidden_vae_100k_2.hdf5')\n",
    "\n",
    "#encoder.save(encoder_model_file)\n",
    "#decoder.save(decoder_model_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Model Interpretation - Sanity Check\n",
    "\n",
    "\n",
    "###  Observe the distribution of node activations.\n",
    "\n",
    "We want to ensure that the model is learning a distribution of feature activations, and not zeroing out features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample_id\n",
      "63    4038.473145\n",
      "37    2433.747070\n",
      "22    2425.689941\n",
      "92    2424.977051\n",
      "36    2240.768311\n",
      "4     2216.216797\n",
      "98    2158.351562\n",
      "25    2005.620117\n",
      "1     1971.211304\n",
      "48    1901.296631\n",
      "dtype: float32\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "sample_id\n",
       "11    412.068726\n",
       "58    386.426971\n",
       "68    386.295135\n",
       "73    374.845093\n",
       "23    359.698944\n",
       "17    314.072388\n",
       "82    292.602905\n",
       "62    235.176392\n",
       "85    227.157471\n",
       "45    131.961945\n",
       "dtype: float32"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What are the most and least activated nodes\n",
    "sum_node_activity = encoded_methyl_df.sum(axis=0).sort_values(ascending=False)\n",
    "\n",
    "# Top 10 most active nodes\n",
    "print(sum_node_activity.head(10))\n",
    "\n",
    "# Bottom 10 least active nodes\n",
    "sum_node_activity.tail(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sample_id\n",
       "63    4038.473145\n",
       "37    2433.747070\n",
       "22    2425.689941\n",
       "92    2424.977051\n",
       "36    2240.768311\n",
       "4     2216.216797\n",
       "98    2158.351562\n",
       "25    2005.620117\n",
       "1     1971.211304\n",
       "48    1901.296631\n",
       "79    1859.887939\n",
       "19    1852.519165\n",
       "64    1820.210205\n",
       "59    1765.718262\n",
       "33    1738.396484\n",
       "76    1705.224976\n",
       "69    1700.465576\n",
       "30    1660.718628\n",
       "26    1635.147705\n",
       "56    1599.621582\n",
       "10    1491.937622\n",
       "61    1491.054077\n",
       "72    1446.554932\n",
       "90    1420.479126\n",
       "13    1406.775146\n",
       "99    1363.797852\n",
       "5     1360.532471\n",
       "95    1328.148682\n",
       "89    1279.744507\n",
       "66    1275.218628\n",
       "         ...     \n",
       "78     622.620239\n",
       "53     620.383423\n",
       "14     569.879883\n",
       "54     567.975647\n",
       "9      565.606567\n",
       "20     554.307373\n",
       "35     550.734741\n",
       "12     548.464294\n",
       "49     545.699280\n",
       "43     544.569580\n",
       "38     527.823669\n",
       "24     491.920898\n",
       "87     490.506134\n",
       "94     474.445435\n",
       "39     470.159637\n",
       "3      468.353210\n",
       "84     463.197601\n",
       "74     456.563446\n",
       "88     452.728607\n",
       "81     447.469543\n",
       "11     412.068726\n",
       "58     386.426971\n",
       "68     386.295135\n",
       "73     374.845093\n",
       "23     359.698944\n",
       "17     314.072388\n",
       "82     292.602905\n",
       "62     235.176392\n",
       "85     227.157471\n",
       "45     131.961945\n",
       "Length: 100, dtype: float32"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25f72b16240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of node activity for all 100 latent features\n",
    "sum_node_activity.hist()\n",
    "plt.xlabel('Activation Sum')\n",
    "plt.ylabel('Count');\n",
    "sum_node_activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does an example distribution of two latent features look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25f05e47be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example of node activation distribution for the first two latent features\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.scatter(encoded_methyl_df.iloc[:, 0], encoded_methyl_df.iloc[:, 2])\n",
    "plt.xlabel('Latent Feature 1')\n",
    "plt.xlabel('Latent Feature 2');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25f05fbe4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "xs = encoded_methyl_df.iloc[:, 62]\n",
    "ys = encoded_methyl_df.iloc[:, 36]\n",
    "zs = encoded_methyl_df.iloc[:, 21]\n",
    "ax.scatter(xs, ys, zs)\n",
    "\n",
    "ax.set_xlabel('X Label')\n",
    "ax.set_ylabel('Y Label')\n",
    "ax.set_zlabel('Z Label')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Observe reconstruction fidelity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cg01682111</th>\n",
       "      <th>cg18391209</th>\n",
       "      <th>cg27260772</th>\n",
       "      <th>cg27363327</th>\n",
       "      <th>cg17882374</th>\n",
       "      <th>cg16620382</th>\n",
       "      <th>cg23357130</th>\n",
       "      <th>cg05528899</th>\n",
       "      <th>cg01893212</th>\n",
       "      <th>cg13885357</th>\n",
       "      <th>...</th>\n",
       "      <th>cg26340740</th>\n",
       "      <th>cg07552322</th>\n",
       "      <th>cg26966083</th>\n",
       "      <th>cg03222009</th>\n",
       "      <th>cg13058453</th>\n",
       "      <th>cg17525418</th>\n",
       "      <th>cg17584014</th>\n",
       "      <th>cg01617071</th>\n",
       "      <th>cg00678668</th>\n",
       "      <th>cg01986630</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CpG</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7796806090_R04C01</th>\n",
       "      <td>0.278768</td>\n",
       "      <td>0.510171</td>\n",
       "      <td>0.275315</td>\n",
       "      <td>0.419898</td>\n",
       "      <td>0.810312</td>\n",
       "      <td>0.428347</td>\n",
       "      <td>0.349760</td>\n",
       "      <td>0.614235</td>\n",
       "      <td>0.31760</td>\n",
       "      <td>0.453203</td>\n",
       "      <td>...</td>\n",
       "      <td>0.826854</td>\n",
       "      <td>0.176029</td>\n",
       "      <td>0.674666</td>\n",
       "      <td>0.852578</td>\n",
       "      <td>0.542331</td>\n",
       "      <td>0.843536</td>\n",
       "      <td>0.568932</td>\n",
       "      <td>0.559831</td>\n",
       "      <td>0.808316</td>\n",
       "      <td>0.635946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6285633051_R04C01</th>\n",
       "      <td>0.546676</td>\n",
       "      <td>0.508289</td>\n",
       "      <td>0.194895</td>\n",
       "      <td>0.529796</td>\n",
       "      <td>0.504901</td>\n",
       "      <td>0.540321</td>\n",
       "      <td>0.321682</td>\n",
       "      <td>0.579690</td>\n",
       "      <td>0.54355</td>\n",
       "      <td>0.502641</td>\n",
       "      <td>...</td>\n",
       "      <td>0.861147</td>\n",
       "      <td>0.149234</td>\n",
       "      <td>0.689864</td>\n",
       "      <td>0.888266</td>\n",
       "      <td>0.554548</td>\n",
       "      <td>0.886767</td>\n",
       "      <td>0.555312</td>\n",
       "      <td>0.645130</td>\n",
       "      <td>0.847621</td>\n",
       "      <td>0.731068</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 100000 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   cg01682111  cg18391209  cg27260772  cg27363327  cg17882374  \\\n",
       "CpG                                                                             \n",
       "7796806090_R04C01    0.278768    0.510171    0.275315    0.419898    0.810312   \n",
       "6285633051_R04C01    0.546676    0.508289    0.194895    0.529796    0.504901   \n",
       "\n",
       "                   cg16620382  cg23357130  cg05528899  cg01893212  cg13885357  \\\n",
       "CpG                                                                             \n",
       "7796806090_R04C01    0.428347    0.349760    0.614235     0.31760    0.453203   \n",
       "6285633051_R04C01    0.540321    0.321682    0.579690     0.54355    0.502641   \n",
       "\n",
       "                      ...      cg26340740  cg07552322  cg26966083  cg03222009  \\\n",
       "CpG                   ...                                                       \n",
       "7796806090_R04C01     ...        0.826854    0.176029    0.674666    0.852578   \n",
       "6285633051_R04C01     ...        0.861147    0.149234    0.689864    0.888266   \n",
       "\n",
       "                   cg13058453  cg17525418  cg17584014  cg01617071  cg00678668  \\\n",
       "CpG                                                                             \n",
       "7796806090_R04C01    0.542331    0.843536    0.568932    0.559831    0.808316   \n",
       "6285633051_R04C01    0.554548    0.886767    0.555312    0.645130    0.847621   \n",
       "\n",
       "                   cg01986630  \n",
       "CpG                            \n",
       "7796806090_R04C01    0.635946  \n",
       "6285633051_R04C01    0.731068  \n",
       "\n",
       "[2 rows x 100000 columns]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# How well does the model reconstruct the input methylation data\n",
    "input_methyl_reconstruct = decoder.predict(np.array(encoded_methyl_df))\n",
    "input_methyl_reconstruct = pd.DataFrame(input_methyl_reconstruct, index=methyl_df.index,\n",
    "                                        columns=methyl_df.columns)\n",
    "input_methyl_reconstruct.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CpG mean</th>\n",
       "      <th>CpG abs(sum)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cg18391209</th>\n",
       "      <td>-0.037168</td>\n",
       "      <td>0.300023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cg05528899</th>\n",
       "      <td>0.012118</td>\n",
       "      <td>0.279065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cg24506221</th>\n",
       "      <td>0.003658</td>\n",
       "      <td>0.264213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cg04131969</th>\n",
       "      <td>-0.016613</td>\n",
       "      <td>0.261929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cg12036633</th>\n",
       "      <td>-0.021231</td>\n",
       "      <td>0.261525</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            CpG mean  CpG abs(sum)\n",
       "cg18391209 -0.037168      0.300023\n",
       "cg05528899  0.012118      0.279065\n",
       "cg24506221  0.003658      0.264213\n",
       "cg04131969 -0.016613      0.261929\n",
       "cg12036633 -0.021231      0.261525"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reconstruction_fidelity = methyl_df - input_methyl_reconstruct\n",
    "\n",
    "cpg_mean = reconstruction_fidelity.mean(axis=0)\n",
    "cpg_abssum = reconstruction_fidelity.abs().sum(axis=0).divide(methyl_df.shape[0])\n",
    "cpg_summary = pd.DataFrame([cpg_mean, cpg_abssum], index=['CpG mean', 'CpG abs(sum)']).T\n",
    "cpg_summary.sort_values(by='CpG abs(sum)', ascending=False).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25f05da8e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mean of cpg reconstruction vs. absolute reconstructed difference per sample\n",
    "g = sns.jointplot('CpG mean', 'CpG abs(sum)', data=cpg_summary, stat_func=None);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}