dropout-proportion-z-tests.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dropout Proportion z-Tests\n",
    "\n",
    "I noticed when doing [dropout visualizations](https://nbviewer.jupyter.org/gist/g-eoj/5097c1277359f8b1f8af763ea0163084) that the proportion of the output elements dropped did not equal the dropout rate. I wanted to see if a hypothesis test would detect a significant difference between the dropout rate argument and the proportion of dropped elements. \n",
    "\n",
    "The TensorFlow [documentation](https://www.tensorflow.org/api_docs/python/tf/nn/dropout) for dropout says each component (as defined by `noise_shape`) is dropped independently. Then dropout is based on a Bernoulli trial for each component individually, rather than randomly selecting from all components. So the count of dropped components is a random variable with a binomial distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "keras version: 2.2.2\n",
      "tensorflow version: 1.10.0\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from keras import layers\n",
    "from keras.models import Model\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import norm\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "keras_version = keras.__version__\n",
    "tf_version = keras.backend.tensorflow_backend.tf.VERSION\n",
    "\n",
    "print(\"keras version:\", keras_version)\n",
    "print(keras.backend.backend(), \"version:\", tf_version)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test Function\n",
    "A z-test is appropriate because a binomial distribution can be [approximated](https://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation) by a normal distrbution, if the sample size is large enough."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dropout_rate_ztest(k, n, p_0, alpha=0.05):\n",
    "    \"\"\"One proportion z-test for whether the true dropout rate \n",
    "    is equal to the dropout rate argument. Also plots a\n",
    "    binomial distribution based on the given inputs.\n",
    "    \n",
    "    # Arguments\n",
    "        k: count of dropped outputs\n",
    "        n: count of all outputs (sample size)\n",
    "        p_0: dropout rate argument\n",
    "        alpha: significance level\n",
    "        \n",
    "    When specifying the counts (`k` and `n`), consider the `noise_shape` \n",
    "    argument to dropout. For example, if `noise_shape=(64,1,1,32)` \n",
    "    after a 2D convolution layer, for each sample and each channel the \n",
    "    entire spatial dimensions get dropped, and should only contribute one \n",
    "    to the counts. In this case you could calculate counts like so:\n",
    "    \n",
    "        component_shape = np.divide(output.shape, noise_shape) \n",
    "        not_dropped_count = np.count_nonzero(output) / np.prod(component_shape)\n",
    "        k = np.prod(noise_shape) - not_dropped_count,\n",
    "        n = np.prod(noise_shape)\n",
    "    \"\"\"\n",
    "    \n",
    "    p_hat = k / n\n",
    "    \n",
    "    if p_hat * n < 9 or (1 - p_hat) * n < 9:\n",
    "        print(\"Assumptions for z-test not met. Increase sample size.\")\n",
    "        return\n",
    "    \n",
    "    z = (p_hat - p_0) / (np.sqrt(p_0 * (1 - p_0) / n))\n",
    "    p_value = norm.cdf(-np.abs(z)) * 2  \n",
    "\n",
    "    print(\"Null Hypothesis: true dropout rate =\", p_0)\n",
    "    print(\"Alternative Hypothesis: true dropout rate \\u2260\", p_0)\n",
    "    print(\"Sample Size:\", n)\n",
    "    print(\"Sample Proportion:\", p_hat)\n",
    "    print(\"Test Statistic:\", z)\n",
    "    print(\"p-value:\", p_value)\n",
    "\n",
    "    if p_value < alpha:\n",
    "        print(\"\\nReject the null hypothesis. There is sufficient evidence to conclude\")\n",
    "        print(\"the true dropout rate is not \", p_0, \" at a significance level of \", alpha, \".\", sep='')\n",
    "    else:\n",
    "        print(\"\\nFail to reject the null hypothesis. There is insufficient evidence to conclude\") \n",
    "        print(\"the true dropout rate is not \", p_0, \" at a significance level of \", alpha, \".\", sep='')\n",
    "\n",
    "    fig, ax = plt.subplots(1, 1)\n",
    "    x = np.arange(binom.ppf(0.01, n, p_0), binom.ppf(0.99, n, p_0))\n",
    "    ax.set_title(\"Binomial Distribution for n = \" + str(n) + \" and p = \" + str(p_0))\n",
    "    ax.plot(x, binom.pmf(x, n, p_0), 'black', ms=2)\n",
    "    ax.vlines(x, 0, binom.pmf(x, n, p_0), colors='gray', lw=5, alpha=0.33)\n",
    "    ax.vlines(k, 0, binom.pmf(k, n, p_0), colors='r', lw=2, alpha=1.0)\n",
    "    ax.annotate('dropped count', xy=(k, 0), xytext=(0.5, 0.2), \n",
    "                textcoords='axes fraction', horizontalalignment='center',\n",
    "                arrowprops=dict(facecolor='black', width=2, shrink=0.05));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis Tests\n",
    "\n",
    "I detect dropped elements by counting the number of zeroes in the model ouput, so I'm careful to create input data and models that won't output zeroes when dropout isn't used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regular Dropout after Dense Layer\n",
    "\n",
    "https://keras.io/layers/core/#dropout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null Hypothesis: true dropout rate = 0.5\n",
      "Alternative Hypothesis: true dropout rate ≠ 0.5\n",
      "Sample Size: 6400\n",
      "Sample Proportion: 0.50515625\n",
      "Test Statistic: 0.8249999999999957\n",
      "p-value: 0.40937159069450757\n",
      "\n",
      "Fail to reject the null hypothesis. There is insufficient evidence to conclude\n",
      "the true dropout rate is not 0.5 at a significance level of 0.05.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch_size = 64\n",
    "units = 100\n",
    "dropout_rate = 0.5\n",
    "\n",
    "examples = np.ones(shape=(batch_size,1), dtype=float)\n",
    "\n",
    "inputs = layers.Input(shape=examples.shape[1:])\n",
    "x = layers.Dense(\n",
    "    units=units,\n",
    "    activation=None,\n",
    "    use_bias=False,\n",
    "    kernel_initializer=keras.initializers.Ones())(inputs)\n",
    "x = layers.Dropout(rate=dropout_rate)(x, training=True)\n",
    "\n",
    "output = Model(inputs=inputs, outputs=x).predict(examples, batch_size=batch_size)\n",
    "    \n",
    "dropout_rate_ztest(\n",
    "    k=np.prod(output.shape) - np.count_nonzero(output), # count of dropped outputs\n",
    "    n=np.prod(output.shape), # sample size\n",
    "    p_0=dropout_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SpatialDropout2D after 2D Convolution Layer\n",
    "\n",
    "https://keras.io/layers/core/#spatialdropout2d\n",
    "\n",
    "Note that `SpatialDropout2D()` is equivalent to `Dropout()` with `noise_shape=(batch_size, 1, 1, filters)` when using channels last data format. See [source code](https://github.com/keras-team/keras/blob/master/keras/layers/core.py#L177)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null Hypothesis: true dropout rate = 0.5\n",
      "Alternative Hypothesis: true dropout rate ≠ 0.5\n",
      "Sample Size: 2048\n",
      "Sample Proportion: 0.48974609375\n",
      "Test Statistic: -0.9280776503073436\n",
      "p-value: 0.35336729199329187\n",
      "\n",
      "Fail to reject the null hypothesis. There is insufficient evidence to conclude\n",
      "the true dropout rate is not 0.5 at a significance level of 0.05.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch_size = 64\n",
    "height = 28\n",
    "width = 28\n",
    "channels = 1\n",
    "filters = 32\n",
    "dropout_rate = 0.5\n",
    "\n",
    "examples = np.ones(shape=(batch_size, height, width, channels), dtype=float)\n",
    "noise_shape = (batch_size, 1, 1, filters) # noise_shape used by keras.layers.SpatialDropout2D()\n",
    "\n",
    "inputs = layers.Input(shape=examples.shape[1:])\n",
    "x = layers.Conv2D(\n",
    "    filters=filters,\n",
    "    kernel_size=5,\n",
    "    padding='same',\n",
    "    activation=None,\n",
    "    use_bias=False,\n",
    "    kernel_initializer=keras.initializers.Ones())(inputs)\n",
    "x = layers.SpatialDropout2D(rate=dropout_rate)(x, training=True)\n",
    "\n",
    "output = Model(inputs=inputs, outputs=x).predict(examples, batch_size=batch_size)\n",
    "\n",
    "# Since noise_shape causes dropout to select groups of points (components)\n",
    "# instead of individual points, we want to divide by the component size \n",
    "# so as not to overcount. In the case of SpatialDropout2D, \n",
    "# the spatial dimensions (height * width) define component size.\n",
    "component_shape = np.divide(output.shape, noise_shape) \n",
    "not_dropped_count = np.count_nonzero(output) / np.prod(component_shape)\n",
    "\n",
    "dropout_rate_ztest(\n",
    "    k=np.prod(noise_shape) - not_dropped_count,\n",
    "    n=np.prod(noise_shape), # true sample size / same as component count\n",
    "    p_0=dropout_rate)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}