practical.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Representing and comparing probabilities with kernels - practical\n",
    "\n",
    "Notebook prepared by [Heiko Strathmann](http://herrstrathmann.de/) with additional code by [Dougal Sutherland](http://www.gatsby.ucl.ac.uk/~dougals/) and Kacper Chwialkowski.\n",
    "Feel free to email any questions you have.\n",
    "\n",
    "In this notebook, we will cover implementation details and applications for three types of kernel hypothesis tests:\n",
    "    \n",
    "* Two-sampling testing using the Maximum Mean Discrepancy (MMD)\n",
    "* Independence testing using the Hilbert-Schmidt Independence Criterion (HSIC)\n",
    "* Goodness-of-fit testing using the Kernel Stein Discrepancy (KSD)\n",
    "\n",
    "On the fly, we will introduce basic concepts of statistical hypothesis testing.\n",
    "\n",
    "The notebook contains a number of `# IMPLEMENT` comments, where you are supposed to insert missing code yourself.\n",
    "We also prepared a solution notebook that contains the code we envisioned.\n",
    "\n",
    "Cells are meant to be executed in order (i.e. cells might depend on previous ones).\n",
    "\n",
    "## Dependencies\n",
    "The notebook was written using Python 3.6, but we made an effort to keep it backwards compatible to older versions down to 2.7 (hopefully).\n",
    "\n",
    "We encourage you to use a `conda` environment so you don't modify your system's Python setup (especially due to the problems that come with install TensorFlow and Shogun).\n",
    "\n",
    "The packages you need are:\n",
    "* A standard scipy setup covers most content: `numpy`, `scipy`, `matplotlib`, and of yource `jupyter`\n",
    "* `tensorflow` for gradient-based optimization of test power on the MNIST-GAN example. Note we recommend to install this using `conda install -c conda-forge tensorflow `\n",
    "* Optional: `scikit-learn` for a cross-validation splitting iterator (can implement yourself or use another lib)\n",
    "* Optional: `seaborn`, `pandas` for convenient visualization in some examples\n",
    "* Optional: `tqdm` for a fancy progress bar\n",
    "* Optional: Shogun if you want to run a faster MMD test in the MNIST-GAN example: `conda install -c conda-forge shogun` (do this first as the package currently uses openblas and not MKL, so some of the other packages need to be re-installed).\n",
    "\n",
    "This is an example how to set this environment up and run the notebook server\n",
    "```\n",
    "conda create --name ds3_kernels  python=3.6\n",
    "source activate ds3_kernels\n",
    "conda install -c conda-forge tensorflow \n",
    "conda install -c conda-forge shogun\n",
    "conda install jupyter matplotlib scikit-learn seaborn pandas tqdm\n",
    "jupyter notebook\n",
    "```\n",
    "\n",
    "See the Anaconda/TensorFlow/Shogun installation pages for more details.\n",
    "\n",
    "\n",
    "## Additional files\n",
    "All files can be found at https://github.com/karlnapf/ds3_kernel_testing.\n",
    "They include\n",
    "\n",
    "* This notebook and the solution notebook (we encourage you to not look at this before the practical has finished).\n",
    "* **Provided Python modules**: We provide a few external modules that need to be in the `PYTHONPATH` of your notebook server (just put the files in the same folder as this notebook and start the server from this folder).\n",
    "To see whether this worked, try ```import mmd```, and if it doesn't work, make sure that the file is present in one of the paths when you execute `import sys; print(sys.path)`.\n",
    "* **Provided data**: Put those into the same folder as this notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "try:\n",
    "    from tqdm import tqdm_notebooks as tqdm\n",
    "except ImportError:\n",
    "    tqdm = lambda x: x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-sample testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us begin with some simple data $X\\sim P_X, Y\\sim P_Y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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/kiQblqy+B3h8WrUMo3tYy0eB91TVz6ZdT+O8TceUdF9m3g7sqapPTbueQSWZO3ZGXJJfA97BKs+a1s66uQf4TRbP/vg+8OGq+sF0q+pfkn3Aq4Bnu6Zds3LWUJL3An8PzAE/BnZX1bumW9XKklwK/C2/uE3HzVMuqW9JvgBcwOIdFJ8Bbqqq26daVJ+S/B7wX8B3WPx/FeDG7mr6VS/JbwPbWfx78wrg7qr6i+lWtbKmgl6SdLympm4kSccz6CWpcQa9JDXOoJekxhn0ktQ4g16SGmfQS1LjDHpJatz/AShKy+z42qtCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.load(\"simple.npz\")\n",
    "X = data[\"X\"]\n",
    "Y = data[\"Y\"]\n",
    "plt.hist(X, alpha=0.5)\n",
    "plt.hist(Y, alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Question: do X and Y come from the same distribution?\n",
    "Or in other words: can we reject the null hypothesis that $P_X=P_Y$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The simplest of all test statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by comparing the means of the samples.\n",
    "Clearly, if the distributions are the same, the mean would be zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean differencce: -0.25887364\n"
     ]
    }
   ],
   "source": [
    "def simple_statistic(X,Y, squared=False):\n",
    "    assert X.ndim == Y.ndim == 1\n",
    "    \n",
    "    # IMPLEMENT: compute mean difference of X and Y\n",
    "    result = \n",
    "    \n",
    "    if squared:\n",
    "        result *= result\n",
    "    return result\n",
    "\n",
    "my_statistic = simple_statistic(X,Y)\n",
    "print(\"Mean differencce:\", my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Significant?\n",
    "What would it be if distributions were the same? What if they were different?\n",
    "\n",
    "Let's assume that $P_X=P_Y$ and look at the distribution of the test statistic (null distribution).\n",
    "For that, we can merge the samples and shuffle them, after which they have the same \"joint\" distribution.\n",
    "We can then re-compute the statistic for multiple permutations to get a feeling for how the statistic is distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "25fa8dc628144343b0c63921bb512479",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "def two_sample_permutation_test(test_statistic, X, Y, num_permutations, prog_bar=True):\n",
    "    assert X.ndim == Y.ndim\n",
    "    \n",
    "    statistics = np.zeros(num_permutations)\n",
    "    \n",
    "    range_ = range(num_permutations)\n",
    "    if prog_bar:\n",
    "        range_ = tqdm(range_)\n",
    "    for i in range_:\n",
    "        # concatenate samples\n",
    "        if X.ndim == 1:\n",
    "            Z = np.hstack((X,Y))\n",
    "        elif X.ndim == 2:\n",
    "            Z = np.vstack((X,Y))\n",
    "            \n",
    "        # IMPLEMENT: permute samples and compute test statistic\n",
    "        \n",
    "        my_test_statistic = \n",
    "        statistics[i] = my_test_statistic\n",
    "    return statistics\n",
    "\n",
    "num_permutations = 200\n",
    "statistics = two_sample_permutation_test(simple_statistic, X, Y, num_permutations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have an idea about what to expect from the statistic in case where the distributions are equal.\n",
    "How likely is our particular value of that statistic?\n",
    "We can compare it against the say 95% quantiles of the null distribution.\n",
    "If our statistic lies outside those, we can reject the null with a confidence of 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_permutation_samples(null_samples, statistic=None):\n",
    "    plt.hist(null_samples)\n",
    "    plt.axvline(x=np.percentile(null_samples, 2.5), c='b')\n",
    "    legend = [\"95% quantiles\"]\n",
    "    if statistic is not None:\n",
    "        plt.axvline(x=statistic, c='r')\n",
    "        legend += [\"Actual test statistic\"]\n",
    "    plt.legend(legend)\n",
    "    plt.axvline(x=np.percentile(null_samples, 97.5), c='b')\n",
    "    plt.xlabel(\"Test statistic value\")\n",
    "    plt.ylabel(\"Counts\")\n",
    "    \n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that, depending on the test statistic, there might be multiple ways to compute the null distribution.\n",
    "Not all of them work via sampling it directly, which also can be costly.\n",
    "For example, if we just use the mean difference as a test statistic, and then plug in two Gaussian distributed random variables, we know that the distribution of the statistic is also Gaussian (see the above plot). \n",
    "We might be even able to analytically work out the parameters of this distribution.\n",
    "\n",
    "In case you haven't realized, this is basically a [t-test](https://en.wikipedia.org/wiki/Student%27s_t-test) where we assume that we know that both distributions have unit variance and we can distinguish them via solely looking at their mean.\n",
    "As it will be useful for kernel based test statistics later, we will also look at the distribution of a squared test statistic, in order to make it strictly positive (and zero in expectation if both distributions are the same).\n",
    "Naturally, the average of squared Gaussian random variables has a chi-square distribution -- something that can be used for the kernel tests that we introduce later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "418185889c25429485debe91c36ea492",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT: use squared test statistic\n",
    "simple_statistic_squared = \n",
    "\n",
    "# visualise test\n",
    "statistics = two_sample_permutation_test(simple_statistic_squared, X, Y, num_permutations)\n",
    "my_statistic = simple_statistic_squared(X,Y)\n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Alternative distribution via explicit simulation\n",
    "\n",
    "As a caveat, please note that the test statistic itself has a distribution under the alternative hypothesis ($P_X \\neq P_Y$), and that our computed test statistic is only a single sample from this distribution.\n",
    "In practice, it is unfortunately not possible to look at the distribution of the test under the alternative, as this would require a way to generate more data.\n",
    "We can try this for a synthetic example where we have infinite data though."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8792f6acf2b84756a7d715bb0a991253",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c8923803d8d84b20b81753687d74a94a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "# we make a model where the null distribution is false\n",
    "shift = .3\n",
    "N = 200\n",
    "X = np.random.randn(N)\n",
    "Y = np.random.randn(N)+shift\n",
    "\n",
    "statistics_null = two_sample_permutation_test(simple_statistic_squared, X, Y, num_permutations)\n",
    "my_statistic = simple_statistic_squared(X,Y) # this is a single sample from the alternative\n",
    "\n",
    "statistics_alt = np.zeros(num_permutations)\n",
    "for i in tqdm(range(num_permutations)):\n",
    "    # IMPLEMENT: generate more data from the alternative\n",
    "    X = \n",
    "    Y =  \n",
    "    \n",
    "    statistics_alt[i] = simple_statistic_squared(X,Y)\n",
    "    \n",
    "plt.figure(figsize=(12,4))\n",
    "plot_permutation_samples(statistics_null, my_statistic)    \n",
    "plt.hist(statistics_alt, alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, even though most of the alternative distribution far larger than the null, we can be unlucky: there are datasets for which the test would not reject the null simply by chance -- we only have a single draw from the alternative.\n",
    "With this fixed seed, it turns out that we have been unlucky and would have not rejected the null hypothesis even it is not true.\n",
    "You could play with the sample size and observe how this impacts the position of the alternative distribution (and as such the test power).\n",
    "\n",
    "Let's try the test on another dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Means: -0.05499658 0.027213123\n",
      "Standard deviations: 1.046988 0.9609663\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eb05c67cf5f849e49d1864a9bffd27fa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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6wazNF3DATV+jVlVfqKp93eZ2Zu5XGAtVtbOqxu0muF88mqOqfgrsfzTHWKiqO4GnRl3HXKrqyaq6t3v/Q2bCamzudq8ZP+o2n9P9jNW/1yQrgDcCHz3cYxv0C0jyviSPA29m/Gb0s70d+NyoixhzPppjCJKsAl4L3D3aSp6pWxa5D9gLbK2qsaoP+DDwHuDnh3vgZ33QJ/mvJA/M8bMOoKquqqqVwI3AO8atvq7PVcz8an3juNU2ZhZ8NIfml+SFwCeBdx7wG+/IVdXPumXWFcDpSU4ddU37JTkf2FtV94xi/CP/i0d6qqrXH2LXfwc+C1y9hOX8koXqS7IeOB84pw7ztbKL+LMbFws+mkMHl+Q5zIT8jVX1qVHXczBV9XSSLzHzece4fLB9JnBBkjcAxwAvTvJvVfWHh2PwZ/2Mfj5JVs/avAB4eFS1zCXJWuAK4IKq+vGo6zkC+GiOASUJcB2ws6o+NOp6DpRkYv9VZ0meB7yeMfr3WlWbqmpFVa1i5u/dFw9XyINBv5BruqWI+4HfZeYT83HyD8CLgK3dJaD/POqC9kvy+0mmgDOAzyb5/Khr6j643v9ojp3AzeP0aI4kNwF3Aa9IMpVkw6hrmuVM4C3A2d3ftfu62em4OAnY1v1b/Qoza/SH9RLGceadsZLUOGf0ktQ4g16SGmfQS1LjDHpJapxBL0mNM+glqXEGvSQ1zqCXpMb9P4qCFxL8Tx8mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.load(\"almost_simple.npz\")\n",
    "X = data[\"X\"]\n",
    "Y = data[\"Y\"]\n",
    "plt.hist(X, alpha=0.5)\n",
    "plt.hist(Y, alpha=0.5)\n",
    "\n",
    "# IMPLEMENT: print mean and std deviation of data\n",
    "print()\n",
    "\n",
    "my_statistic = simple_statistic(X,Y)\n",
    "statistics = two_sample_permutation_test(simple_statistic, X, Y, num_permutations)\n",
    "\n",
    "plt.figure()\n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now for the squared test statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "35b70906f5354b819f96895332f4cc3c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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RkVAKCBERCRVJQJjZA2a22sxWmdkUM0szs6ZmtsTMNpjZNDOrGUVtIiISk/SAMLPGwAAgx90zgWpAX2A08Ly7Nwf+CfRLdm0iIvKtqE4xVQdqmVl1oDbwGXApMCN4fhJwXUS1iYgIEQSEu38KjAG2EQuGvcAyYI+7Hwqa5QONw7Y3s/5mlmtmubt27UpGySIiJ6UoTjGlA9cCTYGzgdOAK0Oaetj27j7B3XPcPadhw4aJK1RE5CQXxSmmy4At7r7L3b8B3gA6AmcEp5wAmgDbI6hNREQCUQTENqCDmdU2MwO6AWuABUDvoM3twJsR1CYiIoEorkEsIXYxejnwcVDDBGAw8KCZbQTqA68muzYREflW9RM3qXju/jjw+FGrNwPtIyhHRERC6JvUIiISSgEhIiKhFBAiIhJKASEiIqEUECIiEkoBISIioRQQIiISSgEhIiKhFBAiIhJKASEiIqEUECIiEkoBISIioRQQIiISSgEhIiKhFBAiIhJKASEiIqFKHRBmlm5mrRNRjIiIpI64AsLMFprZ6WZWD/gb8Gszey6xpYmISJTiHUHUdfcvgB8Cv3b3C4HLEleWiIhELd6AqG5mjYAbgLcTWI+IiKSIeAPiSeAPwEZ3/9DMmgEbEleWiIhErXqc7T5z96IL0+6+WdcgRESqtnhHED+Pc52IiFQRxx1BmNnFQEegoZk9WOyp04FqiSxMRESidaJTTDWB7wTt6hRb/wXQO1FFiYhI9I4bEO7+R+CPZvaau29NUk0iIpIC4r1IfaqZTQAyim/j7pcmoigREYlevAHxO+Al4BXgcHkPamZnBPvKBBy4E1gPTCMWQnnADe7+z/IeS0REyibeTzEdcvdfuvtSd19W+FOO474AvOfu5wNZwFpgCPC+uzcH3g+WRUQkIvEGxO/N7L/NrJGZ1Sv8KcsBzex04L+AVwHc/Wt33wNcC0wKmk0CrivL/kVEpGLEe4rp9uD3w8XWOdCsDMdsBuwiNuFfFrAMuA84y90/A3D3z8zszDLsW0REKkhcAeHuTSv4mG2Be919iZm9QClOJ5lZf6A/wDnnnFOBZYmISHFxBYSZ3Ra23t0nl+GY+UC+uy8JlmcQC4gdZtYoGD00AnaWcMwJwASAnJwcL8PxRUQkDvGeYmpX7HEa0A1YDpQ6INz9H2b2iZmd5+7rg32tCX5uB0YFv98s7b5FRKTixHuK6d7iy2ZWF3i9HMe9F/iNmdUENgM/InbBfLqZ9QO2AX3KsX8RESmneEcQRzsANC/rQd19BZAT8lS3su5TREQqVrzXIH5P7FNLEJukrwUwPVFFiYhI9OIdQYwp9vgQsNXd8xNQj4iIpIi4vigXTNq3jtiMrunA14ksSkREohdXQJjZDcBSYheObwCWmJmm+xYRqcLiPcU0HGjn7jsBzKwhMI/YdxhERKQKincuplMKwyFQUIptRUSkEop3BPGemf0BmBIs3wjMSUxJIiKSCk50T+rvE5tE72Ez+yHQGTDgr8BvklCfiIhE5ESnicYCXwK4+xvu/qC7P0Bs9DA20cWJiEh0ThQQGe6+8uiV7p5L7M5vIiJSRZ0oINKO81ytiixERERSy4kC4kMzu+volcGEeuW55aiIiKS4E32K6X5glpndzLeBkAPUBK5PZGEiIhKt4waEu+8AOppZVyAzWP2Ou89PeGUiIhKpeO8HsQBYkOBaREQkhejb0CIiEkoBISIioRQQIiISSgEhIiKhFBAiIhJKASEiIqEUECIiEkoBISIioRQQIiISSgEhIiKhFBAiIhJKASEiIqEiCwgzq2ZmH5nZ28FyUzNbYmYbzGyamdWMqjYREYl2BHEfsLbY8mjgeXdvDvwT6BdJVSIiAkQUEGbWBOgJvBIsG3ApMCNoMgm4LoraREQkJqoRxFhgEPDvYLk+sMfdDwXL+UDjKAoTEZGYpAeEmV0N7HT34ve0tpCmXsL2/c0s18xyd+3alZAaRUQkmhFEJ+AaM8sDphI7tTQWOMPMCu9w1wTYHraxu09w9xx3z2nYsGEy6hUROSklPSDcfai7N3H3DKAvMN/dbyZ2S9PeQbPbgTeTXZuIiHwrlb4HMRh40Mw2Ersm8WrE9YiInNSqn7hJ4rj7QmBh8Hgz0D7KekRE5FupNIIQEZEUooAQEZFQCggREQmlgBARkVAKCBERCaWAEBGRUAoIEREJpYAQEZFQCggREQmlgBARkVAKCBERCaWAEBGRUAoIEREJpYAQEZFQCggREQmlgBARkVAKCBERCaWAEBGRUAoIEREJFek9qSW5Moa8E9mx80b1jOzYIlI2GkGIiEgojSAiUN538lM3FwDQN8IRgYhUfRpBiIhIKAWEiIiEUkCIiEgoBYSIiIRSQIiISCgFhIiIhEp6QJjZd81sgZmtNbPVZnZfsL6emf2vmW0IfqcnuzYREflWFCOIQ8BD7t4C6AD81MxaAkOA9929OfB+sCwiIhFJekC4+2fuvjx4/CWwFmgMXAtMCppNAq5Ldm0iIvKtSK9BmFkG0AZYApzl7p9BLESAM0vYpr+Z5ZpZ7q5du5JVqojISSeygDCz7wAzgfvd/Yt4t3P3Ce6e4+45DRs2TFyBIiInuUgCwsxqEAuH37j7G8HqHWbWKHi+EbAzitpERCQmik8xGfAqsNbdnyv21FvA7cHj24E3k12biIh8K4rZXDsBtwIfm9mKYN0wYBQw3cz6AduAPhHUJiIigaQHhLt/AFgJT3dLZi0iIlIyfZNaRERCKSBERCSUAkJEREIpIEREJJQCQkREQikgREQklAJCRERCKSBERCSUAkJEREIpIEREJJQCQkREQikgREQklAJCRERCRTHdt0jSZAx5J5Lj5o3qGclxRSqSRhAiIhJKASEiIqEUECIiEkoBISIioXSRWpIiqovFIlJ2GkGIiEgoBYSIiIRSQIiISChdgxBJgCivuehLelJRNIIQEZFQCggREQmlU0wiVUwqfqT4H5s7AJAxZHFC9h/VabWqfipRIwgREQmVUiMIM+sBvABUA15x91ERlyQilUAqjpqqgpQZQZhZNeBF4EqgJXCTmbWMtioRkZNXygQE0B7Y6O6b3f1rYCpwbcQ1iYictFIpIBoDnxRbzg/WiYhIBMzdo64BADPrA3R39x8Hy7cC7d393qPa9Qf6B4vnAevLeMgGwO4yblvVqW9Kpr4pmfqmZKnWN99z94YnapRKF6nzge8WW24CbD+6kbtPACaU92BmluvuOeXdT1WkvimZ+qZk6puSVda+SaVTTB8Czc2sqZnVBPoCb0Vck4jISStlRhDufsjM7gH+QOxjrhPdfXXEZYmInLRSJiAA3H0OMCdJhyv3aaoqTH1TMvVNydQ3JauUfZMyF6lFRCS1pNI1CBERSSFVMiDMrIeZrTezjWY2JOT5U81sWvD8EjPLKPbc0GD9ejPrnsy6k6GsfWNm9c1sgZntM7Pxya47GcrRN5eb2TIz+zj4fWmya0+0cvRNezNbEfz8zcyuT3btiVSef2uC588J/p8amKyaS8Xdq9QPsQvcm4BmQE3gb0DLo9r8N/BS8LgvMC143DJofyrQNNhPtahfU4r0zWlAZ+BuYHzUryXF+qYNcHbwOBP4NOrXk0J9UxuoHjxuBOwsXK7sP+Xpl2LPzwR+BwyM+vWE/VTFEUQ8U3ZcC0wKHs8AupmZBeunuvu/3H0LsDHYX1VR5r5x9/3u/gFwMHnlJlV5+uYjdy/8zs5qIM3MTk1K1clRnr454O6HgvVpQFW66Fmef2sws+uAzcT+ZlJSVQyIeKbsKGoT/PHuBerHuW1lVp6+qeoqqm96AR+5+78SVGcUytU3ZnaRma0GPgbuLhYYlV2Z+8XMTgMGA08moc4yq4oBYSHrjn7XUlKbeLatzMrTN1VdufvGzFoBo4H/V4F1pYJy9Y27L3H3VkA7YKiZpVVwfVEpT788CTzv7vsqvKoKVBUDIp4pO4ramFl1oC7weZzbVmbl6Zuqrlx9Y2ZNgFnAbe6+KeHVJleF/N24+1pgP7HrNFVBefrlIuAZM8sD7geGBV8UTilVMSDimbLjLeD24HFvYL7Hrhi9BfQNPnnQFGgOLE1S3clQnr6p6srcN2Z2BvAOMNTdFyWt4uQpT980Df5hxMy+R2yCzbzklJ1wZe4Xd/+Bu2e4ewYwFviZu6fepwOjvkqeiB/gKuDvxD5hMDxY9xRwTfA4jdgnBzYSC4BmxbYdHmy3Hrgy6teSYn2TR+zdzz5i74xaJrv+VOwb4BFi74xXFPs5M+rXkyJ9cyuxi7ArgOXAdVG/llTol6P28QQp+ikmfZNaRERCVcVTTCIiUgEUECIiEkoBISIioRQQIiISSgEhIiKhFBCSsoIZZAtnAv2HmX1abLlmKfZzp5n9RynaX2pmHUrbzsx+amY3V1T78jCz6ma2JxH7lpNHSt1RTqQ4dy8AsgHM7Algn7uPKcOu7iT2Gfx/xNn+UmA3sLg07dz9xQpuLxIpjSCkUjKz281saTCa+IWZnRK8a349uC/DKjMbYGY3EguZaWEjDzN7wMzWBPcq+B8z+0/gx8DDQfuOZnZtMJf/R2Y218zOLKHdCDO7vxT7Ld7+XDObH7RfHnLfgGfNrH+x5RFmdp+ZnR5st9zMVprZ1SF9dZmZzS62/JKZ3RI8bmdmf7TYfSzeNbOzKuK/j1QNGkFIpWNmmcD1QEd3P2RmE4hNc7AJaODuFwTtznD3PWZ2L3CPu68I2d0g4Hvu/nWx9q8Au919bLCfdOAtd3czuxt4yN0Hh7S7qpT7Ld5+CvCEu//eYpPZHf3mbSowim/vbdwH6Ap8BVzr7l+a2ZnAIuDtOPvxVOAFYt/63R2c7noa6H/8LeVkoYCQyugyYjOD5lpsav1axKZU/gNwnpm9AMwB5saxr9XA/5jZm8DsEtqcA0wPrmOcSmxqhYrYL1AUQA3c/fcA7n7MPTfc/UMz+27wDr8J8A933x6MiEabWWfg38B3zawBEM/1hxZAK2Be0I/ViE2hIgIoIKRyMmCiuz96zBNmrYErgQHE7s1wonfD3YFLiN3Y5ZFgdHK0F4lNpjbHzC4Djrm1ZBn3W1w8c97MJPaaMoiNKABuIzZDaNtgNJVPbP6f4g5x5Iik8HkDVrr7D+I4tpyEdA1CKqN5wA3BO+XCTzudY2YNAXP33wGPA22D9l8CdY7eiZlVA5q4+3zgYaAhsVtkHt2+LvCpxd5m315sfXn3C4C7/xPYbWb/J9g+zcxqh7zuqcROpf2QWFgU1rYzCIfLCb/B1VaglZnVDEYrhffMXgM0NrP2wXFrWuyeFiKAAkIqIXf/mNgNV+aZ2Upip5LOIjbv/p/MbAXwMjAs2OTXwCshF6mrA78N9rEcGO3uXwJvEgugj8ysI7HZNmcBfwR2FNv+6Hal3W9xNwMPBdt8QCxUjn7dfwvWb3H3ncHq14GOZpZL7LrEhpDtthA7zfUxMDmoCY/d9a438JyZ/Q34iNh9CkQANJuriIiE0whCRERCKSBERCSUAkJEREIpIEREJJQCQkREQikgREQklAJCRERCKSBERCTU/wfVcY6zZTJwJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT: visualize test for squared statistic\n",
    "simple_statistic_squared = \n",
    "statistics = \n",
    "my_statistic = \n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, both test statistics essentially have no chance in distinguishing this data.\n",
    "(althogh keep in mind we could have been unlucky as outlined above).\n",
    "For now, let's just assume we only have a single dataset to compute the test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadratic time MMD\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already seen the quadratic time MMD: it was the squared difference of the sample means above, if we had used a linear kernel (where the feature space embedding is the identity function).\n",
    "This test wasn't able to distinguish the above distributions, but let's try a different kernel.\n",
    "\n",
    "We will use the unbiased statistic here, defined as\n",
    "$$ \n",
    "\\frac{1}{n(n-1)}\\sum_{i=1}^n\\sum_{j\\neq i}^m k(x_i,x_j) + \\frac{1}{m(m-1)}\\sum_{i=1}^n\\sum_{j\\neq i}^mk(y_i,y_j) -2\\frac{1}{nm}\\sum_{i=1}^n \\sum_{j=1}^m k(x_i,y_j)\n",
    "$$\n",
    "See the slides for more details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernels\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first need to implement a kernel function.\n",
    "Though we could use a framework to do this for us, it is quite instructive to do this ourselves (at least once).\n",
    "\n",
    "We will start with a Gaussian kernel\n",
    "$$\n",
    "k(x,y) = \\exp \\left( - \\frac{||x-y||_2^2}{\\sigma}\\right)\n",
    "$$\n",
    "with some bandwidth parameter $\\sigma$ (note there are many different parametrizations!).\n",
    "\n",
    "This kernel is translation invariant, and like many other kernels, it is defined in terms of pairwise (Euclidean) distances between the data.\n",
    "Let's implement it this way so we can easily try other kernels that are translation invariant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import squareform, pdist, cdist\n",
    "\n",
    "def sq_distances(X,Y=None):\n",
    "    \"\"\"\n",
    "    If Y=None, then this computes the distance between X and itself\n",
    "    \"\"\"\n",
    "    assert(X.ndim==2)\n",
    "\n",
    "    # IMPLEMENT: compute pairwise distance matrix. Don't use explicit loops, but the above scipy functions\n",
    "    # if X=Y, use more efficient pdist call which exploits symmetry\n",
    "    if Y is None:\n",
    "        sq_dists = \n",
    "    else:\n",
    "        assert(Y.ndim==2)\n",
    "        assert(X.shape[1]==Y.shape[1])\n",
    "        sq_dists = \n",
    "\n",
    "    return sq_dists\n",
    "\n",
    "def gauss_kernel(X, Y=None, sigma=1.0):\n",
    "    \"\"\"\n",
    "    Computes the standard Gaussian kernel k(x,y)=exp(- ||x-y||**2 / (2 * sigma**2))\n",
    "\n",
    "    X - 2d array, samples on left hand side\n",
    "    Y - 2d array, samples on right hand side, can be None in which case they are replaced by X\n",
    "    \n",
    "    returns: kernel matrix\n",
    "    \"\"\"\n",
    "\n",
    "    # IMPLEMENT: compute squared distances and kernel matrix\n",
    "    sq_dists = sq_distances(X,Y)\n",
    "    K = np.exp(-sq_dists / (2 * sigma**2))\n",
    "    return K\n",
    "\n",
    "# IMPLEMENT\n",
    "def linear_kernel(X, Y):\n",
    "    return np.dot(X, Y.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the kernel at hand, we can implement the quadratic time MMD statistic as a function of the kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quadratic_time_mmd(X,Y,kernel):\n",
    "    assert X.ndim == Y.ndim == 2\n",
    "    K_XX = kernel(X,X)\n",
    "    K_XY = kernel(X,Y)\n",
    "    K_YY = kernel(Y,Y)\n",
    "       \n",
    "    n = len(K_XX)\n",
    "    m = len(K_YY)\n",
    "    \n",
    "    # IMPLEMENT: unbiased MMD statistic (could also use biased, doesn't matter if we use permutation tests)\n",
    "    mmd = \n",
    "    return mmd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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     "text": [
      "\n"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_kernel = lambda X,Y : gauss_kernel(X,Y,sigma=0.3)\n",
    "my_mmd = lambda X,Y : quadratic_time_mmd(X[:,np.newaxis],Y[:,np.newaxis], my_kernel)\n",
    "\n",
    "statistics = two_sample_permutation_test(my_mmd, X, Y, num_permutations)\n",
    "my_statistic = my_mmd(X,Y)\n",
    "\n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This seems much better: the Gaussian kernel allows us to very clearly distinguish the two distributions.\n",
    "\n",
    "Now let us try the MMD with a linear kernel and compare it to the above.\n",
    "In particular, compare (and think about) the relationship to the simple squared mean difference statistic we computed above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "05f6bcd6fd1d48e4a8ca37a7b570ce91",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT: visualize test using linear kernel\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is almost the same result as we had for doing the simple squared statistic above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# IMPLEMENT (optional): try mix and matching kernels and data sources\n",
    "# e.g. try a periodic kernel on data that differs in frequency space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Alternative methods to estimate the null distribution\n",
    "\n",
    "There are multiple other way to get our hands on the distribution of the MMD test statistic under the null hypothesis.\n",
    "\n",
    "We know that asymptotically, the distribution is an infinite sum of Chi-square variables -- intractable unfortunately.\n",
    "Techniques to approximate it include\n",
    "\n",
    "* moment matching using a Gamma distribution: fast, but doesn't result in a consistent test\n",
    "* a spectral approximation: use Eigenvalues of the kernel matrix to sample from the null distribution in closed form. Costly (cubic!) for large sample sets.\n",
    "* wild-bootstrap: a technique used for correlated samples that is similar to permuting\n",
    "* linear time statistics: for those, one can often show that the null distribution is Gaussian and its variance can be estimated in closed form.\n",
    "\n",
    "We do not cover those here since they require some more details.\n",
    "The permutation test, while potentially slower, is easy to understand and works for most applications (if implemented well).\n",
    "\n",
    "Some resources:\n",
    "* [a Shogun notebook](http://www.shogun-toolbox.org/notebook/latest/mmd_two_sample_testing.html), old but contains many null approximation methods\n",
    "* Linear time tests based on analytic function comparisons (see notes at end of section)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MMD witness function in the RKHS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One nice feature of the MMD is that we can see where the density functions are different via querying the (empirical) MMD witness function.\n",
    "This is just the difference of the empirical mean embeddings in the RKHS and thus computable (remember the MMD is the RKHS norm of this witness function).\n",
    "See the slides for details.\n",
    "\n",
    "$$f^*(\\cdot)=\\hat \\mu_X(\\cdot) - \\hat \\mu_Y(\\cdot) $$\n",
    "\n",
    "Let's define a grid and evaluate the witness function on it to see where X and Y differ most."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/heiko/software/anaconda3/envs/ds3_kernels/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = np.linspace(np.min(X), np.max(X))\n",
    "\n",
    "my_kernel = lambda X,Y : gauss_kernel(X,Y, sigma=0.5)\n",
    "\n",
    "# IMPLEMENT: evaluate MMD witness function on grid\n",
    "phi_X = \n",
    "phi_Y = \n",
    "witness = \n",
    "\n",
    "plt.plot(grid, witness)\n",
    "\n",
    "plt.hist(X, alpha=0.5, normed=True)\n",
    "plt.hist(Y, alpha=0.5, normed=True);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the witness function is positive where X as a higher density than Y, and negative vice versa.\n",
    "It is zero where both densities match.\n",
    "Intuitively, the RKHS norm of this function can only be zero if the densities match everywhere, and it grows as the densities differ on more and more points in their support.\n",
    "Of course, this kind of visualization only works in few dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notes on efficient implementations\n",
    "Note that the above implemention of the MMD, and in particular the permutation test, is extremelty inefficient since the kernel matrix is re-computed in every iteration of the permutation test (and the data is copied around for concatenation as well).\n",
    "We could precompute it once, but then we still would be required to permute it multiple times.\n",
    "\n",
    "We have written a multi-threaded version in C++ that does not permute the matrix, but simply traverses it multiple times, which makes the algorithm L2 cache friendly and therefore hundreds of times faster.\n",
    "See:\n",
    "* http://shogun.ml for the toolbox\n",
    "* http://shogun.ml/examples/latest/examples/statistical_testing/quadratic_time_mmd.html for an API example\n",
    "* http://www.shogun-toolbox.org/notebook/latest/mmd_two_sample_testing.html for a complex demo in Python\n",
    "* https://arxiv.org/abs/1611.04488 for a paper with performance details\n",
    "\n",
    "We will use Shogun for a larger example below.\n",
    "You could time our handwritten implementation against it, or you can tune the Python implementation and try to beat it ;)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernel learning (aka which kernel parameter to choose?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen that the Gaussian kernel above increased the power of the test.\n",
    "But what happened if we chose a wrong kernel parameter?\n",
    "Let's pick a bad one and see."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8ca84042e3bd4e9980c50d6a69eb2fd4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_kernel = lambda X,Y : gauss_kernel(X,Y,sigma=0.001)\n",
    "my_mmd = lambda X,Y : quadratic_time_mmd(X[:,np.newaxis],Y[:,np.newaxis], my_kernel)\n",
    "\n",
    "statistics = two_sample_permutation_test(my_mmd, X, Y, num_permutations)\n",
    "my_statistic = my_mmd(X,Y)\n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output is quite different, the performance of kernel tests indeed crucially depends on the chosen parameters.\n",
    "How to chose those in practice?\n",
    "\n",
    "For simple datasets, there is a heuristic rule to chose the parameter of a Gaussian kernel: using the median of the pairwise distances of the data.\n",
    "See https://arxiv.org/abs/1707.07269 for details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6585612327494343\n"
     ]
    }
   ],
   "source": [
    "def gaussian_kernel_median_heuristic(Z):\n",
    "    # IMPLEMENT: compute the median of the pairwise distances in Z\n",
    "    # (not taking zero distance between identical samples (diagonal) into account)\n",
    "    sq_dists = \n",
    "    median_dist = \n",
    "    \n",
    "    return np.sqrt(median_dist/2.0) # our kernel uses a bandwidth of 2*(sigma**2)\n",
    "\n",
    "sigma_median = gaussian_kernel_median_heuristic(np.vstack((X[:,np.newaxis],Y[:,np.newaxis])))\n",
    "print(sigma_median)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we could probably get away with sub-sampling the data to compute pair-wise distances to speed up computing the heuristic, as it stabilizes quickly.\n",
    "In addition, we should probably re-use the pairwise distances when computing the kernel matrix; again, see Shogun.\n",
    "\n",
    "Let's try the heuristic for the statistical test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "11b39294d16c430995146d90c843a5e3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_kernel = lambda X,Y : gauss_kernel(X,Y,sigma=sigma_median)\n",
    "my_mmd = lambda X,Y : quadratic_time_mmd(X[:,np.newaxis],Y[:,np.newaxis], my_kernel)\n",
    "\n",
    "statistics = two_sample_permutation_test(my_mmd, X, Y, num_permutations)\n",
    "my_statistic = my_mmd(X,Y)\n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This worked great!\n",
    "But it doesn't always.\n",
    "\n",
    "Let's try the median heuristic on the following dataset, referred to as Gaussian blobs, see https://papers.nips.cc/paper/4727-optimal-kernel-choice-for-large-scale-two-sample-tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.load(\"blobs_zoomed.npz\")\n",
    "X = data[\"X\"]\n",
    "Y = data[\"Y\"]\n",
    "plt.plot(X[:,0], X[:,1], 'b.', alpha=0.5)\n",
    "plt.plot(Y[:,0], Y[:,1], 'r.', alpha=0.5)\n",
    "plt.title(\"One blob\")\n",
    "\n",
    "plt.figure()\n",
    "data = np.load(\"blobs.npz\")\n",
    "X = data[\"X\"]\n",
    "Y = data[\"Y\"]\n",
    "plt.plot(X[:,0], X[:,1], 'b.', alpha=0.5)\n",
    "plt.plot(Y[:,0], Y[:,1], 'r.', alpha=0.5);\n",
    "plt.title(\"All blobs\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, the two distributions are very different.\n",
    "On the grid, the scale at which they differ, however, is somewhat invisible from the median heuristic, which looks at global scaling of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median bw/sigma: 51.60189981691304 / 5.079463545341823\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9a89969b289c41c4bfa3c3c8a8233f66",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma_median = gaussian_kernel_median_heuristic(np.vstack((X,Y)))\n",
    "print(\"median bw/sigma:\", 2*(sigma_median**2), \"/\", sigma_median)\n",
    "\n",
    "# IMPLEMENT: visualize test using median heuristic\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Somehow, the median distance does not really represent the scale on which the two distribution are differing here (they clearly do!).\n",
    "We have figure out how to fix that though."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using cross-validation to select a single kernel parameter\n",
    "\n",
    "As a modern ML scientist, your first reflex might be to just try a bunch of different kernel parameters, and compute a cross-validation estimate of the test power.\n",
    "This involves computing the test for the \"training partitions\" of every fold, and average the number of rejections.\n",
    "Let's start with that.\n",
    "Note that we have to use a different \"training\" dataset to learn the kernel -- otherwise the test would over-fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/heiko/software/anaconda3/envs/ds3_kernels/lib/python3.6/site-packages/sklearn/cross_validation.py:41: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f92aba111d9040c9850194dcb829d8ca",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=3), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Let's start with few values\n",
    "log_sigmas = np.array([-5, 0., 10])\n",
    "\n",
    "num_folds = 5\n",
    "data = np.load(\"blobs2.npz\")\n",
    "X_learn = data[\"X\"]\n",
    "Y_learn = data[\"Y\"]\n",
    "\n",
    "from sklearn.cross_validation import KFold\n",
    "\n",
    "test_powers = np.zeros(len(log_sigmas))\n",
    "np.random.seed(0)\n",
    "\n",
    "for i, log_sigma in tqdm(list(enumerate(log_sigmas))):\n",
    "    # IMPLEMENT: define kernel and mmd\n",
    "    my_kernel = \n",
    "    my_mmd = \n",
    "\n",
    "    rejects = []\n",
    "    for train, _ in  KFold(len(X_learn), n_folds=5, shuffle=True):\n",
    "        # IMPLEMENT: split data into train and test folds\n",
    "        X_learn_train = \n",
    "        Y_learn_train = \n",
    "        \n",
    "        # IMPLEMENT: compute test statistic and null distribution, use prog_bar=False\n",
    "        statistics = \n",
    "        my_statistic = \n",
    "                \n",
    "        # IMPLEMENT: compute p-value as the quantile of the test statistic in the null distribution\n",
    "        p_value = \n",
    "        rejects += [p_value<0.05]\n",
    "    \n",
    "    test_powers[i] = np.mean(rejects)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(log_sigmas, test_powers)\n",
    "plt.xlabel(\"Log sigma\")\n",
    "plt.ylabel(\"Test power estimate\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This seems to give us an idea of which kernel parameter is better.\n",
    "Unfortunately, this approach is quite costly and noisy.\n",
    "In reality, we would also want to use more folds, repeat the x-validation, and try out more kernel parameters (play with it and you will see).\n",
    "\n",
    "We could try one of the faster approximations for the null distribution mentioned above, for example the moment matching Gamma approach.\n",
    "This would speed up the procedure, however, the Gamma approximation has its limits in how accurate it is, especially for extreme values of the kernel.\n",
    "\n",
    "Instead, we will do something better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimal kernel via maximising the ratio of mmd and its variance, see https://arxiv.org/abs/1611.04488"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen that estimating the test power using cross-validation is a bit messy; it is also not differentiable.\n",
    "\n",
    "Luckily, there is a closed form criterion that acts as a surrogate for the test power: the MMD divided by its variance.\n",
    "You have seen in the slides that maximising this directly maximises the power of the statistical test -- without ever computing the test.\n",
    "\n",
    "Long story short, you can\n",
    "\n",
    "1. Pick a training set (not the one you use for performing the test, to avoid overfitting)\n",
    "2. Choose the kernel that maximises the value of the MMD, divided by its standard variance\n",
    "3. Enjoy a test that has higher power"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As implementing the variance of the MMD estimator is slightly more complicated, we have provided a TensorFlow implementation for you (so we can later automagically differentiate it).\n",
    "Feel free to examine the imported code in `mmd.py`.\n",
    "\n",
    "(Note that the provided implementation uses a biased MMD statistic, and as such produces slightly different numbers)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MMD and ratio: (0.003497325, 7.8510857)\n"
     ]
    }
   ],
   "source": [
    "# provided implementation\n",
    "import tensorflow as tf\n",
    "import mmd\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init = tf.global_variables_initializer()\n",
    "    sess.run(init)\n",
    "    print(\"MMD and ratio:\", sess.run(mmd.rbf_mmd2_and_ratio(X,Y, sigma=sigma_median)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As seen above, the most naive way to select a kernel to to come up with a number of baseline kernels, then simply compute the ratio of MMD and standard deviation for all of them, and finally to pick the kernel with the largest ratio.\n",
    "Remember it is important to do this on a separate \"training\" dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "809a3e1c443c4f1ea524bc83c844d322",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=10), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "best sigma: 0.21544346900318834\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.load(\"blobs2.npz\")\n",
    "X_learn = data[\"X\"]\n",
    "Y_learn = data[\"Y\"]\n",
    "\n",
    "# sigma = 10**log_sigma\n",
    "log_sigmas = np.linspace(-2, 2,10)\n",
    "                         \n",
    "ratios = np.empty(len(log_sigmas))\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init = tf.global_variables_initializer()\n",
    "    sess.run(init)\n",
    "    \n",
    "    # IMPLEMENT: compute ratio for every sigma\n",
    "    for i, log_sigma in tqdm(list(enumerate(log_sigmas))):\n",
    "        current_ratio = \n",
    "        ratios[i] = current_ratio\n",
    "\n",
    "plt.plot(log_sigmas, ratios)\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"Log sigma\")\n",
    "plt.ylabel(\"Ratio of MMD and variance (proportional to test power)\")\n",
    "\n",
    "print(\"best sigma:\", 10**log_sigmas[np.argmax(ratios)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was much faster, even for more parameters to try.\n",
    "\n",
    "The curve looks very much like those obtained when cross-validating kernel-parameters for kernel machines (like a support vector machine): you make the model/test more and more complex (bandwidth smaller), until it hits a sweet spot (peak), and after which it starts overfitting (ratio decreasing).\n",
    "Let's try out how it worked."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1835d96f176146ed9051a0747731be04",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma_opt = 0.215\n",
    "\n",
    "# IMPLEMENT: visualise test for best sigma\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Victory!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descent\n",
    "Now, what if we have more than one kernel parameter?\n",
    "Trying out all the different combinations is not the best idea.\n",
    "Instead, we can take a deep learning artisan's mindset and do gradient descent.\n",
    "That is, we maximize the ratio of MMD to standard deviation as a function of the kernel parameters (differentiable!), we could even do this in mini-batches.\n",
    "\n",
    "The implementation of the ratio is quite tricky (you might have checked the imported code).\n",
    "Differentiating it would be a nightmare, but luckily in 2018 we have tools at hand that allow us to do this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GANs\n",
    "\n",
    "Moving to the context of training GANs (Generative adversarial networks).\n",
    "Assume someone came to you with a new GAN, which generates some realistic looking images, supposedly indistinguishable from the images used to train the GAN.\n",
    "\n",
    "Let's assume that person said (https://arxiv.org/abs/1606.03498)\n",
    "> On MTurk, annotators were able to distinguish\n",
    "samples in 52.4% of cases (2000 votes total), where 50% would be obtained by random\n",
    "guessing. Similarly, researchers in our institution were not able to find any artifacts that would allow\n",
    "them to distinguish samples.\n",
    "\n",
    "Let's see what the kernel MMD thinks about this.\n",
    "We will use a slightly different kernel than before: an ARD kernel.\n",
    "This one that scales each of the $D$ input dimensions by a parameter, and then uses a standard Gaussian kernel (unit bandwidth) on top of that.\n",
    "$$ k(x,y) = \\exp\\left(-\\sum_d^D (x_d/\\sigma_d - y_d/\\sigma_d)^2\\right) $$\n",
    "Again, we have implemented this for you in `mmd.py`, feel free to see how.\n",
    "\n",
    "We begin with visualizing the data, and splitting it into train and test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image dimensions: 28x28=784\n"
     ]
    },
    {
     "data": {
      "image/png": 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AoCzJMAAAZUmGAQAoSzIMAEBZkmEAAMqSDAMAUJZkGACAsiTDAACUJRkGAKAsyTAAAGVJhgEAKEsyDABAWZJhAADKkgwDAFCWZBgAgLL+H5DRJTeZhZtAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x216 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x216 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.load(\"samples-to-compare.npz\")[\"target\"]\n",
    "# before fitting the model, we binarized the images\n",
    "X[X<0.5]=0\n",
    "X[X>=0.5]=1\n",
    "\n",
    "Y = np.load(\"samples-to-compare.npz\")[\"model\"]\n",
    "\n",
    "plt.figure(figsize=(12,3))\n",
    "plt.suptitle(\"Train samples\")\n",
    "\n",
    "for i in np.arange(0,16):\n",
    "    plt.subplot(2,8,i+1)\n",
    "    plt.imshow(X[i],cmap='gray')\n",
    "    plt.axis('off')\n",
    "plt.figure(figsize=(12,3))\n",
    "plt.suptitle(\"GAN samples\")\n",
    "for i in np.arange(0,16):\n",
    "    plt.subplot(2,8,i+1)\n",
    "    plt.imshow(Y[i],cmap='gray')\n",
    "    plt.axis('off')\n",
    "\n",
    "# split off a training set, reshape to vectors\n",
    "N = len(X)\n",
    "assert len(X) == len(Y)\n",
    "size = X.shape[1]\n",
    "size2 = size**2\n",
    "assert size2 == X.shape[2]**2\n",
    "half = int(N/2)\n",
    "X_learn = X[half:].reshape(half,size2)\n",
    "Y_learn = Y[half:].reshape(half,size2)\n",
    "X = X[:half].reshape(half,size2)\n",
    "Y = Y[:half].reshape(half,size2)\n",
    "\n",
    "print(\"Image dimensions: %dx%d=%d\" % (size, size, size2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have some code to compute the ratio we want to optimize, and make TensorFlow's Adam optimizer do the rest for us, i.e optimizing the bandwidth variables, $28^2$ of them.\n",
    "\n",
    "Note: this is a very simplistic implementation that might suffer from all sorts of problems.\n",
    "In practice, we would pay more careful attention to the optimization scheme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "start, ratio: 0.1268358\n",
      "step, ratio: 0.1310806\n",
      "step, ratio: 0.14533705\n",
      "step, ratio: 0.17821728\n",
      "step, ratio: 0.24888371\n",
      "step, ratio: 0.39294672\n",
      "step, ratio: 0.6644053\n",
      "step, ratio: 1.1052014\n",
      "step, ratio: 1.7325308\n",
      "step, ratio: 2.5071855\n",
      "step, ratio: 3.348966\n",
      "step, ratio: 4.174197\n",
      "step, ratio: 4.9494605\n",
      "step, ratio: 5.6964183\n",
      "step, ratio: 6.4339848\n",
      "step, ratio: 7.1763763\n",
      "step, ratio: 7.893718\n",
      "step, ratio: 8.585717\n",
      "step, ratio: 9.338504\n",
      "step, ratio: 10.121694\n",
      "step, ratio: 11.094849\n",
      "done, ratio: 11.094849\n"
     ]
    }
   ],
   "source": [
    "sigmas = tf.Variable(np.ones(X_learn.shape[1]), dtype=np.float32, name=\"sigmas\")\n",
    "\n",
    "# provided function. note we are using the \"training\" dataset here.\n",
    "ratio = mmd.ard_mmd2_and_ratio(X_learn,Y_learn, bws=sigmas)[1]\n",
    "\n",
    "# IMPLEMENT: set up adam optimizer tensorflow op to maximise the ratio\n",
    "learning_rate = 0.5\n",
    "optimizer = \n",
    "minimize = \n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:  \n",
    "    sess.run(init)\n",
    "    \n",
    "    print(\"start,\", \"ratio:\", sess.run(ratio))\n",
    "    \n",
    "    for step in range(20):  \n",
    "        # IMPLEMENT: run optimizer and update best found sigmas so far\n",
    "        \n",
    "        print(\"step,\", \"ratio:\", sess.run(ratio))\n",
    "        best_sigmas = \n",
    "    print(\"done, ratio:\", sess.run(ratio))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we now have learnt one bandwidth per pixel, we can visualise the scaled data to see what the resulting test focusses on.\n",
    "Note that we do this on the actual test data, while we learned the weights on the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT: scale images according to sigmas\n",
    "X_scaled = \n",
    "Y_scaled = \n",
    "\n",
    "plt.suptitle(\"Train samples\")\n",
    "plt.figure(figsize=(12,3))\n",
    "for i in np.arange(0,16):\n",
    "    plt.subplot(2,8,i+1)\n",
    "    plt.imshow(X_scaled[i].reshape(size, size),cmap='gray')\n",
    "    plt.axis('off')\n",
    "plt.figure(figsize=(12,3))\n",
    "plt.suptitle(\"GAN samples\")\n",
    "for i in np.arange(0,16):\n",
    "    plt.subplot(2,8,i+1)\n",
    "    plt.imshow(Y_scaled[i].reshape(size, size),cmap='gray')\n",
    "    plt.axis('off')\n",
    "plt.figure()\n",
    "plt.title(\"ARD weights\")\n",
    "plt.imshow(best_sigmas.reshape(size,size), 'magma')\n",
    "plt.colorbar()\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, there seem to be pixel level artifacts that the test focuses on.\n",
    "As it turns out, focusing on those allows the test to fully distinguish training samples from GAN samples.\n",
    "\n",
    "Since our above implementation for the MMD permutation test is very inefficient, we don't use it here to perform the full test -- it would take too long.\n",
    "You can use the below Shogun snippet to perform the test much more quickly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import shogun as sg\n",
    "sg.get_global_parallel().set_num_threads(4)\n",
    "\n",
    "sigma = 1\n",
    "kernel_width = 2 * sigma**2\n",
    "mmd = sg.QuadraticTimeMMD()\n",
    "mmd.set_p(sg.RealFeatures(X_scaled.T.astype(np.float64))) # shogun uses column major format\n",
    "mmd.set_q(sg.RealFeatures(Y_scaled.T.astype(np.float64)))\n",
    "mmd.set_kernel(sg.GaussianKernel(10, kernel_width))\n",
    "\n",
    "mmd.set_num_null_samples(num_permutations)\n",
    "statistics = mmd.sample_null()\n",
    "my_statistic = mmd.compute_statistic()\n",
    "plot_permutation_samples(statistics, my_statistic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT (optional): how does this compare to all weights being one.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that the unscaled features already allow the test to distinguish the distribution quite well.\n",
    "The scaled version above, however, is a much more powerful test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notes\n",
    "\n",
    "Have much more data? Try the linear time versions of the tests\n",
    "* https://arxiv.org/abs/1605.06796\n",
    "* https://arxiv.org/abs/1506.04725\n",
    "\n",
    "\n",
    "Need faster implementations (of the quadratic time MMD tests)\n",
    "* use Shogun!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Independence testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's move on to independence testing.\n",
    "Here, the data we observe is in pairs $(x_i,y_i)\\sim P_{XY}$..\n",
    "The null hypothesis is that the two sets of samples come from independent distributions: $P_{XY} = P_X\\cdot P_Y$.\n",
    "\n",
    "We will use the HSIC, which you can think of as the MMD between the joint distribution $P_{XY}$ and the product of the marginal distributions $P_X P_Y$. \n",
    "Clearly, if those are different, then the samples cannot be independent.\n",
    "\n",
    "See the slides for more details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadratic time test statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's kick of with implementing the quadratic time version of the HSIC statistic.\n",
    "\n",
    "$$ \\frac{1}{n^2}\\text{Trace}(KL) $$\n",
    "\n",
    "where $K$ and $L$ are centered kernel matrices of the samples from the two distribution respectively.\n",
    "(Note that one can center a kernel matrix via multiplying it with a centering matrix $H=I-\\frac{1}{n}\\mathbf{1}\\mathbf{1}^\\top$.)\n",
    "\n",
    "As our kernel will quite expensive to be computed, we here write a version that accepts precomputed kernel matrices rather than a kernel function, and we will permute this kernel matrix for the permutation test.\n",
    "We implement the test statistic as a function of kernel matrices, and with an option to permute the matrices before computing the statistic (for approximating the null distribution).\n",
    "\n",
    "Note that the permutation for dependence testing is different from two-sample testing: in two sample testing, we could just permute the joint kernel matrix (as there is a kernel between $X$ and $Y$).\n",
    "For dependence testing, however, the kernel only is defined between $X$ and itself and $Y$ and itself.\n",
    "\"Breaking\" any potential structure therefore means that we need to shuffle the samples within $X$ and within $Y$ so that any potential pairs $(x_i,y_i)$ do not occur together anymore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HSIC(K_XX, K_YY, permute=False):\n",
    "    assert len(K_XX) == len(K_YY)\n",
    "    N = len(K_XX)\n",
    "    if permute:\n",
    "        # IMPLEMENT: permute the kernel matrices for X and Y\n",
    "        K_XX_ = \n",
    "        K_YY_ = \n",
    "    else:\n",
    "        K_XX_ = K_XX\n",
    "        K_YY_ = K_YY\n",
    "\n",
    "    # IMPLEMENT: HSIC statistic\n",
    "    H = np.eye(N) - 1.0/N\n",
    "    statistic = \n",
    "    return statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with a simple dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.load(\"hsic2.npz\")\n",
    "X = data[\"X\"]\n",
    "Y = data[\"Y\"]\n",
    "plt.plot(X,Y,'.')\n",
    "plt.axis('equal')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, there is some very simple dependence going on.\n",
    "The first thing a statistician in the field would do is of course to check for correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation between X and Y: 0.023122960723689145\n"
     ]
    }
   ],
   "source": [
    "# IMPLEMENT: produce a seaborn pairplot to show the correlation between X and Y\n",
    "print(\"Correlation between X and Y:\", np.corrcoef(X,Y)[0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation is very low.\n",
    "A kernel test for independence is more powerful, even with a bandwidth parameter chosen by the median heuristic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4c9e1f4fce084fb0b1cb7c5d4862471b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT: compute kernel matrices using the median heuristic\n",
    "sigma_median = \n",
    "my_kernel = lambda X,Y : gauss_kernel(X[:,np.newaxis],Y[:,np.newaxis],sigma=sigma_median)\n",
    "K_XX = \n",
    "K_YY = \n",
    "K_XY = \n",
    "\n",
    "statistics = np.empty(num_permutations)\n",
    "for i in tqdm(range(num_permutations)):\n",
    "    # IMPLEMENT: compute HSIC statistic with permuted matrices\n",
    "    statistics[i] = \n",
    "    \n",
    "# IMPLEMENT: visualise test\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Victory once again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## European parliament documents translations and string kernels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now do a slightly more elaborate test that involves some very mild NLP.\n",
    "More precisely we will analyze dependence between documents.\n",
    "We will use transcripts of the Canadian parliament's house debates, downloaded from [here](https://www.isi.edu/natural-language/download/hansard/).\n",
    "Those consist of pairs of French and English transcripts.\n",
    "\n",
    "Our question here is whether we can detect this supposedly strong dependence structure using the kernel HSIC.\n",
    "Note that this approach does not rely on attempting to translate the documents, but rather on comparing within-document structure. \n",
    "HSIC compares the self-similarity within the English documents with self-similarity of the French ones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a first step, we load the data, and store the transcript of each session into lists X and Y, for English and French respectively.\n",
    "We don't do any sophisticated preprocessing here, but feel free to make this more elaborate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# download english and french stopwords (optional)\n",
    "try:\n",
    "    import nltk\n",
    "    from nltk.corpus import stopwords\n",
    "    nltk.download('stopwords');\n",
    "    stop_english = set(stopwords.words(\"english\"))\n",
    "    stop_french = set(stopwords.words(\"french\"))\n",
    "except Exception:\n",
    "    stop_english = set()\n",
    "    stop_french = set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3d2bd3bb472b458c8255f13e25cb5c49",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=504), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from glob import glob\n",
    "import re\n",
    "\n",
    "X = []\n",
    "Y = []\n",
    "for fname in tqdm(sorted(list(glob(\"transcripts/hansard.36.1.house.debates.*.*\")))):\n",
    "    is_french = fname.endswith(\"f\")\n",
    "    is_english = fname.endswith(\"e\")\n",
    "    \n",
    "    if not (is_english or is_french):\n",
    "        continue\n",
    "        \n",
    "    with open(fname, \"r\", encoding='latin-1') as f:\n",
    "        # some very very simple preprocessing, could be more elaborate with special characters\n",
    "        content = \"\".join(f.readlines())\n",
    "        if is_english:\n",
    "            letters_only = re.sub(\"[^a-zA-Z]\", \" \", content)\n",
    "        elif is_french:\n",
    "            letters_only = re.sub(\"[^a-zA-Z\\'ÁÀÂÉÈÊéèáàêâúùûÚÙÛçîô']\", \" \", content) \n",
    "        words = letters_only.lower().split()\n",
    "        \n",
    "        if is_english:\n",
    "            stops = stop_english\n",
    "        elif is_french:\n",
    "            stops = stop_french\n",
    "        meaningful_words = [w for w in words if not w in stops]\n",
    "        \n",
    "        result = \" \".join(meaningful_words)\n",
    "        \n",
    "        if fname.endswith(\"e\"):\n",
    "            X += [result]\n",
    "        else:\n",
    "            Y += [result]\n",
    "N = len(X)\n",
    "assert N == len(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at some excerpts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "liament the speaker accordingly the house stands adjourned until tomorrow the house adjourned at p m\n",
      "ixième législature le président en conséquence la chambre s'ajourne à demain la séance est levée à h\n"
     ]
    }
   ],
   "source": [
    "print(X[0][-100:])\n",
    "print(Y[0][-100:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we are going to construct a string kernel, a  \"bag of words\" kernel between documents $s$ and $t$,\n",
    "\n",
    "$$\n",
    "k(s,t) = \\frac{1}{|\\mathcal{W}|} \\phi(s)^\\top \\phi(t)\n",
    "$$\n",
    "\n",
    "where $\\mathcal{W}$ consists of all words on all considered documents, and each element of $\\phi(x)\\in\\mathbb{N}^{|\\mathcal{W}|}$ contains the number of times that a particular word $w\\in\\mathcal{W}$ appears in $x$.\n",
    "\n",
    "Naturally, the kernel value will be larger, if a word appears in both documents many times.\n",
    "\n",
    "Efficient implementations of string kernels are rare (Shogun has many!), and often based on low-level dynamic programming concepts.\n",
    "Instead, we will here explicitly embed the documents into a feature space and compute (gram) matrix of inner products manually. \n",
    "Note that most string kernel implementations are much more efficient in computing the kernel since they don't do the feature space mapping explicitly.\n",
    "\n",
    "Let's start by building a document embedding mechanism using scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(CountVectorizer(analyzer='word', binary=False, decode_error='replace',\n",
       "         dtype=<class 'numpy.int64'>, encoding='utf-8', input='content',\n",
       "         lowercase=True, max_df=1.0, max_features=50000, min_df=1,\n",
       "         ngram_range=(1, 1), preprocessor=None, stop_words=None,\n",
       "         strip_accents=None, token_pattern='(?u)\\\\b\\\\w\\\\w+\\\\b',\n",
       "         tokenizer=None, vocabulary=None),)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "\n",
    "# IMPLEMENT: fit a vectorizer for the joint set of documents\n",
    "vectorizer = CountVectorizer(...\n",
    "vectorizer.fit(..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at associated words for each feature space dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['unistar',\n",
       " 'gundy',\n",
       " 'sociologue',\n",
       " 'participe',\n",
       " 'négligera',\n",
       " 'haussera',\n",
       " 'transmettrai',\n",
       " 'spectre',\n",
       " 'subventionnaire',\n",
       " 'apportez']"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_names = np.array(vectorizer.get_feature_names())\n",
    "np.random.seed(0)\n",
    "list(feature_names[np.random.permutation(len(feature_names))[-10:]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's define the bag of words kernel, as a product of embedded documents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bag_of_words_kernel(fitted_vectoriser, X,Y):\n",
    "    \"\"\"\n",
    "    Computes the gram matrix between the features of X and Y, where the features are computed\n",
    "    using the provided (fitted) sklearn transformer.\n",
    "    \n",
    "    The kernel is k(x,y) = 1/dim(x) * \\phi(x) \\cdot \\phi(y)\n",
    "    \"\"\"\n",
    "    # IMPLEMENT: transform X and Y documents\n",
    "    X_feats = \n",
    "    if X is Y :\n",
    "        Y_feats = X_feats\n",
    "    else:\n",
    "        Y_feats = \n",
    "    \n",
    "    # IMPLEMENT: compute (dense) gram matrix of pariwise inner products of feature vectors\n",
    "    K = \n",
    "    return K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the kernel matrices (takes some time to compute)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# IMPLEMENT: compute kernel matrices between feature vectors using the bag of words kernel\n",
    "my_kernel = \n",
    "K_XX = my_kernel(X,X)\n",
    "K_YY = my_kernel(Y,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7574e0e748>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,4))\n",
    "plt.subplot(121)\n",
    "plt.imshow(K_XX)\n",
    "plt.subplot(122)\n",
    "plt.imshow(K_YY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a lot of shared (self-similarity) structure between X and Y.\n",
    "The HSIC test quantifies this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1292b1738cae42a097c722e1a8871777",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPLEMENT: visualise HSIC test for given kernel matrices\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A clear reject of the null hypothesis that X and Y are independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notes\n",
    "\n",
    "As for the MMD, there are various linear time tests available for the HSIC, in particular https://arxiv.org/abs/1610.04782."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Goodness of fit testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final topic is testing whether a given set of samples comes from a specified distribution.\n",
    "This problem is slightly different from two-sample and independence testing as we are only given a single set of samples, and the reference distribution will be only available through the gradient of the log density (we cannot sample from it).\n",
    "\n",
    "But there are also similarities, i.e. the test statistic is the RKHS norm of a witness function, we can evaluate the witness function, there is a simple kernel-based quadratic time statistic, etc.\n",
    "\n",
    "Unfortunately, as we cannot sample from the reference distribution, we cannot permute our samples in any way to approximate the null distribution.\n",
    "We will use a slightly more sophisticated (still sampling based) way, called the wild bootstrap.\n",
    "This method was originally developed to approximate null distributions for two-sample tests of correlated samples, however, it turns out that we can also utilise the technique for cases where we cannot permute samples.\n",
    "\n",
    "We start with a simple example where we provide you with code to compute test statistic and p-value.\n",
    "The reest of his section is intentionally kept more sparse, encouraging faster participants to implement more advanced concepts on their own.\n",
    "\n",
    "As usual, see the slides for details.\n",
    "\n",
    "The two main references are\n",
    " * https://arxiv.org/abs/1602.02964\n",
    " * https://arxiv.org/abs/1705.07673 (NIPS 2017 best paper award)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing samples of a student-t against a Gaussian\n",
    "\n",
    "We will begin with a simple synthetic example: given a number of samples from a student-t distribution, can we reject the null hypothesis that those samples came from a Gaussian.\n",
    "How does the test change as we make the student-t look more and more like a Gaussian?\n",
    "\n",
    "Remember, we will only use the gradient of the log-density of the reference Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad_log_normal(x):\n",
    "    \"\"\"\n",
    "    Returns the gradient of the log Gaussian density (zero mean, std-dev)\n",
    "    \"\"\"\n",
    "    \n",
    "    # IMPLEMENT:\n",
    "    grad = -x\n",
    "    \n",
    "    return  grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distributions of p-values\n",
    "\n",
    "In the beginning of this notebook, we saw that every time a statistical test is computed, we only receive a single test statistic.\n",
    "This is a single sample from the alternative distribution, and leads to a single p-value  (remember the example where we explicitly sampled from the alternative distribution?).\n",
    "\n",
    "Again, this number clearly depends on the data used for the test, a different set of test data will lead to a different test statistic and p-value (while the estimated null distribution should be stable).\n",
    "Under the null hypothesis of any test, the distribution of p-values is uniform, since we just take a sample from the very same distribution and then compute its quantile.\n",
    "Long story short: we never know whether we just have been \"lucky\" when computing the test.\n",
    "\n",
    "In order to get a feeling for this effect, we will now run the goodness-of-fit test multiple times and plot the distribution over p-values.\n",
    "We will perform this experiment using samples from a [student-t distribution](https://en.wikipedia.org/wiki/Student%27s_t-distribution), and test the null hypothesis that these samples are distributed as a standard Gaussian.\n",
    "As the degrees of freedom are increasing, the samples look more and more Gaussian, and we will quantify the distribution of p-values along the way.\n",
    "\n",
    "Since we need to compute the test many times to sample the distribution of p-values, the quadratic time statistic would take a long time.\n",
    "This is why we have provided an implementation of a linear-time goodness-of-fit test using the kernel Stein discrepancy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ffa5121074ef4bb4b4684e4be1c4a504",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=1000), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "19cea754024e45ca9d583a3e5e38e4fc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import itertools\n",
    "from ksd import GaussianSteinTest\n",
    "\n",
    "# parameter for the linear time test (see paper if interested)\n",
    "num_random_freq=2\n",
    "\n",
    "N = 500\n",
    "\n",
    "degrees_of_freedom = range(1, 10, 2)\n",
    "num_repetitions = 200\n",
    "results = []\n",
    "\n",
    "for dof, mc in tqdm(list(itertools.product(degrees_of_freedom, range(num_repetitions)))):\n",
    "    # IMPLEMENT: sample from student t with given degrees of freedom (dof)\n",
    "    X = \n",
    "    \n",
    "    # this is how we run the linear time goodness-of-fit test\n",
    "    pvalue = GaussianSteinTest(grad_log_normal,num_random_freq).compute_pvalue(X)\n",
    "    results += [[dof, pvalue]]\n",
    "\n",
    "for mc in tqdm(range(num_repetitions)):\n",
    "        # IMPLEMENT: run the test to sample from the null distribution\n",
    "        X = \n",
    "        pvalue = \n",
    "        \n",
    "        results += [[np.Inf, pvalue]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame(results, columns=[\"dof\",\"p_value\"])\n",
    "sns.boxplot(y=\"p_value\",x=\"dof\",data=df);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that for a low number of degrees of freedom, the p-values tend to be mostly small (i.e. the test rejects the null hypothesis more often).\n",
    "As we make the distribution look more like a Gaussian, the p-values increase.\n",
    "Eventually, the student-t becomes a Gaussian for an infinite number of degrees of freedom, i.e. we are sampling from the (unitform!) distribution of p-values under the null hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadratic time test statistic\n",
    "\n",
    "Let's implement the quadratic time statistic to get a feeling for what quantities are needed: the gradient of the target log-density, the kernel, and the gradient of the kernel with respect to left and right arguments (individually and both).\n",
    "We will use a standard Gaussian kernel with unit scaling, for simplicity in 1D.\n",
    "The first step is to implement kernel gradients (we could do this using an autodiff framework!).\n",
    "\n",
    "See https://arxiv.org/abs/1602.02964 or the slides for the definition of the test statistic. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def k( x, y):\n",
    "    return np.exp(-np.dot(x - y,x - y))\n",
    "\n",
    "def g1k(x, y):\n",
    "    # IMPLEMENT: gradient wrt left argument\n",
    "    return \n",
    "\n",
    "def g2k(x, y):\n",
    "    # IMPLEMENT: gradient wrt right argument\n",
    "    return \n",
    "\n",
    "def gk(x, y):\n",
    "    # IMPLEMENT: gradient wrt to both arguments\n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference 1.3635469770368822\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7f2f07eba71b4a53b81a35ed7bdfa5a0",
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       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=500), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "My implementation: 0.8618654916540869\n"
     ]
    }
   ],
   "source": [
    "from ksd import GaussianQuadraticTest\n",
    "\n",
    "X = np.random.standard_t(1,N)\n",
    "kernel_bw = 1.0\n",
    "# reference implementation: the function returns N*statistic. Nevermind the typo :)\n",
    "print(\"Reference\", GaussianQuadraticTest(grad_log_normal, scaling=kernel_bw).get_statistic_multiple(X)[1]/N)\n",
    "\n",
    "# all elements that the statistic sums over\n",
    "U_matrix = np.zeros((N, N))\n",
    "\n",
    "for i in tqdm(range(N)):\n",
    "    for j in range(N):\n",
    "        # IMPLEMENT: implement the quadratic time KSD test statistic (needs gradient of log-density and the gradient of the Gaussian kernel)\n",
    "        # hint: use four terms\n",
    "        a =\n",
    "        b =\n",
    "        c =\n",
    "        d =\n",
    "        U_matrix[i, j] = a + b + c + d\n",
    "    \n",
    "stat = np.mean(U_matrix)\n",
    "print(\"My implementation:\", stat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you like, try to visualize the witness function of the kernel Stein discrepancy, just as we visualized the witness function of the MMD above (see slides for details)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advanced exercise\n",
    "\n",
    "Let's see if we can quantify convergence of an MCMC chain using the goodness-of-fit test.\n",
    "For simplification, we will thin the MCMC samples so that they are not correlated (see the original KSD paper on how to run the test on correlated samples).\n",
    "This experiment loosely follows one in the KSD paper.\n",
    "\n",
    "In this open-ended las task you will:\n",
    "\n",
    "* Run an MCMC chain using stochastic gradient Langevin dynamics with a large step-size. See https://www.ics.uci.edu/~welling/publications/papers/stoclangevin_v6.pdf\n",
    "* Target a standard Gaussian distribution in 1D (or 2D if you like)\n",
    "* After the sampler is completed, thin the MCMC samples so that they are almost i.i.d.\n",
    "* Run the goodness-of-fit test to quantify at what step-size of the sampler the samples reach a good quality.\n",
    "\n",
    "Good luck :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The end"
   ]
  }
 ],
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