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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Kernel hypothesis testing in Shogun" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### Heiko Strathmann - <a href=\"mailto:heiko.strathmann@gmail.com\">heiko.strathmann@gmail.com</a> - <a href=\"github.com/karlnapf\">github.com/karlnapf</a> - <a href=\"herrstrathmann.de\">herrstrathmann.de</a>\n", | |
| "#### Soumyajit De - <a href=\"soumyajitde.cse@gmail.com \">soumyajitde.cse@gmail.com </a> - <a href=\"github.com/lambday\">github.com/lambday</a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "This notebook describes Shogun's framework for <a href=\"http://en.wikipedia.org/wiki/Statistical_hypothesis_testing\">statistical hypothesis testing</a>. We begin by giving a brief outline of the problem setting and then describe various implemented algorithms.\n", | |
| "All algorithms discussed here are instances of <a href=\"http://en.wikipedia.org/wiki/Kernel_embedding_of_distributions#Kernel_two_sample_test\">kernel two-sample testing</a> with the *maximum mean discrepancy*, and are based on embedding probability distributions into <a href=\"http://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space\">Reproducing Kernel Hilbert Spaces</a> (RKHS)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "There are two types of tests available, a quadratic time test and a linear time test. Both come in various flavours." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Populating the interactive namespace from numpy and matplotlib\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%pylab inline\n", | |
| "%matplotlib inline\n", | |
| "import modshogun as sg\n", | |
| "import numpy as np" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Some Formal Basics (skip if you just want code examples)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "To set the context, we here briefly describe statistical hypothesis testing. Informally, one defines a hypothesis on a certain domain and then uses a statistical test to check whether this hypothesis is true. Formally, the goal is to reject a so-called *null-hypothesis* $H_0:p=q$, which is the complement of an *alternative-hypothesis* $H_A$. \n", | |
| "\n", | |
| "To distinguish the hypotheses, a test statistic is computed on sample data. Since sample data is finite, this corresponds to sampling the true distribution of the test statistic. There are two different distributions of the test statistic -- one for each hypothesis. The *null-distribution* corresponds to test statistic samples under the model that $H_0$ holds; the *alternative-distribution* corresponds to test statistic samples under the model that $H_A$ holds.\n", | |
| "\n", | |
| "In practice, one tries to compute the quantile of the test statistic in the null-distribution. In case the test statistic is in a high quantile, i.e. it is unlikely that the null-distribution has generated the test statistic -- the null-hypothesis $H_0$ is rejected.\n", | |
| "\n", | |
| "There are two different kinds of errors in hypothesis testing:\n", | |
| "\n", | |
| " * A *type I error* is made when $H_0: p=q$ is wrongly rejected. That is, the test says that the samples are from different distributions when they are not.\n", | |
| " * A *type II error* is made when $H_A: p\\neq q$ is wrongly accepted. That is, the test says that the samples are from the same distribution when they are not.\n", | |
| "\n", | |
| "A so-called *consistent* test achieves zero type II error for a fixed type I error, as it sees more data.\n", | |
| "\n", | |
| "To decide whether to reject $H_0$, one could set a threshold, say at the $95\\%$ quantile of the null-distribution, and reject $H_0$ when the test statistic lies below that threshold. This means that the chance that the samples were generated under $H_0$ are $5\\%$. We call this number the *test power* $\\alpha$ (in this case $\\alpha=0.05$). It is an upper bound on the probability for a type I error. An alternative way is simply to compute the quantile of the test statistic in the null-distribution, the so-called *p-value*, and to compare the p-value against a desired test power, say $\\alpha=0.05$, by hand. The advantage of the second method is that one not only gets a binary answer, but also an upper bound on the type I error.\n", | |
| "\n", | |
| "In order to construct a two-sample test, the null-distribution of the test statistic has to be approximated. One way of doing this is called the *permutation test*, where samples from both sources are mixed and permuted repeatedly and the test statistic is computed for every of those configurations. While this method works for every statistical hypothesis test, it might be very costly because the test statistic has to be re-computed many times. Shogun comes with an extremely optimized implementation though. For completeness, Shogun also includes a number of more sohpisticated ways of approximating the null distribution." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Base class for Hypothesis Testing" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Shogun implements statistical testing in the abstract class <a href=\"http://shogun.ml/CHypothesisTest\">CHypothesisTest</a>. All implemented methods will work with this interface at their most basic level. We here focos on <a href=\"http://shogun.ml/CTwoSampleTest\">CTwoSampleTest</a>. This class offers methods to\n", | |
| "\n", | |
| " * compute the implemented test statistic,\n", | |
| " * compute p-values for a given value of the test statistic,\n", | |
| " * compute a test threshold for a given p-value,\n", | |
| " * approximate the null distribution, e.g. perform the permutation test and\n", | |
| " * performing a full two-sample test, and either returning a p-value or a binary rejection decision. This method is most useful in practice. Note that, depending on the used test statistic." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Kernel Two-Sample Testing with the Maximum Mean Discrepancy" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$\\DeclareMathOperator{\\mmd}{MMD}$\n", | |
| "An important class of hypothesis tests are the *two-sample tests*. \n", | |
| "In two-sample testing, one tries to find out whether two sets of samples come from different distributions. Given two probability distributions $p,q$ on some *arbritary* domains $\\mathcal{X}, \\mathcal{Y}$ respectively, and i.i.d. samples $X=\\{x_i\\}_{i=1}^m\\subseteq \\mathcal{X}\\sim p$ and $Y=\\{y_i\\}_{i=1}^n\\subseteq \\mathcal{Y}\\sim p$, the two sample test distinguishes the hypothesises\n", | |
| "\n", | |
| "\\begin{align*}\n", | |
| "H_0: p=q\\\\\n", | |
| "H_A: p\\neq q\n", | |
| "\\end{align*}\n", | |
| "\n", | |
| "In order to solve this problem, it is desirable to have a criterion than takes a positive unique value if $p\\neq q$, and zero if and only if $p=q$. The so called *Maximum Mean Discrepancy (MMD)*, has this property and allows to distinguish any two probability distributions, if used in a *reproducing kernel Hilbert space (RKHS)*. It is the distance of the mean embeddings $\\mu_p, \\mu_q$ of the distributions $p,q$ in such a RKHS $\\mathcal{F}$ -- which can also be expressed in terms of expectation of kernel functions, i.e.\n", | |
| "\n", | |
| "\\begin{align*}\n", | |
| "\\mmd[\\mathcal{F},p,q]&=||\\mu_p-\\mu_q||_\\mathcal{F}^2\\\\\n", | |
| "&=\\textbf{E}_{x,x'}\\left[ k(x,x')\\right]-\n", | |
| " 2\\textbf{E}_{x,y}\\left[ k(x,y)\\right]\n", | |
| " +\\textbf{E}_{y,y'}\\left[ k(y,y')\\right]\n", | |
| "\\end{align*}\n", | |
| "\n", | |
| "Note that this formulation does not assume any form of the input data, we just need a kernel function whose feature space is a RKHS, see [2, Section 2] for details. This has the consequence that in Shogun, we can do tests on any type of data (<a href=\"http://shogun.ml/CDenseFeatures\">CDenseFeatures</a>, <a href=\"http://shogun.ml/CSparseFeatures\">CSparseFeatures</a>, <a href=\"http://shogun.ml/CStringFeatures\">CStringFeatures</a>, etc), as long as we or you provide a positive definite kernel function under the interface of <a href=\"http://shogun.ml/CKernel\">CKernel</a>.\n", | |
| "\n", | |
| "We here only describe how to use the MMD for two-sample testing. Shogun offers two types of test statistic based on the MMD, one with quadratic costs both in time and space, and one with linear time and constant space costs. Both come in different versions and with different methods how to approximate the null-distribution in order to construct a two-sample test." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Running Example Data. Gaussian vs. Laplace" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "In order to illustrate kernel two-sample testing with Shogun, we use a couple of toy distributions. The first dataset we consider is the 1D Standard Gaussian\n", | |
| "\n", | |
| "$p(x)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-\\frac{(x-\\mu)^2}{\\sigma^2}\\right)$\n", | |
| "\n", | |
| "with mean $\\mu$ and variance $\\sigma^2$, which is compared against the 1D Laplace distribution\n", | |
| "\n", | |
| "$p(x)=\\frac{1}{2b}\\exp\\left(-\\frac{|x-\\mu|}{b}\\right)$\n", | |
| "\n", | |
| "with the same mean $\\mu$ and variance $2b^2$. In order to increase difficulty, we set $b=\\sqrt{\\frac{1}{2}}$, which means that $2b^2=\\sigma^2=1$." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# use scipy for generating samples\n", | |
| "from scipy.stats import laplace, norm\n", | |
| "\n", | |
| "def sample_gaussian_vs_laplace(n=220, mu=0.0, sigma2=1, b=np.sqrt(0.5)): \n", | |
| " # sample from both distributions\n", | |
| " X=norm.rvs(size=n)*np.sqrt(sigma2)+mu\n", | |
| " Y=laplace.rvs(size=n, loc=mu, scale=b)\n", | |
| " \n", | |
| " return X,Y" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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ERESOUd6wA4hI1rfgjwWs/3M951c9/5j7uLH+jYycM5Kr66TtThwiIlHUEljm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\ni508d5KNRzcSfTSaDbEbiD4azb6T+yhzSxmqF6pOk+JNeLHei5TKU0p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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa8c74da910>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "mu=0.0\n", | |
| "sigma2=1\n", | |
| "b=np.sqrt(0.5)\n", | |
| "n=220\n", | |
| "X,Y=sample_gaussian_vs_laplace(n, mu, sigma2, b)\n", | |
| "\n", | |
| "# plot both densities and histograms\n", | |
| "plt.figure(figsize=(18,5))\n", | |
| "plt.suptitle(\"Gaussian vs. Laplace\")\n", | |
| "plt.subplot(121)\n", | |
| "Xs=np.linspace(-2, 2, 500)\n", | |
| "plt.plot(Xs, norm.pdf(Xs, loc=mu, scale=sigma2))\n", | |
| "plt.plot(Xs, laplace.pdf(Xs, loc=mu, scale=b))\n", | |
| "plt.title(\"Densities\")\n", | |
| "plt.xlabel(\"$x$\")\n", | |
| "plt.ylabel(\"$p(x)$\")\n", | |
| "\n", | |
| "plt.subplot(122)\n", | |
| "plt.hist(X, alpha=0.5)\n", | |
| "plt.xlim([-5,5])\n", | |
| "plt.ylim([0,100])\n", | |
| "plt.hist(Y,alpha=0.5)\n", | |
| "plt.xlim([-5,5])\n", | |
| "plt.ylim([0,100])\n", | |
| "plt.legend([\"Gaussian\", \"Laplace\"])\n", | |
| "plt.title('Samples');" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now how to compare these two sets of samples? Clearly, a t-test would be a bad idea since it basically compares mean and variance of $X$ and $Y$. But we set that to be equal. By chance, the estimates of these statistics might differ, but that is unlikely to be significant. Thus, we have to look at higher order statistics of the samples. In fact, kernel two-sample tests look at *all* (infinitely many) higher order moments." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Gaussian vs. Laplace\n", | |
| "Sample means: 0.01 vs 0.09\n", | |
| "Samples variances: 0.91 vs 1.19\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print \"Gaussian vs. Laplace\"\n", | |
| "print \"Sample means: %.2f vs %.2f\" % (np.mean(X), np.mean(Y))\n", | |
| "print \"Samples variances: %.2f vs %.2f\" % (np.var(X), np.var(Y))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Quadratic Time MMD" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We now describe the quadratic time MMD, as described in [1, Lemma 6], which is implemented in Shogun. All methods in this section are implemented in <a href=\"http://shogun.ml/CQuadraticTimeMMD\">CQuadraticTimeMMD</a>, which accepts any type of features in Shogun, and use it on the above toy problem.\n", | |
| "\n", | |
| "An unbiased estimate for the MMD expression above can be obtained by estimating expected values with averaging over independent samples\n", | |
| "\n", | |
| "$$\n", | |
| "\\mmd_u[\\mathcal{F},X,Y]^2=\\frac{1}{m(m-1)}\\sum_{i=1}^m\\sum_{j\\neq i}^mk(x_i,x_j) + \\frac{1}{n(n-1)}\\sum_{i=1}^n\\sum_{j\\neq i}^nk(y_i,y_j)-\\frac{2}{mn}\\sum_{i=1}^m\\sum_{j\\neq i}^nk(x_i,y_j)\n", | |
| "$$\n", | |
| "\n", | |
| "A biased estimate would be\n", | |
| "\n", | |
| "$$\n", | |
| "\\mmd_b[\\mathcal{F},X,Y]^2=\\frac{1}{m^2}\\sum_{i=1}^m\\sum_{j=1}^mk(x_i,x_j) + \\frac{1}{n^ 2}\\sum_{i=1}^n\\sum_{j=1}^nk(y_i,y_j)-\\frac{2}{mn}\\sum_{i=1}^m\\sum_{j\\neq i}^nk(x_i,y_j)\n", | |
| ".$$\n", | |
| "\n", | |
| "Computing the test statistic using <a href=\"http://shogun.ml/CQuadraticTimeMMD\">CQuadraticTimeMMD</a> does exactly this, where it is possible to choose between the two above expressions. Note that some methods for approximating the null-distribution only work with one of both types. Both statistics' computational costs are quadratic both in time and space. Note that the method returns $m\\mmd_b[\\mathcal{F},X,Y]^2$ since null distribution approximations work on $m$ times null distribution. Here is how the test statistic itself is computed." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "220 x MMD_b[X,Y]^2=3.26\n", | |
| "220 x MMD_u[X,Y]^2=2.73\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# turn data into Shogun representation (columns vectors)\n", | |
| "feat_p=sg.RealFeatures(X.reshape(1,len(X)))\n", | |
| "feat_q=sg.RealFeatures(Y.reshape(1,len(Y)))\n", | |
| "\n", | |
| "# choose kernel for testing. Here: Gaussian\n", | |
| "kernel_width=1\n", | |
| "kernel=sg.GaussianKernel(10, kernel_width)\n", | |
| "\n", | |
| "# create mmd instance of test-statistic\n", | |
| "mmd=sg.QuadraticTimeMMD()\n", | |
| "mmd.set_kernel(kernel)\n", | |
| "mmd.set_p(feat_p)\n", | |
| "mmd.set_q(feat_q)\n", | |
| "\n", | |
| "# compute biased and unbiased test statistic (default is unbiased)\n", | |
| "mmd.set_statistic_type(sg.ST_BIASED_FULL)\n", | |
| "biased_statistic=mmd.compute_statistic()\n", | |
| "\n", | |
| "mmd.set_statistic_type(sg.ST_UNBIASED_FULL)\n", | |
| "statistic=unbiased_statistic=mmd.compute_statistic()\n", | |
| "\n", | |
| "print \"%d x MMD_b[X,Y]^2=%.2f\" % (len(X), biased_statistic)\n", | |
| "print \"%d x MMD_u[X,Y]^2=%.2f\" % (len(X), unbiased_statistic)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Any sub-class of <a href=\"http://www.shogun.ml/CHypothesisTest\">CHypothesisTest</a> can compute approximate the null distribution using permutation/bootstrapping. This way always is guaranteed to produce consistent results, however, it might take a long time as for each sample of the null distribution, the test statistic has to be computed for a different permutation of the data. Shogun's implementation is highly optimized, exploiting low-level CPU caching and multiple available cores." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "P-value of MMD value 2.73 is 0.00\n", | |
| "Threshold for rejecting H0 with a test power of 0.05 is 0.96\n", | |
| "H0 is rejected with confidence 0.05\n", | |
| "H0 is rejected with confidence 0.05\n", | |
| "H0 is rejected with confidence 0.05\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "mmd.set_null_approximation_method(sg.NAM_PERMUTATION)\n", | |
| "mmd.set_num_null_samples(200)\n", | |
| "\n", | |
| "# now show a couple of ways to compute the test\n", | |
| "\n", | |
| "# compute p-value for computed test statistic\n", | |
| "p_value=mmd.compute_p_value(statistic)\n", | |
| "print \"P-value of MMD value %.2f is %.2f\" % (statistic, p_value)\n", | |
| "\n", | |
| "# compute threshold for rejecting H_0 for a given test power\n", | |
| "alpha=0.05\n", | |
| "threshold=mmd.compute_threshold(alpha)\n", | |
| "print \"Threshold for rejecting H0 with a test power of %.2f is %.2f\" % (alpha, threshold)\n", | |
| "\n", | |
| "# performing the test by hand given the above results, note that those two are equivalent\n", | |
| "if statistic>threshold:\n", | |
| " print \"H0 is rejected with confidence %.2f\" % alpha\n", | |
| " \n", | |
| "if p_value<alpha:\n", | |
| " print \"H0 is rejected with confidence %.2f\" % alpha\n", | |
| "\n", | |
| "# or, compute the full two-sample test directly\n", | |
| "# fixed test power, binary decision\n", | |
| "binary_test_result=mmd.perform_test(alpha)\n", | |
| "if binary_test_result:\n", | |
| " print \"H0 is rejected with confidence %.2f\" % alpha" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now let us visualise distribution of MMD statistic under $H_0:p=q$ and $H_A:p\\neq q$. Sample both null and alternative distribution for that. Use the interface of <a href=\"http://www.shogun.ml/CHypothesisTest\">CHypothesisTest</a> to sample from the null distribution (permutations, re-computing of test statistic is done internally). For the alternative distribution, compute the test statistic for a new sample set of $X$ and $Y$ in a loop. Note that the latter is expensive, as the kernel cannot be precomputed, and infinite data is needed. Though it is not needed in practice but only for illustrational purposes here." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.96801934862538119" | |
| ] | |
| }, | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "num_samples=500\n", | |
| "\n", | |
| "# sample null distribution\n", | |
| "null_samples=mmd.sample_null()\n", | |
| "\n", | |
| "# sample alternative distribution, generate new data for that\n", | |
| "alt_samples=np.zeros(num_samples)\n", | |
| "for i in range(num_samples):\n", | |
| " X=norm.rvs(size=n, loc=mu, scale=sigma2)\n", | |
| " Y=laplace.rvs(size=n, loc=mu, scale=b)\n", | |
| " feat_p=sg.RealFeatures(np.reshape(X, (1,len(X))))\n", | |
| " feat_q=sg.RealFeatures(np.reshape(Y, (1,len(Y))))\n", | |
| " # TODO: reset pre-computed kernel here\n", | |
| " mmd.set_p(feat_p)\n", | |
| " mmd.set_q(feat_q)\n", | |
| " alt_samples[i]=mmd.compute_statistic()\n", | |
| "\n", | |
| "np.std(alt_samples)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### Null and Alternative Distribution Illustrated" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Visualise both distributions, $H_0:p=q$ is rejected if a sample from the alternative distribution is larger than the $(1-\\alpha)$-quantil of the null distribution. See [1] for more details on their forms. From the visualisations, we can read off the test's type I and type II error:\n", | |
| "\n", | |
| " * type I error is the area of the null distribution being right of the threshold\n", | |
| " * type II error is the area of the alternative distribution being left from the threshold" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def plot_alt_vs_null(alt_samples, null_samples, alpha):\n", | |
| " plt.figure(figsize=(18,5))\n", | |
| " \n", | |
| " plt.subplot(131)\n", | |
| " plt.hist(null_samples, 50, color='blue')\n", | |
| " plt.title('Null distribution')\n", | |
| " plt.subplot(132)\n", | |
| " plt.title('Alternative distribution')\n", | |
| " plt.hist(alt_samples, 50, color='green')\n", | |
| " \n", | |
| " plt.subplot(133)\n", | |
| " plt.hist(null_samples, 50, color='blue')\n", | |
| " plt.hist(alt_samples, 50, color='green', alpha=0.5)\n", | |
| " plt.title('Null and alternative distriution')\n", | |
| " \n", | |
| " # find (1-alpha) element of null distribution\n", | |
| " null_samples_sorted=np.sort(null_samples)\n", | |
| " quantile_idx=int(len(null_samples)*(1-alpha))\n", | |
| " quantile=null_samples_sorted[quantile_idx]\n", | |
| " plt.axvline(x=quantile, ymin=0, ymax=100, color='red', label=str(int(round((1-alpha)*100))) + '% quantile of null')\n", | |
| " legend();" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa8bebdd8d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot_alt_vs_null(alt_samples, null_samples, alpha)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### Different Ways to Approximate the Null Distribution for the Quadratic Time MMD" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "As already mentioned, permuting the data to access the null distribution is probably the method of choice, due to the efficient implementation in Shogun. There exist a couple of methods that are more sophisticated (and slower) and either allow very fast approximations without guarantees or reasonably fast approximations that are consistent. We present a selection from [2], which are implemented in Shogun.\n", | |
| "\n", | |
| "The first one is a spectral method that is based around the Eigenspectrum of the kernel matrix of the joint samples. It is faster than bootstrapping while being a consistent test. Effectively, the null-distribution of the biased statistic is sampled, but in a more efficient way than the bootstrapping approach. The converges as\n", | |
| "\n", | |
| "$$\n", | |
| "m\\mmd^2_b \\rightarrow \\sum_{l=1}^\\infty \\lambda_l z_l^2\n", | |
| "$$\n", | |
| "\n", | |
| "where $z_l\\sim \\mathcal{N}(0,2)$ are i.i.d. normal samples and $\\lambda_l$ are Eigenvalues of expression 2 in [2], which can be empirically estimated by $\\hat\\lambda_l=\\frac{1}{m}\\nu_l$ where $\\nu_l$ are the Eigenvalues of the centred kernel matrix of the joint samples $X$ and $Y$. The distribution above can be easily sampled. Shogun's implementation has two parameters:\n", | |
| "\n", | |
| " * Number of samples from null-distribution. The more, the more accurate.\n", | |
| " * Number of Eigenvalues of the Eigen-decomposition of the kernel matrix to use. The more, the better the results get. However, the Eigen-spectrum of the joint gram matrix usually decreases very fast. Plotting the Spectrum can help. See [2] for details.\n", | |
| "\n", | |
| "If the kernel matrices are diagonal dominant, this method is likely to fail. For that and more details, see the original paper. Computational costs are likely to be larger than permutation testing, due to the efficient implementation of the latter: Eigenvalues of the gram matrix cost $\\mathcal{O}(m^3)$.\n", | |
| "\n", | |
| "Below, we illustrate how to sample the null distribution and perform two-sample testing with the Spectrum approximation in the class <a href=\"https://shogun.ml/&QuadraticTimeMMD\">CQuadraticTimeMMD</a>. This method only works with the biased statistic." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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mnoKV6uiLtjvhTUmbZiJGG3EfpvVioVQPYraRzGYN0r5dppmr8HloBKkZZTXN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rqfkR4PXsd1k4fA5Puhu4ryOkrX2gzgINp4M4Vba8hY+4oqj820Ktj6JH4WLo0x//U4zvfYxHJu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\n34/1LPec3hoxCD18gtSqqF8uFU8UJciXw+D5wUTO9TVwn49Ty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UYftayiLLO4ZQmttL/x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yszEEng5X22d2q7Q6yXAZKVOEDabsrOJA3o3Kuon/ZaYiDQx2AA30v49JZgn1JgOvyuxP2x\nz4SzxspFmBoMOPeXoMrVowOxwkSw3lT/940jMCXizj7oJkGJ96PC5yFppYsoVZlmKCyXZMraZwyo\nR220Ogg/IwhMMZvAwddapcr3BF6WSKakvQcp09WXl8hVmMM2TRE43EDI1pZO8x4epa40Xe7vN7qv\nfMOEEi+fVKxWQqVmP2+YTAk8WicVXo5oe6e1ZYCb3R3ReIs0V0wy9eJQddzmq9jXTqspd3PQDy8H\ndJlSbRH4d8F5R/Dvxldm62S+HJx3Pifp461RWLarUlNt3l41ASwIHIBW+DnbpRxMCIxKn5eNss0b\nUwe361SnrjdJkS+tjRqx/5Rt0hC4InS4pq3N5miTKunCW+1Rv8s0QzoUlhKrjZTaTXm989pMKrWp\n5CrYXey7Wo3tNG+hP076fNk4yrz9GPzGx6fpiMFvyjo6pHvukb74RenkyYvdm9hiiy222C62/VbA\n72/rIIrEyksbBfZvNjqoCwTNUemWMLJEltU6jcrUTJRCUFkJVhbo3rAesAHP+1QiLUPKwR/gS+23\nPfw6N8gBUJWalKmGMOJZJQfVNYI2e0g/L4IZdDrsYd/qygaCcikHPao5Fq1skciRtA0vhWOROAOP\nawV7FLiyLchUkTfJH+zDiG4YeQz9U+PjKTZF6xCsE1j92uexur9fMTC0Q4PUoqEO+GpNZZliBzty\nJejAo39Jj6aFYKRRUKJXdLXVM6bNfdDovi5OAdXLZEB3INLCcPPh/T5LKiwdpMWmON1Hbzn4Dms0\nGxiuAakA2yAJo+CFYQkceaRUFsn3+sJWuiew8R9ALJMM3CZtTU2T138OBG0GXodJ9JarhAeCEh9T\nGKkO+xwI9llppLFSCqDukSk3hyWn1vpclbj6d6vASvkUg0V8HQA/ptm2eVIkjxiHZZVarYTQIaym\nLhKD/c6dYOfb5kIgKEuB6Skh0G9L+Xy8fE3JgaOvR5JeiirpfaxQ+rn9Yr0rVmdI4eaN+abClLg3\nycbf4H7cpKi+MGyXFiJlvW/zqZv91q7b4aXBKlKK0Jy0UlBPhnNQ6xtUgUWpp0gtGmpq5DT7BoOi\n0lZ2T1/4H8L4iI9P6hGD3/PtV7+S7rxTys+XTp++2L2JLbbYYovtYtpHeeb7UGrPvw1LJBIq0wy+\nkcjEciT3klKK7aTcurgIHizys4pwtjXwz8DLdFad1Z4FJIaWAF1I8gDzCfy8iTB4LEwCfT5B4vHA\nVYXL/XqpNopZwLdWQuL2UqA7Hel3c8nRwPsW5mH+Ryq3Y7xfoPwFJGobKSGXOVRgGZTf8jGcsn7x\nIqFq7SId4VuJP8bUrUf67/f+B9eik6/OVyUuZQEPXCY49ncw5S9MeZlvWr9m9iKxIiClFtzT2xiD\npXS78nFjkYs6dbb7IKMf7O/8+QzgB9yoq1iXeMP7NwgV3EmiSdDy/jbeZ1lFlj8760foittI/CJg\npCbyWmK99ffVBSTmCdYfAp51v/SEFd+EmQtJ+TwL+KWPKcysTQf+wn1jGax6YAGJ0hK/+HHrb9bD\nsHMRljn+MKHo1yR9gTWJMKcWUwGPRM2GYensH6A87qZtC0iMCKLzdGgBVFqO76hbtkF1EY+pnfcS\nS1iQK2j8O2+vc5uFWM71G5jacRfrZ8HD8HQRnVW5bQ1dDvQkyRzmkyS1Vnq6Pzql4Hd5GM4V8e8V\n1IcDpzisP6dvYn6n74rs6FEEJ1a4T/thPh/s55mK+j4WMHC2IuV0M1u71SxgGkno/TC0FZFkAfOp\nBbYAD9tw94fn2TXTz/0ZR7v8CFtvx4EfkBIGmwss9PfzUaz2HNunxD7ras8fZOfOwe23w3vvQXU1\npL1ffzK22GKLLbbPhH0UteeLu5u9GGWo1SOJRnPlwTCPtSSqZRtGNMtAc1WkcpDGWETpKU33qFWx\n9itd6zTOIoTTZNFNAmmgRZmLw/xT2nQwyr0t1QrdanmbuRKzLGq8V32kbZ4XPElid4dWK1+v6GrL\n64xoyp7Duv+UoNip2IHoZpG39q6I2ZIqLV+xBJw+u1G6wnI4mSZRJ+nbSAVel3YCFrlNSqyXRR49\nYpyhVrvmFMtDhman+p6MIoDMtzzWVmVYNLC30bSrwSLOhfK82I1aqck2D9kWbT1zzCiyDSBWyMa4\nVII9qg0j9jsl2C6WyX7HRp+TYk3SKulJNEuLPBJZ45TcVp/LpM9Dh6BKAagCpDlouLbanGUSRVCb\nlBnVYe44YlTYeo1UFZaPqkw7T4VIKz3/dIGtj1ZlWA3gQzhLYK3ma55WK99qDJMUe88ocL9MVaXn\noQaCPT6mKo9+hpT7QGyStBijCjfZvPCCLMe2SPab2ySjZ7da1HKNBGVGA97UKed3rjESAtA76qVF\nmuXR2UqxxuoPl4H2gEaqXndriUaq3qPSle4rr438iI17lSYZnT7MD6dE5SqQaqyNbseOaKhaPMJe\nqXn6jl3vBYn+vhZ/an6zyPp2keM5uv0tF1/PWzQ6zK/W8zhTIymqpLS29qj98B62mt2BqJL66C0b\nQ29ZTeYxqNuxIyqNWCFJMSvMC65Qe1e0SpNUA9HanKyVylRTlKdt9X4vfBcwPuLjk3oQR34/0N57\nT/rTP5W+9jXp3LmL3ZvYYostttguhn2UZ76L+h86s40CGoKNZpAWYgI33SRNN7Br4LZUWoYB38V4\njuFBFYODtQ6RYYDPHpzLxV7LR237HNIBF3oi0Gw9pvRz+y0vM8cf5PNxemWFwICIgYsGaQPSFURt\n654QENQ47XK7OtKNgtvsD/sGrPY4xbhCpQ5gtMrGkNbWrvauJtyjGoySPd9yRZv94b7YAaFyEQ8Z\n3TukzcJB6Xnz3UjVS7fglNOQxlwpNVh/6zRKOzRIugencbdJy0xUKK2tXcUOrKxdA4IUy4DlVwzs\nqMDEqDQdy9sdiOVUFyBNcBGlFyQ4qbXRnLbpxOlLxAuSHjBBKcurbhVLPKd1iXTmmAFPEzbyPNAm\nOXW5QlwmbdVwqcDGs07jFGBz0ADa5z6rIRRKqnUhpwabr2U+b686VZeTndbJdqkvOnH6ElV4G6q0\n9ThVBj5ZLu1VHxe2CgRJKdvmsQSkITYvykMaZ3MGaz3fPNAEPWdiU2NCUC1xgzyPtczBcqneUS8F\n7ruVmiwWSxqDdDMm5pVl66LS18dq5Yv5shzkYbKNoIck2Odrt8Tz0feJLlKJr6kG0MlLLQdXqxCL\nnd7s13tT/VUZbhblmODUWNWaoFWlfa8N9n1J5HPLdbf7YI+LcG203PFiOT2/PhKmgmod9DkxEbNy\nNWP0d1WG92KztASjQN9r6yEJtsmRj/QVm6/t4KA/zPe+8D+E8REfn9QjBr+/3k6dkq6/Xpo50+jQ\nscUWW2yxfbbsozzzXVCpo4/d1ptiVp6/rQP4oReTGQvHn4VqpnmZ0e4cvacbB4CzhXBVHtCtH6eA\ntCeAYQnYb/ROIyf/kkmDVgNw+Vfhx1dMooqvAXAnlRx9egBvANxghM6f1wLLwOiUP6cnYZGY/VAB\n635h5NE0QD+GO1gJDLYqMAznuaNAtveLfkxoegV4C26xNvMwguieW/pzAJh2eTU9b4F1vwKWw+Ym\n4AW48Qoj8ObleDXfH8LWRmAadFsGZJnP6NEPlsNR4Gv8CGbC/6QS6AlTAI6yKW8kPYGV3E7WP71l\n7NlCgN1Qae1Pu7yaUzYVDMkHMtKsUM9tZ9ny8jgO/cTm4t9+4mOeCTVD8vnnfXAH/8jxHwN3wZRL\nV0M10PvzvEFYrGoH/9D1Tob/yWvwY+/nRIBM0gqOczsrSSs4TmWv6VTxNW7sCkbJTYMqmHppNdAP\njh2nkjvhLiPI39DyImnAMyensRnIuNl8dnN6WLxqsJdzGkZP4Og93axg03IYNeZFYEc0l3Al6w7D\nyq63sxcjnB8osJJSt7MSVkOvgoMM+uG79P9aWDu6C5tbjGx8HKj7OTAa3tgMP3sRq13EIFhhv76D\nlVQzjZ+97KfzM9gE/8jtQDq8AHCKf+BO0rE5nX64hksKTto5d8Hxe9PgTthss8dmn1dug35Wnpjb\nT/7QJrJLhhOdz7LuMECG3U/YvbYZeO6k+WzXLRlw22kjhN92mjdehqE/Psgf4+uvya73NX4Ey803\nQ398kFcnZDPSx29Vp7szEkjcAjCEn68FOMRK7oDbzloJJzJ5LXQBR1kH/EvudXzhn/YAv+SqPFj3\nnl3j2YE3AsPhaXi3sAdMgxNVfWxchcCdcOgnNl8vhp/RvVP7scUW26fdunWDmhrYvRv+/M+NLxNb\nbLHFFlts/6FdKFr+uA5AUCbdgwvdlEvftqiUapAOeTkTthuVdZJM1fl1TGRnp7RCt+qIuqkEvDxP\nsVo0VHUaJQicjrvWIpI9pJCqnHQqriqQKtARdVNHOp3orkYbnasihUJaGmcU4ld0dSRY1F9vSq1o\nnr4j5bvKcotEnVK0zeUSBBY1bUVkS3oVi4CtljTdy9hkmT/Sz+2Xvo3Ye0YFKreoVibSBIuwhRHc\nlZqsKpAOGGWYQr9mljzyGIiMUPjLIp3cJqfiJlULmq6ntBFMHOt+RIP0iq7WEt1tkWhqdfJSpFfR\nwTDCVyhxmaQxFslu+xziQXnErdLEmSpDSnlSYKWQWsPIdyVapFlSpkdjM3FF32Zlqsn93yCosjar\nZdFszoiZpg4dgNHPaTRBrTpJc20+pqpS2dqikarXVFXa+HOlRZqliii6bXToJmVaOaoJ1gc1YGst\nx3xU4nTbMOqfEl87I2VZNLTjCFIeaj+XJg1BusIikZlqUo2vJ1MhbpYGptaX0eXbvZRUKKIlrdRk\n6ZD7Jgs7Z5atfRbLRKQ24LTuNosmr5f00zCSXaanNN0i1QTSBCs5deaYRbcLVC4twMpqPeDrJQtp\nR+p6SYx6b0JaJdLzFuUu9UhwEsRgS084cwwX1vJ0hadtjiwCHAj2SdlIT9p9riVOgyewUmf9lRJK\na5ExDXLsfp2lRXaf5Prn1Ni4bpN4ULY2V2Lr/QaZoNyyOPIbH5+ugzjy+xutvV3KzZX+6q9METq2\n2GKLLbbPhn2UZ76L+h86BJqlRZ6L2a7peko6YA/ejQ70oFQVDtRgo6nQUm9gJRfRJOkRXE03MKDr\n9NQS8FxNyfI1DWSYSnCxxsrpsU0G+qxcTaBI8bjQ2tEqV9pdL1EtvaNeBkobDMRqupXuOYiBqDfV\n30oRReVYAjFR6nbsiKBWffSWA+0OA84/Rc/oRgNF/R1EdJOYIrWfS9NzmmBgaK6BzVlaZIDieXTJ\nwRMOsrarvauBrqhGKjWuclwhTTcAFqo363XbUCjFQO99srJKHelGvw6cNtukTK3FgH2DXweqVaYZ\nqsU2BGCPA7ykNBBdpw2mLEwgqFIS22DYiOf23uTgrm8I2KoEpZ7THLj6dlJlEcgNZHT07VYPNi8E\nxaVen9Z9NljiBlkOao4MIC6TYKOpPld0KplVJ7FG0lc8b5cq9debXvqpVlHOM0nr68xUji5Vspza\n0RJ7z+gpTdd2jI69QdfpxOlLpOcxRWQC3xgo7VSuJ4jGFNUaDtW8F0uXHDwhZRHV/bVc6Y2CNk1V\npYaqxSjZlEeK6VUR/Tpp/tlkvvyevi6NsfrO7LQ1NVWVKtJcB7e1CrDc8/B6KrBNmrAE0XBt1Vpw\n5e5aV+ReayWPdnfYxlSdvATSGSm/87yZAnWYrpCv1ZGau+W+13h96UB0kZWVolZQbTT9VqNPB37P\n2riaBXvUpEyNUp2nIDToar3iOcUX/ocwPuLjk3rE4PfD2ZEj0ogRUlHRxe5JbLHFFlts/1n2Owh+\nmy1n8kkisFOM5fH1OHHYHninedkfmpWtLarHwNV+pYullu+4kfBhv1od6aRAwA4DcPUaaRHZB2XA\n72ZED6kSexg/CJGgkgGRSsvfvN/Or/Dvz/SytpMOhsiS+utN8aBHr5pk/UIOxssMJJGUlhkAGaQd\nBpgb0AZdp2IHBvZw3yq9bRG2I+omLUzlGa/QrTbOBsvdDMXAmkFagpVzmmBAYZYWCZLqduyIbRAs\nlVp9A8E2EcpMBGqx9aO9q0V1WzTUoohfwUrJDDMQPFQtBgAfQHdridjdYe8XWN/m6TvSJgzor3Yg\nVmHjZ5OVoUmC9Ag2l0VSnUZJOZaPTIPEFEkN5u9IvKnOgB1UieXS1/U96Rafh4GIieaDrRpu49mB\n1bMdLemntnaU6wJit1guueVNl1sbfREPOdDfZMJSVT5eCLym8klt1XA1R5sxgaDSxv+sRbQDEPtP\nKfB/Jz1CWuZgWY8gpigFnqkwMLtYsjJJrfb5GkljPId1oAHRAMuHHql6lWmGynydloFIWqR4i7It\n7zvT1hBLFW0GBSAW28bLPpAW2blJj+RmyEopNZC63naQNuHR5bWWB73QrpupJm13sKyFFknXYtvA\n0ELPQ06mNk+YJa3TOGN3TJLnYhcLilWMbd6E0fj9Slcy9P9OiXttrWdri20SdJPau9o6nqfvKPD5\nKvX7GDa68NWF/yGMj/j4pB4x+P3wdvCg9N/+m/T44xe7J7HFFltssf1n2O8c+F2lSarTKI/EBmrR\nUAMqbxuF9latcPVko0kW+0N50gFjKIJlQkvlJsrzCC7qdMaBk0WAqz3SCCVioqRKo4FCjbTMQZ3X\nQO11+h2jhQ5B3Cux/5Qp9C4gJdw0Wv4QXykoMbEhyr1fSRMxWh5SOg2k66f2oG4gzx7sVytf3Y4d\n0XzN0zqNUw1G4a7AotljVetKvM2uFlzutO4yA7c1Rh0NwIWuAgNWXQwYarpTfZcpAmeskTLUakrU\nSFqM6jXSwVq5CzNtl76NK29XWYQ1WxHg+J6+LgZbFDHwMRqwLNOpEyZCxWr5hkK7ReSGyeey1EBa\ngQStBq7G+SbGbBuDbVxIkNRwbdV277vyLDKtB5Butoh0qftsLUbPhmKLdFIiTXfhsFyPfHLSaNIL\nMJVlSlWuAotsvmriaVHkPDsc0z5XvQ7r+QYq0lwDiSst6g8VmqsizdZjGqtaQbEpeVMshkkaE6p8\nF4vdHZqromjdW8Oj83cAACAASURBVHR3n22K3IxFrmeZb2brsUipPMAi7dphr5YW0OwsgmpRaEAT\nSp3F0Owib6WCSulJW1OtytAqTdIWZfu5rb7R0Gp9XC7V+2bPdD0l7XEGRV1q46XM16cq8XUU6OSl\noaJ6qUWVp8gF31plNY+L9Y56mQ8HW18rwJXEz6gcY0CU+BqDEg1Vi7fZIK1CWkS0jkPa9VYNjyL6\nR9QtBr/x8ak6YvB7YbZvnzRkiLR06cXuSWyxxRZbbL9t+yjPfBdV8Op61rOe68lwxav1TKRl+39n\n08CRwC95iS+yfzOYBJAJU+0Z05+zwFUAnIObgE327Xg22vubgMvSgP2ACVftBjYdBugOLcBPYX3X\nicBxuAk2Mt7aGQxf7FoPfwJcjwla1XWjji9Zu/nwUvsXrQ3Oea/OspEvAae8X2ehARgvE48aBv3y\n4GB+L44Cu/IygEMMAtZzPafXp1PHl7i+/UXygA1MZCTw+THwfw79D+oYDxyKxrme64FTnF6fztEv\nd4ODLt7UFHr2CGTBYay/rxH6yKzXxIPsfzGTnmOwdr9s1xweevl6gMOwAb/2cep/9Uew066zF/98\nL7zEH9ETa6fbP3n/Lp1ARi70mPguuwDYy/858j9cyey4++wQNNp5u4Ejm2Bcuvsb4HkfB2cZTx2v\n4WO8HvPtTXD2Jet3pvtsTFfoN8bm5dqBPg/5XqF2Aq6otpeMcbvgy75OOMVGvsQuYGfuIDb0Gpeq\n4rwTH9MB99/+yIcb+RJXZsLpLxPNfR3j2ciX2HTgi8A52tf3t17vhiMNvsZIY+QfvMxE1rPZ2/rj\nw5uADHYA/Akc/3Ka++YAL/HFqAJvP18vr2UNZz3Xs+VX5r9MAH4JjXB9+4tE9wUDWM9Ee88v4cu2\nptZzPRv5EuuZ6HfWAd4a1wc4YH1sgLF9Ie2P4EtspGHI1Tb0Oq9wvcnE2z4/Bs7ejK8jez/A19BL\nfBFGw+ZfuP84Apzz/gA55rcD+HxelsZV2N+A44TVrc+yZ/MXvMLwUagFvmzroCe2Bjf0Gsd6ro8q\nGW8I248tttg+k5aRARs2wKJFUFFxsXsTW2yxxRbbJ80uKvgt437up4xNjgK+0V7O5C/8kLG1rwF9\nuYsVZBRA+Eg9ABj6xEH6YUq18HtQAhSeBdJZTqG9LwWOHYJuGYApwo4HxuYBnDLl2TkwubEWyIBF\ncC9PkFZ4HPb+G2uab4GlcKQCqIKhd2znHp6Av7G27+q1wlWLuwDpQHfuYRmQbviKNLgNWJ6wh/jd\n/8bmzdC/tJ1hQOaK/XBZP7YB91NG9tRXuYcnKOt1N/8EfOPk37MeeKMW7upXYddmGBQKSOd+yoDf\nY/jU10h/7DTkuEOnhJ4dDC1iBMD3YWpfYKapYHcH2pf1Z9y4F9j6L8Bl/eBx+AZl7tOerno9HGZB\nIcuBfhR+bjkhrsgD69NYuIsKA0S9+9E8PRNIZ9Lmf2FTI5xY1sdPuYq7Lq9wYNvPrsFw7+9wJgKX\n3wWrjgJP2zXendMDel8OpFHRPpOv9bLPtQzzbQmkFcKf/eJpXnOfPfsebH4ZoDvP7PN5+L6tGy2H\nPve8DVzJ/qcyU+uEntzDE0wEsp5+ixteftGUoQEm4mMaATNtHKHdwzLW7YJujxPN/T08wT0sY8aA\nCqALI/90k623sTY+8+UpXnt+LN/nG0wdaH1c2vfrwBsmiLwUei46C9MARlDI8gj4HgLuO/wDRv5k\nB/cd/gE3Zpr/TOG4H0yDsl53E90X7OAblPmsp8PjtqbuO/wD7mEZ9//q+65oPoJB338XGMG9PAEF\n8KPD8LPnYBn3MHptM4yGS+49ab6ZCSN8faY9jq0jf7/b11Ahy6Ea8sb5WiID6E7Brmfsx+vhG3zf\nlKILgGOHqAPu5/sMJlQL705+Xo3f/cNgDj4uA+GFLOeGl1/k/vfKfAMGbmlZQ2yxxfbZtiFD4J//\nGR5+GH70o4vdm9hiiy222D5RdqGh4o/rwKmyAbiysOUnNoTU3MWWO8pqRfm839PXVQx6StNNNXa8\nU3tzcHGqZlWBC0AVq1JTBUnpeatRS4uMUrvB8kEDEI3WRgV4zmSxYKPqCemc5RGds9LbrgFpm1Or\nl0kMc3rzbFnOKa2eL1zlvyuWso1O+6jmqNjpztpgYz1IqDQt6QGn9y7C8j79u+u0wai793q/J5qK\ncgnoHfVSi4YaBZpKr49brPtUoo1gCtJfsfxao0xXG2V3iOX2VoSU4kpEgeUHT9Iq8aDlRfO0ImXp\nJmXqVq1QMUYbr8LUotdpnNGap3We02qN0zoVaa7W4vm2DRI5Mkr7k6YUnK/VokouylVhc5Ab1sFt\nFjQoQ63aquGWYzrH53i5X2uV978QV82W1ZntYXm839PXtQerQWsU5RpVOhWeLKvzPEHPRdTiRZpl\n6+RtxDDPNc7Hc6kDQanR18fZ3JSAKDIqcBm4wJUiWvOpE4jqVA6wUYDbnBa9MaJ3j1S9Gny+tRBN\nVaXKnOpcphmRCnSYB57WZnRyPWtUdlNSlhgb5tZa7V1GSxTb9TXk/DaKNFdTValiUtfTTRjt/woE\ne5TE1ayzXKn7ZstD1kBX8M40ursGYrWUc8Lrl4km2VpqkujWSQWdEgVgvv2K3yNLrV+LNMsEvTKs\nbvYS3a1sbRFTrN16jdR+pauSFAXaBONCCv6FU2DiIz4+qQcx7fkj2xtvSP36STU1F7snscUWW2yx\n/TbsozzzXdw6v70tBnhkm71NA0Zc6t+1eJ3d3NNO5z1FLo2cAvLYbLTQ3U7tzQF2AvTjAEayBNjK\ntfaPlyGXrQz6wk4Ajo9Lg2z/UaO1MThshzQgnb3AG+8BdOfz2RZ5O4zRMYcDb2X3AfYb/Xkv9PU+\n0wBwFEbbuRZOTeNQi0WrwjE0ci1ssrhxv2yPbWdYf7pj7ezaZ9caDGw7OQKutXH2xMZ++QhrczN5\nfGHfHjTW/HSioQ+QRi6N7AVyPvc65ELeyS3kndwC9OTKK+DnP7dzD+FtNli7O4AmciAbo9Q2WT+a\nr8jk6l/s4loa6Qds7prHcGBA41EaybUJMxf7nPYkl0YayWUE0HjpSJu3vfA6OTDWXnNoglw51bc7\ncA6ysDY5CvQlhyZGHt7BNoA8p8XmOBV6s/usEQ7tBDhia+aE2Os+3wkkcsI2e3IYeAvrSz/gGpqc\nXmtrBaB5YCYM876Ohiau8V+cs2jytrB3NveDMRcYffwQGcZHZvOloyD3bCqiTDpwOSO6bgOO++Lr\nQi5b2eUjZjS8zjUMBjJ37iePLfCyjTesUTzi8jfY9qsRNm9Ndg4ZNqZDfqV+PkZarN1dPw9XuPks\nj800ksspUtcjz9r72S+shbPA5s/lwTXum1wYxWZ27bM2f77L1t2ufdh63xvWyO5OxtW7bC01AqdD\ncrJ91xO4lka/V4AG61cuW7mWrbAfRqTbb1reyoEsG1fuydcY0HTU6d42jmtphGgGY4sttthgxAhY\nswYKC6G29mL3JrbYYosttk+CXVzw22bg7fIR9vYssO2kf5ftFMrGbg5Ku9NILt0xwMZoYJgDj0Yg\nC+AQAyACGaPCrMoxBjbf2p4FQM8Xz3rOLpBrbewN2+EsYA/WV3UFOMXxJnvo7utt7wAGtbwLZBiI\nHuwgPBt/kE93EHzK+Ztn6ZdtAHMzeRHoYKyBh0MtDtj3W39OYe1kDjTK9l5gxKXbYKuN8zg29iPb\nDCzksZntA4eSeNH81GP0u8BZGsllGND0q2ug0UDY5ktHAcf52S9gSKad2w9v0306HAyQtmA5uzk2\n5qv37aL5iky2ksshIO+9zewADuSmk0ujTZi5mMuvAThOI7nk0sg2IK/9Ncg1f11DE2yyVwNHCfuO\n40AX2Gmg1UZ4mCZyeK3vcKNyv+xz3GSzxRj3WS70ywK43NZMjwSD3edZgJrCNo/TFxiE9eUQRGuL\ncH35eNntfW0IzwXowgEgMSLsnc39XswFOwDox35LeLYNh4Y0z2MFm/UjNJ3MAXr64jtHI9eS6SM2\n37zOXmBXVgabGQVjUsD3LLDtyFW2sTHa5ohNvoaGOejFQfBg6186kDkkXOHms83kkUsj3Uldj83W\n3pVXWAtpQN6vNsPrvmmzGbaQR+ZAa3NIpq27zIE2FwwO6c+n2N+c6ZsbQLc0UnaK48BWcv1eAUZb\nvxq51jauMuC1o/ab7EFNsNPG1XjpSA7kpHs+uY1jK7kQzWBsscUWm1luLvzkJ3DHHfDSSxe7N7HF\nFltssV10u9BQ8cd1AFbfs0leyzMQ+0+JG6Th2mrU11mhWnKJIFCN01NrwcvQJK0+bQ8Zvfl1oxV/\nT183tWWqFZY2Kgnp1KwVbFctWJkiSqyNhyR6SyyzOr7P6EbtVR+jX2ZJVEnzNc9KrsyUoNEprMX2\nutr78EBIbT1jFNE8o+dqj1GJq8BrkdYYNbdOIkdiiaR8jDa994w015SHuU1eEqfMav+SNAopSZEt\nr/e60VWOWyNaLtVG516pyZEa83asjE2lpoqxUscRU9Keo0dtHmaaT+s1UlBulOfZsjHeK0GD9oUU\n7aclqBf3hmV1avw1qQy1SjusPJMp9VbaOKj3uUwKygX7BOUqxhWZV4X1nAMvf1MT0Y8DTEF6i7IF\nJ7VEd6vEqb+a7j6rwJXCA6O2E2ilJqsmPG+wBFVarXzN1zw9ptnWl2qjPo9VrYaqxejQBIIGnekV\nUrHlr4EdSyU1uBr2cvdRsURSPtZA5MrGTr35IWltbNXwSLUYAitRVWBrfbXydatWCNrMR0mjt691\nenFaW7tGql5pbe1+frnXyS0RHJTybQ7mqsjozlW+VijW1/U9dRyx8kKsl9jpqQWUe6mgcu+jpBqj\nqWuVlRqCenGZ3DdGPz5zDM1QmXTIxnHmGK4UnhQPSaNUF/UxvIeN6h1YfeCGkAouUSS7d9bbNSLF\n7fHyNIYybQTNVZFa8bres6VB2iF2d3hN5kB99FZMe46PT9VBTHv+WGz9eqlPH6mh4WL3JLbYYost\nto/LPsoz30X9Dx0CAzujJTijG/WMTpy+RP31pmo9tw9KVYbVsYVae3D3PEllGnjUEqL8SqrkpVMC\ne7DOsrahygCkl2SBYg3XVvvNeuk5TfDatIEdRYpAjOosN5JqiWVSi4ZazdTnPf8332rdbvcH+fZz\naVZLmMBBTGBj3N0hWKu0tnYviXTS6vO+jpekCUQP6UY9Y4BgovSm+muFbrWc1sVWtmi6nkrlV7ZY\nXis0S30tNzgs+wLVDmbKPQe5wY9AOmA50xVYvqiBTgNazApzM4u1QdepysGjja9RUKVHNUcNERjd\nHuWYnrzUasEa8AsElk/aqgw1ek6s8jxHNzMEgJUG2DP8nNskSKqCzrV1K+za98o2DZZLUOIbCR3m\ns96yGr9PWq6uHggBZ62d93wnUFUt8bSkcWi+5gkq1e3YEa/xu1ZQpVYfUwDSHFJ+XS+VaYatrUap\nRPepwTcVVmmS9qqPVImXawq87FKpVmpyan0RCMo9Lz2IfMV8iRZJY8w3dk6zjYF9Gqd1Sj+332tf\nl7v/zljOuufOKxMvi2UlmZTdqRb2eKubPUuLfONk7Xl1ildqsjQH2yi4QRGgrAcrK8Za3+CpERNt\n/Iy3PjNRgnYpDy+5FAjKFPiGieaiUarzkleBZqhMUO2lyQKBPK/a/K9b8A2a2mg92rgaBNu1Qddp\nqFosn596TdBzulqvxOA3Pj5VRwx+Pz5bs0bq21d6/fWL3ZPYYostttg+DvudA7+TtVJ6FQdOgfS8\ngUw9Yg+8z+hGF/FpFCQt4ltogDMETRqDR4qrRaOkTLyeb7MDXxPSOnkpDgCLxWJpv9JdnKpZGoM2\n6DqNVL1gj1huIHCjg+fJWhkJ/ugKE9xivmTRrI2Ccq8HW5N6SG+RmBKCyD2qBGm6CXrpHhMFCkDa\nY9HDHRqkGSpTEqSf2viqMbGmFg0VnHFgVm2gl0oDwV9BTJNFY5fJQcQewUG1YqJdykfdjh1ROV4f\nuVCarccs6pcjKRepIfRpVQTitccEsWCjVmmSmG2RurbPYfVUZ0qrNMkAZa681nGVtMTndKZMNOky\nB4uF8rmsMHBfZSuwIx3pSQem2TaGdRqXqqW8XtIYA87NOFvgCqzuayh29dOUKFkoSAVlau9qAlSN\neH3m/jJhsmysjjPlOnH6EqmvrQ8t8nknELPDMVntZ4u8B4LARKhAugmvXbtWTcrUFmUb84ASq3VL\nUhRKWhZuFCRFUhqqFgPxJP13G6VMEz/TzbYhA4pq8a7FwLeeRZrrr7cY8LV5axBr5HWZKxwI13gt\n6woDrRO83vWzSAeQ6vCIqTzqL23VcPU6/Y5Ksfssra3d7scC6Wq9oo2gHicOa7uvT+WHNXkDVUf3\nZYU26DrRWw6U5QC+tNMGU4e0wzZz0traBc02j2+b/0OxubkqcgGxdr2p/lKOreESbG1qsY0j7IMB\n9Av/Qxgf8fFJPWLw+/Haj38s9e8v/exnF7snscUWW2yx/b/a7xz4hcApvB1G/V0vzdN3xGKjgE7S\nKkGxAkxRGCrEg/KHeVN2Zpq0Q4Mc7AQWffKoY9vnwshfvaBUIUXZwHUyUgtmmjRO6xycBHYMUwR2\nVmmSgZ8bJEYbwND9RBHMBgcEJWEEdi7S6+FDfm30sM8sCcrFQ3I6bb3Ye0YrdKsD+MCAa50E2wXS\n3VqibG1RuUdPSxz8VXmkkXvlVNNqaZGp3qYiv2W+AVBiFGqq/Ahc0dj7MUkWwaPRIuH9QzpsUvla\nrQBTAlZB2EaZKUjfhEcPq9WRbtcsJ4zKdiikYDfiqr43m79qQ+BU4YrL0dwctHPqzO/qi29+BL7R\nUGWA6lUcGCdTkcA6yWjUclDbblTwLF8vvaV1GufAPrC5HG9Rc6PiltqGxjKfIxp9vIHWYmrHISjO\n12qLbnNSzJT6600lQVfrFY1SnUXzs1LRfGMBFPvmStDpKPGNjPB9qa27Qkk/NUBn51RHAJY1sjW9\nxua1woFv4KA2BKFMMh/2Ov2Oahw4W0Tdz91/ypS3Kbe5flDR9QwwtzloDcRiSfmm9J3a6Cmz7wus\nTQPdEmxULSG1PxAUq8pBcXtXbMNjvre7U4Iyj+4GBpD3n3L/l6kZS2OACr+/kz6uKkG1RfuXydXg\nK23DZMVH+0MYH/HxST1i8Pvx2z/8gzRggLRr18XuSWyxxRZbbP8v9jsIfkulOTiFs0JaaBE6bUDa\ngwPEZqOxTpNFKfc48Gm0qON+pasU9Kb6C4q1RdkR5bIeo2lSLdFFBiw9EgzVFjlcitFUr/CoKIEg\nqRW6NSptU+URviZlqlZjddDBxFC1RHnG+go6rB4GIhs7lXRxCna+Vltu5DBJOyySR5WiSLZF6srU\n7dgRaaHRmaeq0kr7ZCPlGXV0r/pIcyw3tAbLuyzHInNBGMm938fRW06bbTfwM0V2kNRGLPK+1kG1\n5li0sUVD9Zhme/maWovK1hlwKfHr0E1SvvXn5KVGk17rEb9XdLX0bAh+kgIr+RPmCmuZRbM10CO2\nA8PIYKMyFOYsNwoqLddzjRwYnxS3SY9qjgIsUg8NBo7XSFpgIPZGPaNRqtNwbVWBym38OVKR5qoS\nHPwm1aRM1WtkVLoHJG3DykVlmY+KfUwd6RZVtmhkIOiQcg0otp9Lk8bZPCgLKdOimVfrFfdJ4MCt\n0X0aKCz1A22+OVOmkPb7lKbr1An3zRBrj0Jb+yQlLUFqQFqM4KCtmzWSng2jrmVaqckRXVw3We61\n3rb1OVWVFi0tQPq2r8chSG/79bJsrEPV4lT4EqmOqIxTWBqK/rY+j6ibb1J5/vlyi/JbmaRAsMfY\nGEuIylsZrTmwdXqZUps1jbINhyxbY3NVZJHpbHkuc7WNa4rELGcM1GCbWeMlcmXlumLwGx+foiMG\nv78de+IJadAg6a23LnZPYosttthi+6j2Owd+7WG9w6O/QRQ5onf4vjGKKEJgEaIs6cTpS1ygJ7CH\nXioFgVFep0kUygFwUhBY1LECq5M7WoJSi3b18OtMlCzSWqUWDTXQ/JAsJ3Sm0UfhoD10z5Qs57BE\nqYhdoDC3N+oX5VK25ZO2KsNAcbZM3GuYFNbhhZPe/h4FeL4s0ljVOvW1Xikhq8oIfNlrjYEiz821\nCKr157B6mOjTbEX1c5uUqSZluk9rPVpa7LmdHR7FDVxgK+mbB82dAGmJ6jRKWmnAy3zQ6DVWix0s\nBubXFlnkdrFvAkRiV6G/kt7fpLTENjrSz+33voaA0SL11SAVeg74EgnKxUy5yFcq6pihVo9mBk6l\nDWz8h/DzqgVJA7FTlBKmos36OVjiMkWiWVDiY0rKIq/JTkB1j0UpR0sWcQ58nrb7WAMDeV0kKPGN\nnFaB1VEuBq9vG0S1hfWIr7tc+XWSglat0zidOWb1bkGeGy0HhIGPP1CYXwuBmBT6pS3l87HyOZev\nO3lecjIC/NbHCqsV/YLT6fv7OqHKfVMhbbLNEkbLI6+BWG+ANYziagG+qZNM9aGL/dYi3mek5629\nWo31e+ekAfHKFHMiFNSq9Ij2Vg33NdcsLrPxGDMkcLbGhf8hjI/4+KQeMfj97dnf/q00bJj0i19c\n7J7EFltsscX2Uex3DvxC4JHIjUZXnCgThRrsD92rpZB2armDJf6waxTYwMHPJK3qRPU9IzDgo0Uh\nmKzwh3d7CLcc2kBky/MJJVaoE1UzcHBnwG+oWlz1uMNAw3pThK7Goq4BFv00oFSlPeBKwoEBNQID\nRD1k/egtz02sEAVGm6VY/rtqB+NVggYDc4slDbRIbRjBDcDAXjdJ2yyK/oqullbiQk2BUlTipEex\nSxUCZAOH9R6Jk89Dpfu0NRJPoiolimV0WKcoPygDQqslKItyOQOP1FkudCBISoWITZIOWMQ7AGmM\n52yO6QyOLCJoQkiBVNk52hqC5VaV6D4Hb4EBOirdZzWCeqcC1zoNPQTprcrWlk5q3B2K8mVny9rv\nrYgmDuF4AynfadsOVpuUmRLS6iIxX3atJbJIf4P5LP3cfjv/gF9zaTjHQTQm5XLee9gnulgEWHn4\nOaXep3Ibb4Z80yfp0eQKVUMkqBXeFyH4Dzzqbp812Lkz5RTiYuvDZbLXJUa1t7kwcTQGS9oTMjRc\nHZ1i/16CemM90KBIhGuFUmPMsTzeMDc8ivDfZtefrcf8t1W+uWTtJ8Fp0CWdNsFCf5QZhTpLvnlT\nYms556P9IYyP+PikHjH4/e1aMildeaX07rsXuyexxRZbbLFdqP3ugd/xVsakhlRkRzelhI80xOmz\nt8kAVquL/ryK0yqVynX0CFAQRZRLXfk1kPJMbMiEhSyHlzovs+J04Y50HMCVKaQJWxmWtdIjJrQU\ntq2cMJ+z3qN07UbP7C/vV43nRTY4pbYsEunqOGJjuE4bpDFEZZsOelTrIJbr2ZFu4k3KM4EpqmWU\n3N5h6RdJc6zN+1QiLQkVdj13lTLtV7qSDsS1A2klHrVtlgrsOmNlSro1YECqhwO5OumSgydsPGMl\nZXp0cqnRv5sxhWtlIj3i81Qk0UWRWBI0a53GqceJw1KuqyrfJsEZ0WBiTjRIG3SdRqnOxKyoVUgX\nN7BVLZCW6G5pma2N9nNpCjChswqQsm0sewhziBtdyGmPrZdWO0+LwvJWrZ3WSbsaQbUaq6SDxBCs\nLtIsG9NOWaRy7xmFmwr7MEAX4JsNw0wk7eSlOKBviOjn8zVP12lDJyC/Tww2KjZU+MZDiVZpkpLe\n5l71EZusjJQWYZTsmSYkVoy9zlWRUZ5zbO3s0CAHtCm1blOa7hBZ9lmVn7vRfdVxxDYmkthre1ek\n1y39oJLUepijR03B+oB9f0TdVOl9rfJrhfcvnHGwWm3R5zo5qG3tlFpQobVYuoJFn0ulK6xfOoC2\narjgoHQLluqwXOIFv98rsajyQJuvKvDSVqV+z174H8L4iI9P6hGD39++zZsnXXON9K//erF7Elts\nscUW24XYR3nmS9h5//mWSCR0n0r4+8RxYABwAEgDznZ6BQqLYHmRn/VN4HtAIbAJ2AZ0B04B0Kqn\n+MPELCCNUubwAIGflwddboSJoI4EidoA6opg/EK/TqqNChYwcw8khpYAXdC4B0i8GLbT3V9P/Qcj\nG+H9As1dQOLxWirJ507KgcPAXwJ/69fNAzZHZ07X7/PDxH8B3gKGAUeBQ7/Bk2Hfvwo8G31azQKm\nIeBvIPub0FIE3GH9WvqHJGYFQD9vP2xjJPAakG7XXl5k/j/PbgWuBDp/fjPwHIN0G28lqrD564uW\n3E1ivuDE+9t4n/UoggJg2QqUfxeJ2oBux/6C05f9HQCHVULfzF/C7p8B690v3eHBb8HihaR8Pgj4\npY9pMLAX6ImtlxV+HqhyAYk7i/3ip1J9OLHQP/tL4HGATmNyqyuC8eF4Bnibv349qGIBibsCuLcI\nlhWhmgXQC54cV8Dd11RCUxG3aghXJWYyv7eg7W+wtdG5za/6tXYAL6Y+Hv0wNBSRmjco0ACeThwA\nuhPwEAuiewDzGT29z+F9NhdYyHn3HLj/TlGrleQnbuj03Vz3TQAsA457m4ew9TQMeNnGPmQBiS8I\n1hR1ateu08wCribA1lERpSzgAaqxeZwLfJ7UGvsm8Dc21tGL3B/Hgee8PYAZwHJ/Px9JiffPRWyx\n/S5aIpHQxfp/+rNiEsyeDVu2wPPPQ3r6xe5RbLHFFltsH8YSicSFP/NdKFr+uA5AsM8iOQ8Y9TUJ\nqXI8DU4jfjCkSdZrqipVhZUGUqvRVes94mcKw7VqxaOoJL0ETbGOqJv66K2Idqq5iCyLUA5Vi+qx\naGwohgTVlq86waJJtR7h2u5th1FEesgUa6d5pK1KFqXijJSNoNwp1knpfou0TdBzqgSdOH2J3lGv\nKOpqkbo26XmPbm9DKrDIVuBR1n0gnvZrPWQiUzUe9Vqiuz3SWOO5k0lla4vlmr4gqa+VkQqjjZUg\nzbR+NHaK1m9feQAAIABJREFUSrNUUhZGLR7vc7D/lOWoPmnXyVBrFHEvxlSnTU1aotj8qjlGx01r\na1edRtlnq9Ag7RAzXRRpOirTDMsvnS2nYDvFt4dcBbhNsFZskkWes5FyvK5zofXvxOlLzGersDJS\nGbIc3lxTs56qSikH1RNGFCvUHK6b28yfaW3tqvTIr9VZDpyaLhtfLzzPNFBI7dUCorXB+hTrIMyT\nrfYop1YR0Y8jei+NLua13ceYFLs7pL5GDdcEEwYLMJbBrVqhOo2Kor7Fvt6KNFcnTl+iXqff8ahr\nm5gtj/gGESWfTaZsrZl2buBrfoKe0xLdrSpsbgMs/1pL8fzrepWDVGMR7hv1jDrSTexLBUTlx6BC\nKjDxNGaGIlYlYonVQc5Uk8hxVgHFClXcM9XkpcmS0h7r1416xu7XG4w+PlkrjWo92Mb1qOaoUlNV\n7L5OQlQfuCSO/MbHp+wgjvz+p1hHh/RXfyX91/8qPfvsxe5NbLHFFltsH8Y+yjPfRf0PPRTmgY2W\nvzdeVh83wynJVRL8/+y9f3hX9Z3m/YqSS6wMuqkgxVCRITPg4JBaRrQwDyzjw6gXTHFVHpknXenC\nWl3ZkS0+jFrtCduvbtg1c5GByTApbpiJ45Nhog8ZNWhGmnRCa1SooYLQSFMUqECBJQ4UNtLczx/3\n+3y/0Z3OFqctYM/7us4VknzPOZ9fJ5z7877f9534BftL5EGRawLT+lTTY//Jmt9VaIJe1Ydrfg2A\nEjFOYV8jsVq6XhtVqL/cY4BCYvC9SIVrvyDt1rA8hTQBcXda89ug7RAgM1Gh5rctxHiqXF9Zb8DA\nHXJtaKWUr/mdrgBIHaaMVkkqMyiowhTXBAwQBskbAdRYjKo+gOGHan5dx1mo+XUtZUcICynmoSHG\nsdv1piRirUx/bZK9fdOa31RIqkmCmqBTB9gaF3Oa1nzea3DYd7RAFdY0g0lvMKQ1v82CJNqaSOuC\n8v2Bmt/tUU8dglbXyeM4XXF+W1BrW2I+0prf7QZaSweuk+P5uYOcqfNjY44Gpf1NpNmx4RJiXDt0\nRcxXq8fu/qhRr5LrftsN2oYcOyhIClY+j6dznOT7lK+tHljzS2wOTCHOSWt+a93fEcpbPXmTpV7N\nWNW5UPMbomiLvFZq03VOh8+tUNRJV/k+Q5S/n2uuB9T8lkraZ4o8VEX5QJWvFdfsPVUc30fN7+pC\nXzXZGw/VIMoVftVJ0L1T4bdE0BDWSQVwzK5+QXUA5CT6Fet4bczXDf6boFVEvfnp/yHMjuz4RR6Y\nhrIVeB14NX72r4BW4HvAi8DFP+VcZfHLi3/4B6msTJo7Vzp48Ey3Jossssgii38uPso733n/wmzz\nvzxuAxgPTcAcmPVbfws3mkQ55v/aDhSb0LkI4EK4Ib5SSglAOSxkTYGwOboYRgz1v1fDtud/B9Mx\nU3okXPN3O/yPWUE6LoeShfv4IvWFdg0uxXRS+AINpuWO9bUn/n4nV6z9EbMv8hvNWIA7UqJqKVfN\ndJscKX9qPEyPtk/HDE0ugzvg357/VzA/7cFomAOmuY7n+mnf4Lz5x/n7t+CL1Pset5lo+m/5K5gK\n1AAMZdo3X6Vn/gg25DtxIQy5DBgU7RkaB1Rc3uA2rQYmEPe8LM4r45VgY5fe+Ra7gLJbt1JSfTLO\nL/Z41PjnUAJ/kb8j3Eg6KsCFvP8kXPt736S4xuN9OfDdb8K/2bmB734jPas4f85Tx/8wP3+fnJf2\nZVDc+yr3ZUS0I233gDG7Cd9/MkT/LwSu4ousNfuZmMvRn2A0uC/p2rrRY8mpH1BScxKAHzzr+Tzw\n//rUNSyM+Rrr8a8wkbh44XsMnn+E66d9g5uAL1zUAEBRDUAxgxce4YMxyIzsgfM1qBSmw8Lev2TL\nt4hzSqIPJe7nDel8DaJ9m/v/BnDnnnUQn2ZcMEDuKJDbmQQw3ufeQTx7F7LlW8B02PItKJ7/XqyV\nK/xZ4n41xPMxlPnUR3vGw3W+5przF8bnL+Ny/Dw5innlFROhpwDMgp6/+a182+DCAc9KafzMc3s1\ncOuv/zVwIU8fjI+MK4rfl1B651uerzkAv8aP7h0Cs8gii7Mx+oHpkj4j6dr42QPAS5J+E/gG8OAZ\na10W+fjd34WtW+GKK+Dqq6Gx0Vt8WWSRRRZZfEzidNHyz+sA01IbILKviemVU4LSeZ19PCfqZfuc\nUqf+w5E1fAdpnDNZCZieGvYvSdAgoTqv3qyZFoP6vJ4SJLYFWh8UzMiMHTqfsOWpEezP00uhWbq3\nkLHMgTQKi2axObJOfVaNHqvIxLUE/bkjrJIK1OmDGqIENEvrpNmmQqsiKNfTLXBUB9KVQWkeF4JK\nL8nZ4tLIxCJpvq/5sB6UnrKoF9REtrBWXSpTFSFW1I70og/YLN1seu0srVNCQVyLSyOL2SWxze1h\nlqThWIF4nT12OwgBrOFIq0xNZbHyAkme0816Sp9XqbqlsrDqudvzxK5+ezPv6tfTukll6oqMdYsz\noLnwjaVZcFyVWio94wym9rnfI/R9fz/NY3bofEK9e3tQ2PeoCnvw1oK01CJZsHWA4FW/2rBSchJ0\nYmcxEz2heWJxCH89X8jkQpW2Q54u3hkZzR6cdffa3JrPFFfrHo3XlgEZ+W5xqULluCGy1tWqU4Wq\n45rHTp4ndtojWV9HOoC0xP1IxdgWaKVVtGeYvn1QQ0L9uiB41ZZmfCcpT7Gvja/1sR7ZGZ/f6T7o\nRa+5JhCDVBBNW+F2aaPpzSldvyXu1QzRZ0XGvtEewF0KRe09oTqdCOrUiGno2uRnROPcrt5TxWrV\nVEGvNMPzR5NEYzzvz3vNHb+oIP6l132NjPacHWfjAfwA+OSHfrYTuCz+PQLY+VPOVRZnJl55xUrQ\nn/98ZoeURRZZZHE2xkd55zuTLwNWqp2cgpBEGofUndJ2e6WnwtsVCaqkmw04UrADnWoGrddMA4o5\nppua4tmYr/FtBmkFUQOcaLy2aJ6eMLAb5NpMrSK8cpvEBOVBCOxXt0ql+QaItQEOrBpcL1vutMZL\nf0+0qzaAjcIrt0kJpn5qnpWjWWvVZs10u/QQot331TjfJwFpE9IyxFQF4O4JSnKn9qrE4Gaba1uv\nVbuBY6kM2pdEfXK3a3h1JdIo97nvKHlLmsYAvg0BHHMY8D6sB4Oe3S89Y/DXX4LVhxcidvdJzwQ1\n+cmwbGKrjl8U1x4k06rvl9SOztt/LOayTdwm1ybfJunrBbXl1Jd2ol4O2nuNuEHS60jDC/WddXgD\nQqNC7XdcoZYVGuNaze7/zT6vS2WmKw/xBoI3N1qlCqQGb0D0XoB0u9fjkGMH3acKaaUWxCZMorRu\nPCFqXu/1OtGjMTadpr+ntGn2ntBGXe868aARk1N45laHT2691Ow+tGGaNXMkLQ8F6ZleN7rSwFRX\nRo329LS2ODYL2iXoDAXm2th86RAcyoNVXYk0G6kcqQIxRwbwcyQ96lrjVHWauw3A2dWvDZom3VKo\nL0+Br8c8lx8PaIt66W6rVs9S+Ps2DaAvd0jTkB7yJgo0etNntsffG1EtVpee7c2FtOZfo2KzKqyw\n0jpwyIWf8un/IcyO7PhFHkAPVqV7DVgYP/sfH/rMkZ9yrrI4c3HypPTww9KwYVJ9vWuDs8giiyyy\nODvi3AO/KG8dlNYqdqYv048blLFeAQ6atFILVEVkIFf5xb8OnG1dKMFWNQ7IRNn3NCc9H5nJbTJw\n2UhBpGqzr1EfoMD1hm3qJPWYrVPvBSHsFBmzZghv3T7XNo4NgZ/FcrvoDkDUGJ+rkiYYiFZqqaoI\nj9uN7ut+Cj6sui8AynK3pyV+N1Wt9mG9O9p9g7NrNRg8b9MYWz7REBlK11J2YL9Z3YLada3ada2g\nSdtBKnM76lNQ1ICYL3XjjDD3R5b5yQDI7xhAztXavNBUI2ivSmyzNFb5cbV/bZOmaYMqtVQtRAav\nU6Jcmqu10tfRXK01CG5UbCDUeQ4mKbJ/WwWdKlW3tmi8M5P3hZXSmoLVVQLSwlgLyOJPQ7z5sEJ3\nqQfbR9kjuFkNRGZznGu1p2lDHjynHs16x9n8BVopzWSAH22NBbxmePyrQVS6Tr02DwCVz/SeOIZo\njDp2Ejm7fSjmqS02BHK6Rh3qjPnWMgt11eIsa63ulA4U2AcJ3kyYoWc9788pAKPE9PBmJpdnUVDl\n++vKD16jUkt1qxpUReF+uhnpFsK2y3ZRvaeKpXGR7b/ZY6FRsRlUFkB7FLaEKk/vXyu6VMj+DlYe\nKEO1Egb6J1dJq8hnmW9Vgyi1wNUK3eXa/djc6tA12quSvNVSQipGluoAnP4fwuzIjl/kAXwqvg7D\ndb+/+2GwCxz+KecqizMf3/mOVF4u3Xij9PbbZ7o1WWSRRRZZSPpI73xnuOb3sL9MgLQm9y2iZnGC\nzY/YBkPKfwQMpYtyLgPe4GrXL46FUuC9t4BxAEcYTVo5eorf5g1gELoO3uQq2Ba33QzsjirK8n2U\n4prIvT/wefAe4y+AoeP9/Y7/6Xre9Nr70msMKoZy/+J9og2TAC6DLoAT7JtQ4mteDcOj7SXA1bzB\nycluzg5s0AM/jvPjOuNhb/zuKt7kxzvSsXJDdvzE9ZwjtvXyOp+Je17IVRe9CXGvMuBI1+WwDboo\np4ty4AS7or2foct1r+k9x0LZSLePnTZnYkLUjG6GLj7Dm1zFCeCizn4OAK9TTjldbuzYqPudAPCP\nvMlVlNPFXqB4C1xcvh/GxvU3QzldfJerPTfl6fgXw27/zj18j73by+iinCtHAW/EHG+LVfOhMeOS\nuFYplMU4XHklvHEk7st7jI75ZKzn9k2uogRXk77B1YV1sjfasSM912N8BOBqVxm/F2N5BB+7AYZ4\nXgEGvwLsTI2WYp45wLGuYXi1/xiAN3uv4uqLovK6y/c7guftDX6brcPLKI4zioH+bRdxFW/aMav8\nZMz/j2F09I33XSM+1vNxeczLQFOjN7iaq3mDyyjcjzdi/CYAHOTXgKGb3+fATs8/O/CcxZr25wbB\n1fCjSUNgbGrQ9X6+H8MmvgOl6VM+KN+CN9K55xRM8k/f4Gpff7TH8nXK3c9d7lcXn+F1yjlIWsHu\nz8DQvBlZFlmcTSHp3fj6I2A9cC1woKio6DKAoqKiEcSf238qKisr80d7e/svocVZfDg+8xlbIU2d\nCp/9LPzFX0B//5luVRZZZJHFr1a0t7d/4P/EjxKDfr5NOt2IV9c9kL4MX4ZdbtkbILgUju0dBpxg\nFHt4DxjFHpPI9hs+Dx3uf8OFHKDgkLqHUcApit6CkZPf5a3Sif7FlcCl/tyR3SN9DeDyEuDIIOBC\n9v5PuOqHAIO4HL+0H8HQrATg0/HNbuBQ3HA/bhfv+fffGsTlB48Ag+Adnz+KPfxjtO2Kt34EGJR4\nIj4R58d1fuh7pZ//xHCPS3ovbwTAyStjTEYBnOKHjIS41wHgvNLjMNLfn89PgBkGWO/CDxjNgRSW\npWN6IMZuBPxazMXQGLdR7GEkPzSIGeOfX8luf/4Sn38K4B3Px0h+yG5GMyLO7909AvbH9cf466fZ\nw/7SMc6HpMDo0nT+3gMuZMjoHzGKPRz+IXzy9+ItsTRWzYfGjKNx/6MGYaPYw3s/hMvPh82Myq+T\nT8Q4FgMj+SH/GGtnlBek18klsJvRMDJtj8f4wujjkVgb7DXoH5Suj2MF+TDKgLcYAMyKgaEw+mT0\n7xMAjLz4XXYfDzD9ad/vt4HR7GYUe7jyJ7t5P854P/r/LiO9YzR4sNccn4BD6bZSsdu23+07ArDn\ng26+o9jDHkbxr/D9rop7syedw1/z83QlXBZrKF1L/DA2bfZ4TPghDPvBMdifPtnFUAo/5FP8aN9w\nOJre+xTpaOTX7VuFefS6Hc5bhybyyfi+nX8Nl7pfo9jDKPbwLgW08Gn2ABP/WQfuLLI4E1FUVPQJ\n4DxJx4qKii4CZgLLgL8D5gPLsVF180+7xkf9Dz6Ln28UF8NXvgJz5sAXvwh/8zewZg2MGXOmW5ZF\nFllk8asR06dPZ/r06fnvly1bdvoXOd1U8c/rAKR96C6tCH/SRA/qEfGSgsJYq+JDva6PpT5Pi35Z\nE5UQHq1UWZzobgmqXYvYg6mXpRJ0C5K8j6/p0HVisKSZ9k+FevWeKrbd0P0S5bZ6UTOuw31B4nFp\nmja4/vB1CwOlVFWoFVSFt26NxanCgmfIsYOm1k6SNNuU4YS0jrlHbaB5ekKslsZri7TD1NylqrTQ\nUQWiS/ZIpTmo3TVhDVMtVsm+qhw39fYSKe8jO7UgDlSPa3irMH17jLaJJuXrlPuOontUHWMdljG0\nSGVo8NHD7uPeE4JCLbRtb/p13v5jQeftCdpttWnpN9vT13ZDnUE571fBdqo15qhVVUQdaxlRs5qE\nT/AeQaJKLVVttF0rYjxfN138a1qiTjxmGklQaHP5GlA9H5ToxxE5CTZrol62gFS319AMPasqTAtf\nq7kD/Hjl+0WNsmtnE0GiCXpVmoJ2a1jUWtdojLbZFqsr1sZar0vo13bC45hq3aSntUXjgxqcmBo/\nKOq914VX7jiPTam6817PDUFT3qBpqtTSqOttcb0udRZc2+E+2V6pTzP0bIx3jQ5qiFRRoDov1mPR\n19YQS2t1G+fI9ffzXU/vmvq+glfxnFhbFaa8p8JeqiiUHJSc2ivWKCjgrTHvuaCdJ2K+n7Mk1ial\nptvfqoYBonVV4rmUKt0kzTZ1viro5YOPHtZazdUSfS0/Zyu1IKM9Z8dZdeBttC68vfcG8ED8vAR4\nCVsdtQKX/JTzlcXZF++/L/23/yZ98pNSTY30k5+c6RZlkUUWWfzqxUd55zuTLwSCxEDuBgl6NU9P\nSPusyNsJ9lOlRvUpSKTNL9V0WExpksGhvprW5yYGq+EPXA15FWhoCqCaRC1mlaaq1QCkS3pZEwO8\nJT5WKC9wpGcsAsRLvva7utg1s50WJ9I815LuxyDm+xohTUuvddxfb1AAyVYN09tR49uvB/WI9GJa\ns5gTI+S+DpaYI/WeKtZ6zTTYeMhCP/eo2iI/z7vusxkE29V7gceuOg/emkP0qz4AytY4EgOuWVGH\n2qkA1BbO4uEUcFSrS2VqibrTzrgPNKlWd6o1fg49AYBz0sgQ3pquPBDPgQ5rsNqI2uqZAUiHFwSq\noCY8dhNxowQ51cZmh69T73s/IPvRhr+wFbxlgahSiRvlGthyWShslQxe75dUT8EPul2ukw0BJ2jU\nCH1f16gjwFpD9NdCTqmyNiSiMcTHJkns7tMTmqftuH66VVNdH/s8Urs/3waCmqhhTgYc9XHv1Oe4\nwUrde09I40JQS1PlTZw2wSHdqgZdoR2hhF2X97pujHpeyPm52OSxXKG7pCkWimOn19StalClloZf\nb6sS0MUn31WCVdE137XQBvyJytSlFpAeNZBVhUE3c2Qf3lnyeM6RoE+aOXDeDHDrYgNiptbbp5hE\nS/Q1QXNeYIxBCn/sVoPdLxEbFG159Wr3a6ugR10q0zXqCF/iTl2jjlB4P/0/hNmRHWfrkYHfszu+\n9z1p6lRpyhRp584z3Zosssgii1+tOPfA72iDr+0BKqpBGkU+u9SDxZqolKBe39cIJYQ68kxnOhOQ\nlhrsQK9yhAAR1QZEJNKXnOU1sElssbMqRKpyvsZWCJGqakG3avOZ4kbpZosj5SL72HtBaiu0Xdyh\nPPjgOrldtFlUi1YDMGq0PbJ3WzReCQFg7w1QMC2sgcZJGhcKzdMs/tV3sVWi2dUvfdVZz1oQl0qa\n4WvWqULqDNsaavMqyc9qhmqwqJTqcVY8tWCaYEB0j6rz1jm63W1oiKwazzkbx0KLN7VqqvQaWqu5\nasJqy3tAet4KzNwhMdrj6gx4mx7TYl2vjTp+UQD8SolBUsmpveo76vmt1j15JWlvUuTEotQKqFWw\n39n418OSqT3ssPaecDa4gvzacfa6JzZDjqsG9H2NMDi8nciEduTnMp275VqUF0/apjHKW2LdIV2h\nHdKq1CYpEVSpFWeeE0J86waLa6VzBj0G6SR6WjdpyLGDAaYTg7dBCuBudXGo0oN6pKDyvcOAtDP6\nu1vDpFUFResqAkjuPWGwer8s0DVO4pJY2+S8LodIzFJeUC61B6rB6zgFvvn7rR6w7vB5DbpVus9j\no9VeC6k43eZ43jpjg4ZBinlo0ES97LVUVXg+U1Bch9eEFcWrpZlu1zaNsc0Ukspig2WzxOPul7q9\n5rrj/jVgUTFq4/qn/4cwO7LjbD0y8Hv2x09+Iq1c6Szw8uXOCmeRRRZZZPGLj3MP/P4zmd/NnKWZ\n36Zffub3Wc3IMr8fNfO7WvplZ36PnTzvF5r5HaNtWeY3y/xmx6/IkYHfcyd6eqQZM6Tf+R3pjTfO\ndGuyyCKLLD7+cQ6C3+3O2K32S3tqG9MUmccExB2KF9qtmqiX1QG6Xhvt2bvKGck20pf9ZvvQpiAg\najpf1kS/+N8vA79bnDVuiOxZmsFrCbADDdJkpC8ZAKaWKn0XI40ygNJ8xFhpmN4u1EJ2SXtVIpA9\nhKnNg1qtMgC5QjsMmF9zjWlVAAO/3HdL7ziTdViDpUcLljRPaJ4zcZ2uDWW1bV+2grTKmVfNMDhZ\npOWCnAYfPeza11XOos/TE7GJUGs7neVux6HzPe47dIV4QdLs8E4e535doR0GgEsMvNnV7+8fddse\n1oPSJgR9osnjqq+7/2zyZkEOpK9G5rVS9r2dFN7Km+U60840817jlbnJwA6axFq5PvyWwjxwg8H7\nFo13f3ZQqAl+0ewBleMa39vtB3zs5HmCOnvnDkc8EHO3SWrDn3GNdSLd5z69qgnant+MSZRa6mgd\n+Yw+u/vymeMcBt+ptZGWka+TLQD5Nm+wsF9pbTovSJoSczrKwDcBLdHXdI06VKeKPCOhFrMWntLn\ntUXjdY06pHFeQ6xQfjMoAfG4VHyo1zZRj/rclCFxhXZog6apM4Bvgvukds8XtNjaa7ktnMrUpW7C\nPuvRqNVeHgyJR70BQGVh84TF0rOaoZv0tJil8MGuElSpCvLtgpz2qkS5dPx3StzttT5Br7pWeIj7\nVaE6PawHlcR81cRzDG1RR336fwizIzvO1iMDv+dW9PdLdXXSpZdK//k/S319Z7pFWWSRRRYf3zgH\nwW+9VG7RIqiRZkRmcKkzR86YHZL2GWgyXxZjutsiUPeoWmovUH+hWuoOP1mSoNE2OuM6QbLgUhIv\n4B32he1BajcwLYCTKu3WsBD6sVdq38VYkOqwaa4NAUR36ArN0LPqL0FP6fMWk3p8gJ9peAt/TUsM\nCG+T9Lgz1eftPyaVGYT0xHjM0LPSDL/wr9QCNREA4yG3b63mSpPss1oN0lNBT10lZ5MHSWqOfkw3\n8GRQtCenEH1yVnWF7lLvBUidSJPQCH1fK3SXXtUEaaEzxR2YctsamxKskphkcN9KeNo+ac9haHI/\nv0Rk8HIWYSr3uS0gvWNRI80LqvK8mFv2BzDPOatIizPpD8ggaojECuUFz3QAwR5ptrOWmmZv4se0\nWOzu011aoSu0w/2fL3XoGgPwstgYecNtuUlPe52MlTcD7iWo7Dn3N4SWEojNhUTQoz2E1+0znssN\nmqbuAI5NOMtaE+vJmyr78/R+g79aA/tZUiroxohgDayLDZaKKAlYI7MQ2mUP3mWESJykJe7/sZPn\nBY273psEr/tefRejO1WrDl0jvWgGg27GnrxTYoNgPtJqpPkFMH+nauOZqpEe8jynm1EJ3nhYqQVS\nc+qdfMjsiF39mqu1Ayje/X7Odnh9Ocvb4E2BceSF2SDRGG3zpsYdEuXStWr3s1qhANhtFrOrknjS\nNHPdG/24X2KIIit9+n8IsyM7ztYjA7/nZrzzjnTTTdLEifYIziKLLLLI4ucf5xz4PW//MeneAujU\nPGfXnMHaLr2T1vIdV0qp7S8xEPWLfou2R+YROsXDfiE22GgOFejEWcF5+MWZnNjdp2rdEzWZx53p\neh0DJ1rFbc5emj7s7JpWu16ylWjTZgnqBD0GSCsQbI521ThbfakiE2Xa5vGLsIrucL+s1waofVYz\npOcL1FNVGPykdGG9iBghLVWloDNqk1u1XjMNOtdKmyOLZvAog/tpzoyp3lnf7gDSjDWIzOF2pPXO\n1bEpUBufeVYzInu+x2Cz3ffRLRjIN0k6EJn3B+TsHm3S5JjT0XJbZ5m+zXrFXDaLCZE1nyBpofuZ\nkGZ6E1NZU+C7SNIqZ0Rrcea/NUC5ZgeIriCfeS3QgRvc/5E+r04VpvJOkDqJdtMkrXL/NRxpEsEc\nSER79Ok6KxMzVUopy2r2vfaA1OCNAm1E2pTWXtcVaM7r3f+UBs10mXL9lLOgpvI3Sg95U2V/ZDuZ\nIGmTNzc0PObyFrdPt+BNjtEpyD6kMdqmIccOClqiDrc+r9wN29Uda0q3YAC90OuRcUF3HyepnbwK\ncw4zDFSGaJQ3Nq505lWT/fs9FKjkOYiNpWbT6jluED5Ogj5BQ9TEJ36+lyDNdE06tLh+e1n073Zv\nXG3ReAPiS3z/zbGG28AbV5OQ5hObL7koNzj9P4TZkR1n65GB33M3+vulv/orafhw6StfkU6ePNMt\nyiKLLLL4eMVHeec77/TNkX5+0b/pIvjWgB90wrhtb/ODnQClsBG+fdH1MOgTwCCYDK8egeLJqYdq\nCTuAKXwbGA5dsANbhsJ7MMmXLQOYBm9PGga8z8QrtvBtPsd7m4HBn+ANgI3wu/yDz9sG+wi/VQ7w\nOb4N3/S1dwGDN8IVn92JvUpLgaHwTYDLol3FTOYVOATjgdR19dXjwHWw5SAwCUYDfAtf/xvQu2mE\nPWK/BcOxJ2rJN0762uPicwyPMSvhc3yb7/wEmCo+Oxwmf/IVd3g0wBGY4n7wez63rAzKytyJ6364\n1Z6rk+C7cc/LcR+OAEyADv4P+AbA5bARSqbu47MjPZZ8E86behxa4ZoLfJ1XfjIZGM7hzTGfu+Oz\nE2CZRwHJAAAgAElEQVToxvcpnvpezGUJTMBjNMGf+TafC+fXAx4rJsN1eIy3uQ+/PdJetZ/j2+wi\n2rcFrgB4Je8aDQy1vy1D3f/Jvurv0gHl7n9hnXzS4zvN83JgMzDFVymZus99GhdrrJxC/IO/vAEx\n95f760YY9s1jwFA+9z+/7dUw9T2+ff7n4nPATqDTfYJijrRfDpyAaZ6v7xJjM87Xm3yx+3B19PPN\nH/jryd/zuhgd/ZjMKxzbNIz0uYAT+bUCpXyX8Nl9xfPNJjzGE+CVX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lCjbpVK9/oaM/Rs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\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kxa2YdpjFX67QrxkdxIH1WBz0Xow5fnq87OmCWIdpHvcJHvObJaj5Mdw3FebGCYWelBMQ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\nEiwrhl1fBR5jthr4XDCD+7SR2m8EbHn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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa8c74dad90>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# optional: plot spectrum of joint kernel matrix\n", | |
| "\n", | |
| "# TODO: it would be good if there was a way to extract the joint kernel matrix for all kernel tests\n", | |
| "\n", | |
| "# get joint feature object and compute kernel matrix and its spectrum\n", | |
| "feats_p_q=mmd.get_p_and_q()\n", | |
| "mmd.get_kernel().init(feats_p_q, feats_p_q)\n", | |
| "K=mmd.get_kernel().get_kernel_matrix()\n", | |
| "w,_=np.linalg.eig(K)\n", | |
| "\n", | |
| "# visualise K and its spectrum (only up to threshold)\n", | |
| "plt.figure(figsize=(18,5))\n", | |
| "plt.subplot(121)\n", | |
| "plt.imshow(K, interpolation=\"nearest\")\n", | |
| "plt.title(\"Kernel matrix K of joint data $X$ and $Y$\")\n", | |
| "plt.subplot(122)\n", | |
| "thresh=0.1\n", | |
| "plt.plot(w[:len(w[w>thresh])])\n", | |
| "title(\"Eigenspectrum of K until component %d\" % len(w[w>thresh]));" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The above plot of the Eigenspectrum shows that the Eigenvalues are decaying extremely fast. We choose the number for the approximation such that all Eigenvalues bigger than some threshold are used. In this case, we will not loose a lot of accuracy while gaining a significant speedup. For slower decaying Eigenspectrums, this approximation might be more expensive." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Spectrum: P-value of MMD test is 0.01\n", | |
| "Bootstrapping: P-value of MMD test is 0.02\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# threshold for eigenspectrum\n", | |
| "thresh=0.1\n", | |
| "\n", | |
| "# compute number of eigenvalues to use\n", | |
| "num_eigen=len(w[w>thresh])\n", | |
| "\n", | |
| "# finally, do the test, use biased statistic\n", | |
| "mmd.set_statistic_type(sg.ST_BIASED_FULL)\n", | |
| "\n", | |
| "#tell Shogun to use spectrum approximation\n", | |
| "mmd.set_null_approximation_method(sg.NAM_MMD2_SPECTRUM)\n", | |
| "mmd.spectrum_set_num_eigenvalues(num_eigen)\n", | |
| "mmd.set_num_null_samples(num_samples)\n", | |
| "\n", | |
| "# the usual test interface\n", | |
| "statistic=mmd.compute_statistic()\n", | |
| "p_value_spectrum=mmd.compute_p_value(statistic)\n", | |
| "print \"Spectrum: P-value of MMD test is %.2f\" % p_value_spectrum\n", | |
| "\n", | |
| "# compare with ground truth from permutation test\n", | |
| "mmd.set_null_approximation_method(sg.NAM_PERMUTATION)\n", | |
| "mmd.set_num_null_samples(num_samples)\n", | |
| "p_value_permutation=mmd.compute_p_value(statistic)\n", | |
| "print \"Bootstrapping: P-value of MMD test is %.2f\" % p_value_permutation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### The Gamma Moment Matching Approximation and Type I errors" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$\\DeclareMathOperator{\\var}{var}$\n", | |
| "Another method for approximating the null-distribution is by matching the first two moments of a <a href=\"http://en.wikipedia.org/wiki/Gamma_distribution\">Gamma distribution</a> and then compute the quantiles of that. This does not result in a consistent test, but usually also gives good results while being very fast. However, there are distributions where the method fail. Therefore, the type I error should always be monitored. Described in [2]. It uses\n", | |
| "\n", | |
| "$$\n", | |
| "m\\mmd_b(Z) \\sim \\frac{x^{\\alpha-1}\\exp(-\\frac{x}{\\beta})}{\\beta^\\alpha \\Gamma(\\alpha)}\n", | |
| "$$\n", | |
| "\n", | |
| "where\n", | |
| "\n", | |
| "$$\n", | |
| "\\alpha=\\frac{(\\textbf{E}(\\text{MMD}_b(Z)))^2}{\\var(\\text{MMD}_b(Z))} \\qquad \\text{and} \\qquad\n", | |
| " \\beta=\\frac{m \\var(\\text{MMD}_b(Z))}{(\\textbf{E}(\\text{MMD}_b(Z)))^2}\n", | |
| "$$\n", | |
| "\n", | |
| "Then, any threshold and p-value can be computed using the gamma distribution in the above expression. Computational costs are in $\\mathcal{O}(m^2)$. Note that the test is parameter free. It only works with the biased statistic." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Gamma: P-value of MMD test is 0.45\n", | |
| "Bootstrapping: P-value of MMD test is 0.01\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# tell Shogun to use gamma approximation\n", | |
| "mmd.set_null_approximation_method(sg.NAM_MMD2_GAMMA)\n", | |
| "\n", | |
| "# the usual test interface\n", | |
| "statistic=mmd.compute_statistic()\n", | |
| "p_value_gamma=mmd.compute_p_value(statistic)\n", | |
| "print \"Gamma: P-value of MMD test is %.2f\" % p_value_gamma\n", | |
| "\n", | |
| "# compare with ground truth bootstrapping\n", | |
| "mmd.set_null_approximation_method(sg.NAM_PERMUTATION)\n", | |
| "p_value_spectrum=mmd.compute_p_value(statistic)\n", | |
| "print \"Bootstrapping: P-value of MMD test is %.2f\" % p_value_spectrum" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "As we can see, the above example was kind of unfortunate, as the approximation fails badly. We check the type I error to verify that. This works similar to sampling the alternative distribution: re-sample data (assuming infinite amounts), perform the test and average results. Below we compare type I errors or all methods for approximating the null distribution. This will take a while." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# type I error is false alarm, therefore sample data under H0\n", | |
| "num_trials=50\n", | |
| "rejections_gamma=zeros(num_trials)\n", | |
| "rejections_spectrum=zeros(num_trials)\n", | |
| "rejections_bootstrap=zeros(num_trials)\n", | |
| "num_samples=50\n", | |
| "alpha=0.05\n", | |
| "for i in range(num_trials):\n", | |
| " X=norm.rvs(size=n, loc=mu, scale=sigma2)\n", | |
| " Y=laplace.rvs(size=n, loc=mu, scale=b)\n", | |
| " \n", | |
| " # simulate H0 via merging samples before computing the \n", | |
| " Z=hstack((X,Y))\n", | |
| " X=Z[:len(X)]\n", | |
| " Y=Z[len(X):]\n", | |
| " feat_p=sg.RealFeatures(reshape(X, (1,len(X))))\n", | |
| " feat_q=sg.RealFeatures(reshape(Y, (1,len(Y))))\n", | |
| " \n", | |
| " # gamma\n", | |
| " mmd=sg.QuadraticTimeMMD(feat_p, feat_q)\n", | |
| " mmd.set_kernel(kernel)\n", | |
| " mmd.set_null_approximation_method(sg.NAM_MMD2_GAMMA)\n", | |
| " mmd.set_statistic_type(sg.ST_BIASED_FULL) \n", | |
| " rejections_gamma[i]=mmd.perform_test(alpha)\n", | |
| " \n", | |
| " # spectrum\n", | |
| " mmd=sg.QuadraticTimeMMD(feat_p, feat_q)\n", | |
| " mmd.set_kernel(kernel)\n", | |
| " mmd.set_null_approximation_method(sg.NAM_MMD2_SPECTRUM)\n", | |
| " mmd.spectrum_set_num_eigenvalues(num_eigen)\n", | |
| " mmd.set_num_null_samples(num_samples)\n", | |
| " mmd.set_statistic_type(sg.ST_BIASED_FULL)\n", | |
| " rejections_spectrum[i]=mmd.perform_test(alpha)\n", | |
| " \n", | |
| " # bootstrap (precompute kernel)\n", | |
| " mmd=sg.QuadraticTimeMMD(feat_p, feat_q)\n", | |
| " p_and_q=mmd.get_p_and_q()\n", | |
| " kernel.init(p_and_q, p_and_q)\n", | |
| " precomputed_kernel=sg.CustomKernel(kernel)\n", | |
| " mmd.set_kernel(precomputed_kernel)\n", | |
| " mmd.set_null_approximation_method(sg.NAM_PERMUTATION)\n", | |
| " mmd.set_num_null_samples(num_samples)\n", | |
| " mmd.set_statistic_type(sg.ST_BIASED_FULL)\n", | |
| " rejections_bootstrap[i]=mmd.perform_test(alpha)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Average rejection rate of H0 for Gamma is 0.00\n", | |
| "Average rejection rate of H0 for Spectrum is 0.67\n", | |
| "Average rejection rate of H0 for Bootstrapping is 0.76\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "convergence_gamma=cumsum(rejections_gamma)/(arange(num_trials)+1)\n", | |
| "convergence_spectrum=cumsum(rejections_spectrum)/(arange(num_trials)+1)\n", | |
| "convergence_bootstrap=cumsum(rejections_bootstrap)/(arange(num_trials)+1)\n", | |
| "\n", | |
| "print \"Average rejection rate of H0 for Gamma is %.2f\" % mean(convergence_gamma)\n", | |
| "print \"Average rejection rate of H0 for Spectrum is %.2f\" % mean(convergence_spectrum)\n", | |
| "print \"Average rejection rate of H0 for Bootstrapping is %.2f\" % mean(rejections_bootstrap)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We see that Gamma basically never rejects, which is inline with the fact that the p-value was massively overestimated above. Note that for the other tests, the p-value is also not at its desired value, but this is due to the low number of samples/repetitions in the above code. Increasing them leads to consistent type I errors." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Linear Time MMD on Gaussian Blobs" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "So far, we basically had to precompute the kernel matrix for reasonable runtimes. This is not possible for more than a few thousand points. The linear time MMD statistic, implemented in <a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a> can help here, as it accepts data under the streaming interface <a href=\"http://shogun.ml/CStreamingFeatures\">CStreamingFeatures</a>, which deliver data one-by-one.\n", | |
| "\n", | |
| "And it can do more cool things, for example choose the best single (or combined) kernel for you. But we need a more fancy dataset for that to show its power. We will use one of Shogun's streaming based data generator, <a href=\"http://shogun.ml/CGaussianBlobsDataGenerator\">CGaussianBlobsDataGenerator</a> for that. This dataset consists of two distributions which are a grid of Gaussians where in one of them, the Gaussians are stretched and rotated. This dataset is regarded as challenging for two-sample testing." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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im1evFrl3t9vMYcnmyqDG0CI1mtKYQGNCJRFU4TfK4te+JsaEG2/MvoGgkmKh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\n99ZJXvbv53FdXZTbkRGGz37wA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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa8be8a6b50>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# paramters of dataset\n", | |
| "m=20000\n", | |
| "distance=10\n", | |
| "stretch=5\n", | |
| "num_blobs=3\n", | |
| "angle=pi/4\n", | |
| "\n", | |
| "# these are streaming features\n", | |
| "gen_p=sg.GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)\n", | |
| "gen_q=sg.GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)\n", | |
| "\t\t\n", | |
| "# stream some data and plot\n", | |
| "num_plot=1000\n", | |
| "features=gen_p.get_streamed_features(num_plot)\n", | |
| "features=features.create_merged_copy(gen_q.get_streamed_features(num_plot))\n", | |
| "data=features.get_feature_matrix()\n", | |
| "\n", | |
| "figure(figsize=(18,5))\n", | |
| "subplot(121)\n", | |
| "grid(True)\n", | |
| "plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')\n", | |
| "title('$X\\sim p$')\n", | |
| "subplot(122)\n", | |
| "grid(True)\n", | |
| "plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)\n", | |
| "_=title('$Y\\sim q$')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We now describe the linear time MMD, as described in [1, Section 6], which is implemented in Shogun. A fast, unbiased estimate for the original MMD expression which still uses all available data can be obtained by dividing data into two parts and then compute\n", | |
| "\n", | |
| "$$\n", | |
| "\\mmd_l^2[\\mathcal{F},X,Y]=\\frac{1}{m_2}\\sum_{i=1}^{m_2} k(x_{2i},x_{2i+1})+k(y_{2i},y_{2i+1})-k(x_{2i},y_{2i+1})-\n", | |
| " k(x_{2i+1},y_{2i})\n", | |
| "$$\n", | |
| "\n", | |
| "where $ m_2=\\lfloor\\frac{m}{2} \\rfloor$. While the above expression assumes that $m$ data are available from each distribution, the statistic in general works in an online setting where features are obtained one by one. Since only pairs of four points are considered at once, this allows to compute it on data streams. In addition, the computational costs are linear in the number of samples that are considered from each distribution. These two properties make the linear time MMD very applicable for large scale two-sample tests. In theory, any number of samples can be processed -- time is the only limiting factor.\n", | |
| "\n", | |
| "We begin by illustrating how to pass data to <a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a>. In order not to loose performance due to overhead, it is possible to specify a block size for the data stream." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "MMD_l[X,Y]^2=0.63\n", | |
| "MMD_l[X,Y]^2=0.83\n", | |
| "MMD_l[X,Y]^2=0.41\n", | |
| "MMD_l[X,Y]^2=0.51\n", | |
| "MMD_l[X,Y]^2=0.39\n", | |
| "MMD_l[X,Y]^2=0.52\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "block_size=100\n", | |
| "\n", | |
| "# if features are already under the streaming interface, just pass them\n", | |
| "mmd=sg.LinearTimeMMD(gen_p, gen_q)\n", | |
| "mmd.set_kernel(kernel)\n", | |
| "mmd.set_num_samples_p(m)\n", | |
| "mmd.set_num_samples_q(m)\n", | |
| "mmd.set_num_blocks_per_burst(block_size)\n", | |
| "\n", | |
| "# compute an unbiased estimate in linear time\n", | |
| "statistic=mmd.compute_statistic()\n", | |
| "print \"MMD_l[X,Y]^2=%.2f\" % statistic\n", | |
| "\n", | |
| "# note: due to the streaming nature, successive calls of compute statistic use different data\n", | |
| "# and produce different results. Data cannot be stored in memory\n", | |
| "for _ in range(5):\n", | |
| " print \"MMD_l[X,Y]^2=%.2f\" % mmd.compute_statistic()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Sometimes, one might want to use <a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a> with data that is stored in memory. In that case, it is easy to data in the form of for example <a href=\"http://shogun.ml/CStreamingDenseFeatures\">CStreamingDenseFeatures</a> into <a href=\"http://shogun.ml/CDenseFeatures\">CDenseFeatures</a>." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Number of data is 100\n", | |
| "Linear time MMD statistic: -0.17\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# data source\n", | |
| "gen_p=sg.GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)\n", | |
| "gen_q=sg.GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)\n", | |
| "\n", | |
| "num_samples=100\n", | |
| "print \"Number of data is %d\" % num_samples\n", | |
| "\n", | |
| "# retreive some points, store them as non-streaming data in memory\n", | |
| "data_p=gen_p.get_streamed_features(num_samples)\n", | |
| "data_q=gen_q.get_streamed_features(num_samples)\n", | |
| "\n", | |
| "# example to create mmd (note that num_samples can be maximum the number of data in memory)\n", | |
| "\n", | |
| "mmd=sg.LinearTimeMMD(data_p, data_q)\n", | |
| "mmd.set_kernel(sg.GaussianKernel(10, 1))\n", | |
| "mmd.set_num_blocks_per_burst(100)\n", | |
| "print \"Linear time MMD statistic: %.2f\" % mmd.compute_statistic()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### The Gaussian Approximation to the Null Distribution" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "As for any two-sample test in Shogun, bootstrapping can be used to approximate the null distribution. This results in a consistent, but slow test. The number of samples to take is the only parameter. Note that since <a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a> operates on streaming features, *new* data is taken from the stream in every iteration.\n", | |
| "\n", | |
| "Bootstrapping is not really necessary since there exists a fast and consistent estimate of the null-distribution. However, to ensure that any approximation is accurate, it should always be checked against bootstrapping at least once.\n", | |
| "\n", | |
| "Since both the null- and the alternative distribution of the linear time MMD are Gaussian with equal variance (and different mean), it is possible to approximate the null-distribution by using a linear time estimate for this variance. An unbiased, linear time estimator for\n", | |
| "\n", | |
| "$$\n", | |
| "\\var[\\mmd_l^2[\\mathcal{F},X,Y]]\n", | |
| "$$\n", | |
| "\n", | |
| "can simply be computed by computing the empirical variance of\n", | |
| "\n", | |
| "$$\n", | |
| "k(x_{2i},x_{2i+1})+k(y_{2i},y_{2i+1})-k(x_{2i},y_{2i+1})-k(x_{2i+1},y_{2i}) \\qquad (1\\leq i\\leq m_2)\n", | |
| "$$\n", | |
| "\n", | |
| "A normal distribution with this variance and zero mean can then be used as an approximation for the null-distribution. This results in a consistent test and is very fast. However, note that it is an approximation and its accuracy depends on the underlying data distributions. It is a good idea to compare to the bootstrapping approach first to determine an appropriate number of samples to use. This number is usually in the tens of thousands.\n", | |
| "\n", | |
| "<a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a> allows to approximate the null distribution in the same pass as computing the statistic itself (in linear time). This should always be used in practice since seperate calls of computing statistic and p-value will operator on different data from the stream. Below, we compute the test on a large amount of data (impossible to perform quadratic time MMD for this one as the kernel matrices cannot be stored in memory)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 19, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "m=20000 samples from p and q\n", | |
| "Binary test result is: Rejection\n", | |
| "P-value test result is 0.00\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "mmd=sg.LinearTimeMMD(gen_p, gen_q)\n", | |
| "mmd.set_kernel(kernel)\n", | |
| "mmd.set_num_samples_p(m)\n", | |
| "mmd.set_num_samples_q(m)\n", | |
| "mmd.set_num_blocks_per_burst(block_size)\n", | |
| "\n", | |
| "print \"m=%d samples from p and q\" % m\n", | |
| "print \"Binary test result is: \" + (\"Rejection\" if mmd.perform_test(alpha) else \"No rejection\")\n", | |
| "print \"P-value test result is %.2f\" % mmd.compute_p_value(mmd.compute_statistic())" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Kernel Selection for the MMD -- Overview" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$\\DeclareMathOperator*{\\argmin}{arg\\,min}\n", | |
| "\\DeclareMathOperator*{\\argmax}{arg\\,max}$\n", | |
| "Now which kernel do we actually use for our tests? So far, we just plugged in arbritary ones. However, for kernel two-sample testing, it is possible to do something more clever.\n", | |
| "\n", | |
| "Shogun's kernel selection methods for MMD based two-sample tests are all based around [3, 4]. For the <a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a>, [3] describes a way of selecting the *optimal* kernel in the sense that the test's type II error is minimised. For the linear time MMD, this is the method of choice. It is done via maximising the MMD statistic divided by its standard deviation and it is possible for single kernels and also for convex combinations of them. For the <a href=\"http://shogun.ml/CQuadraticTimeMMD\">CQuadraticTimeMMD</a>, the best method in literature is choosing the kernel that maximised the MMD statistic [4]. For convex combinations of kernels, this can be achieved via a $L2$ norm constraint. A detailed comparison of all methods on numerous datasets can be found in [5].\n", | |
| "\n", | |
| "MMD Kernel selection in Shogun always involves coosing a one of the methods of <a href=\"http://shogun.ml/CKernelSelectionStrategy\">CGaussianKernel</a> All methods compute their results for a fixed set of these baseline kernels. We later give an example how to use these classes after providing a list of available methods.\n", | |
| "\n", | |
| " * *KSM_MEDIAN_HEURISTIC*: Selects from a set <a href=\"http://shogun.ml/CGaussianKernel\">CGaussianKernel</a> instances the one whose width parameter is closest to the median of the pairwise distances in the data. The median is computed on a certain number of points from each distribution that can be specified as a parameter. Since the median is a stable statistic, one does not have to compute all pairwise distances but rather just a few thousands. This method a useful (and fast) heuristic that in many cases gives a good hint on where to start looking for Gaussian kernel widths. It is for example described in [1]. Note that it may fail badly in selecting a good kernel for certain problems.\n", | |
| "\n", | |
| " * *KSM_MAXIMIZE_MMD*: Selects from a set of arbitrary baseline kernels a single one that maximises the used MMD statistic -- more specific its estimate.\n", | |
| "$$\n", | |
| "k^*=\\argmax_{k\\in\\mathcal{K}} \\hat \\eta_k,\n", | |
| "$$\n", | |
| "where $\\eta_k$ is an empirical MMD estimate for using a kernel $k$.\n", | |
| "This was first described in [4] and was empirically shown to perform better than the median heuristic above. However, it remains a heuristic that comes with no guarantees. Since MMD estimates can be computed in linear and quadratic time, this method works for both methods. However, for the linear time statistic, there exists a better method.\n", | |
| " \n", | |
| " * *KSM_MAXIMIZE_POWER*: Selects the optimal single kernel from a set of baseline kernels. This is done via maximising the ratio of the linear MMD statistic and its standard deviation.\n", | |
| "$$\n", | |
| "k^*=\\argmax_{k\\in\\mathcal{K}} \\frac{\\hat \\eta_k}{\\hat\\sigma_k+\\lambda},\n", | |
| "$$\n", | |
| "where $\\eta_k$ is a linear time MMD estimate for using a kernel $k$ and $\\hat\\sigma_k$ is a linear time variance estimate of $\\eta_k$ to which a small number $\\lambda$ is added to prevent division by zero.\n", | |
| "These are estimated in a linear time way with the streaming framework that was described earlier. Therefore, this method is only available for <a href=\"http://shogun.ml/CLinearTimeMMD\">CLinearTimeMMD</a>. Optimal here means that the resulting test's type II error is minimised for a fixed type I error. *Important:* For this method to work, the kernel needs to be selected on *different* data than the test is performed on. Otherwise, the method will produce wrong results.\n", | |
| " \n", | |
| " * <a href=\"http://shogun.ml/CMMDKernelSelectionCombMaxL2\">CMMDKernelSelectionCombMaxL2</a> Selects a convex combination of kernels that maximises the MMD statistic. This is the multiple kernel analogous to <a href=\"http://shogun.ml/CMMDKernelSelectionMax\">CMMDKernelSelectionMax</a>. This is done via solving the convex program\n", | |
| "$$\n", | |
| "\\boldsymbol{\\beta}^*=\\min_{\\boldsymbol{\\beta}} \\{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta} : \\boldsymbol{\\beta}^T\\boldsymbol{\\eta}=\\mathbf{1}, \\boldsymbol{\\beta}\\succeq 0\\},\n", | |
| "$$\n", | |
| "where $\\boldsymbol{\\beta}$ is a vector of the resulting kernel weights and $\\boldsymbol{\\eta}$ is a vector of which each component contains a MMD estimate for a baseline kernel. See [3] for details. Note that this method is unable to select a single kernel -- even when this would be optimal.\n", | |
| "Again, when using the linear time MMD, there are better methods available.\n", | |
| "\n", | |
| " * <a href=\"http://shogun.ml/CMMDKernelSelectionCombOpt\">CMMDKernelSelectionCombOpt</a> Selects a convex combination of kernels that maximises the MMD statistic divided by its covariance. This corresponds to \\emph{optimal} kernel selection in the same sense as in class <a href=\"http://shogun.ml/CMMDKernelSelectionOpt\">CMMDKernelSelectionOpt</a> and is its multiple kernel analogous. The convex program to solve is\n", | |
| "$$\n", | |
| "\\boldsymbol{\\beta}^*=\\min_{\\boldsymbol{\\beta}} (\\hat Q+\\lambda I) \\{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta} : \\boldsymbol{\\beta}^T\\boldsymbol{\\eta}=\\mathbf{1}, \\boldsymbol{\\beta}\\succeq 0\\},\n", | |
| "$$\n", | |
| "where again $\\boldsymbol{\\beta}$ is a vector of the resulting kernel weights and $\\boldsymbol{\\eta}$ is a vector of which each component contains a MMD estimate for a baseline kernel. The matrix $\\hat Q$ is a linear time estimate of the covariance matrix of the vector $\\boldsymbol{\\eta}$ to whose diagonal a small number $\\lambda$ is added to prevent division by zero. See [3] for details. In contrast to <a href=\"http://shogun.ml/CMMDKernelSelectionCombMaxL2\">CMMDKernelSelectionCombMaxL2</a>, this method is able to select a single kernel when this gives a lower type II error than a combination. In this sense, it contains <a href=\"http://shogun.ml/CMMDKernelSelectionOpt\">CMMDKernelSelectionOpt</a>." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### MMD Kernel Selection in Shogun" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "In order to use one of the above methods for kernel selection, one has to create a new instance of <a href=\"http://shogun.ml/CCombinedKernel\">CCombinedKernel</a> append all desired baseline kernels to it. This combined kernel is then passed to the MMD class. Then, an object of any of the above kernel selection methods is created and the MMD instance is passed to it in the constructor. There are then multiple methods to call\n", | |
| "\n", | |
| " * *compute_measures* to compute a vector kernel selection criteria if a single kernel selection method is used. It will return a vector of selected kernel weights if a combined kernel selection method is used. For \\shogunclass{CMMDKernelSelectionMedian}, the method does throw an error.\n", | |
| "\n", | |
| " * *select\\_kernel* returns the selected kernel of the method. For single kernels this will be one of the baseline kernel instances. For the combined kernel case, this will be the underlying <a href=\"http://shogun.ml/CCombinedKernel\">CCombinedKernel</a> instance where the subkernel weights are set to the weights that were selected by the method. \n", | |
| "\n", | |
| "In order to utilise the selected kernel, it has to be passed to an MMD instance. We now give an example how to select the optimal single and combined kernel for the Gaussian Blobs dataset." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "What is the best kernel to use here? This is tricky since the distinguishing characteristics are hidden at a small length-scale. Create some kernels to select the best from" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 20, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Choosing kernel width from ['0.03', '0.06', '0.12', '0.25', '0.50', '1.00', '2.00', '4.00', '8.00', '16.00', '32.00']\n", | |
| "Best single kernel has bandwidth 0.03\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# mmd instance using streaming features\n", | |
| "mmd=sg.LinearTimeMMD(gen_p, gen_q)\n", | |
| "mmd.set_num_samples_p(m)\n", | |
| "mmd.set_num_samples_q(m)\n", | |
| "mmd.set_num_blocks_per_burst(block_size)\n", | |
| "\n", | |
| "sigmas=[2**x for x in np.linspace(-5, 5, 11)]\n", | |
| "print \"Choosing kernel width from\", [\"{0:.2f}\".format(sigma) for sigma in sigmas]\n", | |
| "\n", | |
| "for i in range(len(sigmas)):\n", | |
| " mmd.add_kernel(sg.GaussianKernel(10, sigmas[i]))\n", | |
| "\n", | |
| "# optmal kernel choice is possible for linear time MMD\n", | |
| "mmd.set_kernel_selection_strategy(sg.KSM_MAXIMIZE_POWER)\n", | |
| "\n", | |
| "# must be set true for kernel selection\n", | |
| "mmd.set_train_test_mode(True)\n", | |
| "\n", | |
| "# select best kernel\n", | |
| "mmd.select_kernel()\n", | |
| "\n", | |
| "best_kernel=mmd.get_kernel()\n", | |
| "best_kernel=sg.GaussianKernel.obtain_from_generic(best_kernel)\n", | |
| "print \"Best single kernel has bandwidth %.2f\" % best_kernel.get_width()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now perform two-sample test with that kernel" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 21, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Bootstrapping: P-value of MMD test with optimal kernel is 0.29\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "mmd.set_null_approximation_method(sg.NAM_MMD1_GAUSSIAN);\n", | |
| "p_value_best=mmd.compute_p_value(mmd.compute_statistic());\n", | |
| "\n", | |
| "print \"Bootstrapping: P-value of MMD test with optimal kernel is %.2f\" % p_value_best" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "For the linear time MMD, the null and alternative distributions look different than for the quadratic time MMD as plotted above. Let's sample them (takes longer, reduce number of samples a bit). Note how we can tell the linear time MMD to smulate the null hypothesis, which is necessary since we cannot permute by hand as samples are not in memory)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 23, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "m=5000\n", | |
| "mmd.set_num_samples_p(m)\n", | |
| "mmd.set_num_samples_q(m)\n", | |
| "mmd.set_train_test_mode(False)\n", | |
| "num_samples=500\n", | |
| "\n", | |
| "# sample null and alternative distribution, implicitly generate new data for that\n", | |
| "mmd.set_null_approximation_method(sg.NAM_PERMUTATION)\n", | |
| "mmd.set_num_null_samples(num_samples)\n", | |
| "null_samples=mmd.sample_null()\n", | |
| "\n", | |
| "alt_samples=zeros(num_samples)\n", | |
| "for i in range(num_samples):\n", | |
| " alt_samples[i]=mmd.compute_statistic()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "And visualise again. Note that both null and alternative distribution are Gaussian, which allows the fast null distribution approximation and the optimal kernel selection" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 24, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa8bf13f3d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot_alt_vs_null(alt_samples, null_samples, alpha)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Soon to come:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| " * Two-sample tests on strings\n", | |
| " * Two-sample tests on audio data (quite fun)\n", | |
| " * Testing for independence with the Hilbert Schmidt Independence Criterion" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## References" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "[1]: Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., & Smola, A. (2012). A Kernel Two-Sample Test. Journal of Machine Learning Research, 13, 671–721.\n", | |
| "\n", | |
| "[2]: Gretton, A., Fukumizu, K., Harchaoui, Z., & Sriperumbudur, B. K. (2012). A fast, consistent kernel two-sample test. In Advances in Neural Information Processing Systems (pp. 673–681).\n", | |
| "\n", | |
| "[3]: Gretton, A., Sriperumbudur, B., Sejdinovic, D., Strathmann, H., Balakrishnan, S., Pontil, M., & Fukumizu, K. (2012). Optimal kernel choice for large-scale two-sample tests. In Advances in Neural Information Processing Systems.\n", | |
| "\n", | |
| "[4]: Sriperumbudur, B., Fukumizu, K., Gretton, A., Lanckriet, G. R. G., & Schölkopf, B. (2009). Kernel choice and classifiability for RKHS embeddings of probability distributions. In Advances in Neural Information Processing Systems\n", | |
| "\n", | |
| "[5]: Strathmann, H. (2012). M.Sc. Adaptive Large-Scale Kernel Two-Sample Testing. University College London." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 2", | |
| "language": "python", | |
| "name": "python2" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 2 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython2", | |
| "version": "2.7.10" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 0 | |
| } |
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