{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "_6bsJCE7fDHC" }, "source": [ "# Fitting pairs of coupled GMMs\n", "\n", "Several papers have recently proposed a Wasserstein-like distance measure between Gaussian mixture models\n", "{cite}`chen:16,chen:19a,chen:20,delon:20`. The idea is that:\n", "\n", "1. there is an analytic solution for the Wasserstein distance between two Gaussians, and\n", "2. if one limits the set of allowed couplings between GMMs to the space of Gaussian mixtures, one can define a Wasserstein-like distance between a pair of GMMs in terms of the Wasserstein distance between their components." ] }, { "cell_type": "markdown", "metadata": { "id": "LeqURwOw4YUy" }, "source": [ "In {cite}`delon:20`, the distance $MW_2$ between two GMMs, $\\mu_0$ and $\\mu_1$, is defined as follows:\n", "\n", "$$MW_2^2(\\mu_0, \\mu_1) = \\inf_{\\gamma\\in \\Pi(\\mu_0, \\mu_1) \\cap GMM_{2d}(\\infty)} \\int_{\\mathbb{R}^d\\times \\mathbb{R}^d} \\|y_0-y_1\\|^2 d\\gamma(y_0, y_1)$$\n", "\n", "where $\\Pi(\\mu_0, \\mu_1)$ is the set of probability measures on $(\\mathbb{R}^d)^2$ having $\\mu_0$ and $\\mu_1$ as marginals, and $GMM_d(K)$ is the set of Gaussian mixtures in $\\mathbb{R}^d$ with less than $K$ components (see (4.1)).\n", "\n", "One appealing thing about this distance is that it can be obtained by minimizing the sum,\n", "\n", "$$MW_2^2(\\mu_0, \\mu_1) = \\min_{w \\in \\Pi(\\pi_0, \\pi_1)} \\sum_{k,l} w_{kl} W_2^2(\\mu_0^k, \\mu_1^l)$$\n", "\n", "where here $\\Pi(\\pi_0, \\pi_1)$ is the subset of the simplex $\\Gamma_{K_0, K_1}$ with marginals $\\pi_0$ and $\\pi_1$ and $W^2_2(\\mu_0^k, \\mu_1^l)$ is the Wasserstein distance between component $k$ of $\\mu_0$ and component $l$ of $\\mu_1$ (see (4.4)).\n", "\n", "We can obtain a regularized solution to this minimization problem by applying the {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` algorithm with the {class}`~ott.geometry.costs.Bures` cost function." ] }, { "cell_type": "markdown", "metadata": { "id": "vPHc0DtQ-ZRQ" }, "source": [ "{cite}`delon:20` suggest an application of $MW_2$: we can approximate an optimal transport map between two point clouds by simultaneously fitting a {class}`~ott.tools.gaussian_mixture.gaussian_mixture.GaussianMixture` model to each {class}`~ott.geometry.pointcloud.PointCloud` and minimizing the $MW_2$ distance between the fitted GMMs (see section 6). The approach scales well to large point clouds since the {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` algorithm is applied only to the mixture components rather than to individual points. The resulting couplings are easy to interpret since they involve relatively small numbers of components, and the transport maps are mixtures of piecewise linear maps.\n", "\n", "Here we demonstrate the approach on some synthetic data." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sys\n", "\n", "if \"google.colab\" in sys.modules:\n", " !pip install -q git+https://github.com/ott-jax/ott@main" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "KA9iIYeri_En" }, "outputs": [], "source": [ "import jax\n", "import jax.numpy as jnp\n", "import numpy as np\n", "\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "from ott.tools.gaussian_mixture import (\n", " fit_gmm,\n", " fit_gmm_pair,\n", " gaussian_mixture,\n", " gaussian_mixture_pair,\n", " probabilities,\n", ")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "id": "QcEMLjo4iRty" }, "outputs": [], "source": [ "def get_cov_ellipse(mean, cov, n_sds=2, **kwargs):\n", " \"\"\"Get a matplotlib Ellipse patch for a given mean and covariance.\n", "\n", " Adapted from: https://scipython.com/book/chapter-7-matplotlib/examples/bmi-data-with-confidence-ellipses/\n", " \"\"\"\n", " # Find and sort eigenvalues and eigenvectors into descending order\n", " eigvals, eigvecs = jnp.linalg.eigh(cov)\n", " order = eigvals.argsort()[::-1]\n", " eigvals, eigvecs = eigvals[order], eigvecs[:, order]\n", "\n", " # The anti-clockwise angle to rotate our ellipse by\n", " vx, vy = eigvecs[:, 0][0], eigvecs[:, 0][1]\n", " theta = np.arctan2(vy, vx)\n", "\n", " # Width and height of ellipse to draw\n", " width, height = 2 * n_sds * np.sqrt(eigvals)\n", " return matplotlib.patches.Ellipse(\n", " xy=mean, width=width, height=height, angle=np.degrees(theta), **kwargs\n", " )" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "id": "4khUqSBufTLv" }, "outputs": [], "source": [ "key = jax.random.PRNGKey(0)" ] }, { "cell_type": "markdown", "metadata": { "id": "kstORL0SY0FN" }, "source": [ "## Generate synthetic data\n", "\n", "Construct 2 {class}`~ott.tools.gaussian_mixture.gaussian_mixture.GaussianMixture` models that we'll use to generate some samples.\n", "\n", "The two GMMs have small differences in their means, covariances, and in their weights." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "ewlhSeocM5DK" }, "outputs": [], "source": [ "mean_generator0 = jnp.array([[2.0, -1.0], [-2.0, 0.0], [4.0, 3.0]])\n", "cov_generator0 = 3.0 * jnp.array(\n", " [\n", " [[0.2, 0.0], [0.0, 0.1]],\n", " [[0.6, 0.0], [0.0, 0.3]],\n", " [[0.5, -0.4], [-0.4, 0.5]],\n", " ]\n", ")\n", "weights_generator0 = jnp.array([0.2, 0.2, 0.6])\n", "\n", "gmm_generator0 = (\n", " gaussian_mixture.GaussianMixture.from_mean_cov_component_weights(\n", " mean=mean_generator0,\n", " cov=cov_generator0,\n", " component_weights=weights_generator0,\n", " )\n", ")\n", "\n", "\n", "def rot(m, theta):\n", " # left multiply m by a theta degree rotation matrix\n", " theta_rad = theta * 2.0 * np.pi / 360.0\n", " m_rot = jnp.array(\n", " [\n", " [jnp.cos(theta_rad), -jnp.sin(theta_rad)],\n", " [jnp.sin(theta_rad), jnp.cos(theta_rad)],\n", " ]\n", " )\n", " return jnp.matmul(m_rot, m)\n", "\n", "\n", "# shift the means to the right by varying amounts\n", "mean_generator1 = mean_generator0 + jnp.array(\n", " [[1.0, -0.5], [-1.0, -1.0], [-1.0, 0.0]]\n", ")\n", "# rotate the covariances a bit\n", "cov_generator1 = jnp.stack(\n", " [\n", " rot(cov_generator0[0, :], 5),\n", " rot(cov_generator0[1, :], -5),\n", " rot(cov_generator0[2, :], -10),\n", " ],\n", " axis=0,\n", ")\n", "weights_generator1 = jnp.array([0.4, 0.4, 0.2])\n", "\n", "gmm_generator1 = (\n", " gaussian_mixture.GaussianMixture.from_mean_cov_component_weights(\n", " mean=mean_generator1,\n", " cov=cov_generator1,\n", " component_weights=weights_generator1,\n", " )\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "height": 390 }, "executionInfo": { "elapsed": 3327, "status": "ok", "timestamp": 1643139121297, "user": { "displayName": "", "photoUrl": "", "userId": "" }, "user_tz": 480 }, "id": "ozZUSGTzYycd", "outputId": "3c276a66-7233-41ca-9877-39688c879b9f" }, "outputs": [ { "data": { "image/png": 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XDvCxhUaxuIYpLT+h6lpUHQvHMmiULWzb4MCYR8svhiY6lkGSS4I4JVcQJpLp\nuotrG/pwhqZpj62d/XeXuxGnFrtUPZtLG/7WuYqRnSUSfpKT5BKpoGRb5MPLjALmkmvxky8fLILn\nM+v8zvtrOFZR7jYqmdieCMEQegdOu44OgrXHzmgrzt/WlizOFHXP4qmpKldbAX6SMllxsEx4cqpG\nwytOHi91AsJUUvNs6iWL2YaHaRo8N9/gYwuNYmGNU95b6XFwrEzVLS7z/EKDCxsD3lsZsNaLaQcp\n37jYYrrm8excnZcOjfHy4XG+dm4T1zau65d5M7q/paZpj6rR+jUaNgTDuSvq2vkrO1tcztY9Zusu\n3Sil7tlMVNytaZw7+whLQKoi8JZKbbXDLDsWYZpzoRUgc6V34LTr6CBYeyTdLDCseTYvHx5jqRvx\n8qExSq611SeyH2c8M1vjjYstokRiWgJTwbcudzAMuNoKaHoOaa5I85xm2WHCNfFsk36c4ScZUaaI\nUknJsZBKIYFPHZ2k5tkYgBKC00tdLFPgWSZ+XLRKOzpTY6bh3VFAu9wJ+eLpVTxT6ElzmqY9UrYH\nrEkmeWq6Si4Vhycq12Vkt5dQGMDrZzdo+Qkl2+TQRHlrjV3shNdkjJe6EU3P4sBYiU6QEqeS+YbH\ncifETzKkVERJxnTN0ztw2nV0EKw9cm41i74fpbx+dgM/zqi4xbjkmmfzMrDUjZisOryz2KVWtjAU\nrPsJYZIz3/RYRLA+iLBMg7WeoupZlGyTMVmM7HxvuU/Ljzm11KMbJDi2wWTF4Wo3Iooz3lnqUfeK\ndmuNks3JpS4TPZeKazPX8K7ZIrxVhrcfpXzp3VVOL/co2SZHJsp6Adc07ZGxs8ThhQMNKp6965q3\nfT3sRRmDOGO86jGOKjK8w8vtzBiPAt6FJkzUXL7vyQkkbGWIXz40ds0OXBgXY+3nG54ujdB0EKw9\nem41i365Ew5rzywubvi8cKABzQ8nBp1d7dELU2QuWfdTHMfAsQwypZiqu+QSZuouy90Qx7K2GrSD\noFm2WetHGELx3nKPWsnmH37pDIcnKkyUbSarLuNli3NrfeIspxNkHJ2qcm5tsHVgA24dyI8ep0LR\nCRIW44xBkvHZ52fv4zOtaZr20e0MWLf3At5u53r4zGyNJJe0BhGOZXJ4orJVPrYzY9yPUhbGSlSc\n6lYt8PZ1daFZYqbhsdyNWO9F/PxXL2IaAtMQfP7VJ3UgvM/pIFh75BgwbD+WgCG4bmK8EKN/bH28\n3AnZGMRUXYs3L3eI05wkUxyaKPHZ5+Z4b7XHeiekbBu8vzqg5cdYpuDQmEezXGQX3rrS4fz6gPeX\ne7SDYtpRKhV5rnBMg9V+yJhncW4tZXOQYJoC2xAo8eH92l4ft9VHeHPAmdXBNX00oXgBEQiaJYe5\nhseRifI1E5c0TdMeZttL0+aHO2E7bU2WSzIOjVe4vDnga+c2aZZsxGSVTxwZ5+iOtXH07y+cXOHU\nYheA5xcavHCgccMEyZmVPmfXB5zfGPDxA002BhFvXy2SJXp3bf/SQbD2SBnNokcpTi71ODFf481L\nbV7btpDNDQ+qDeKMwxNlaq7F62c3uLjhs9aPUQo+dWyS8xs+s7US37rc5uz6gDxTeLY5zCpYHJ2q\n8tLhcWZqLpKi08Mrh8c4tz5gDMikxBQGKTkIsCjqdrthhmsLMglSKsq2wTNzDWqudU19HMDlzeIw\nXZTmnFzqXnN6uebZfOa5GZRgqyZYTzrSNO1RMVqvc6VY7oTXrNP9KGW5G/H2lQ5Syq3JclGu8Ozh\niGM7YvoGwfNyJ2SxE+LYBo5pMogzEGLX/sOj3cMDzRJfCBK+fnGTKJEcn6mR5VKftdjH9Cuq9kgZ\nLWbjFZeSbTJe9ciVuuYdf82z+dyJ2WvqyxzL4AeOT3FyscsHKz3ObwRYCD755DjfutweDtGI6QYJ\n/SjHrhv0opSLGz4tPyHJJFGac6kVkKQSqRQVx6LsmoyVLUwBRyYrtMOUIM2JM6h7NsdmKnz6mRle\nPNgsMsBJRnl4oO6lQ2P0o4wozdn0UzpBypcUfOa5ma3+mXPNEn/ypQXdHULTtEfOjUrXRuUP64OY\nSxs+rx6fAorJcvMNjzcvtbnc8olTef1OH0UA/fbVLmvdkKudiJl60Tmi5lq7DsgYlWW044yPLTSY\nqrmsdmPmm+XrXj+0/UUHwdojZbSYbQ4iwiynNYiZqLrXZUh39qg0hWAQZ8w3S5gC3l3u4TlFzfBK\np1hITQQvHmxSdi2emKyyOYho+QlSQS+IWe5EfP1im1YYYwhBxbGZbbh87vk5vnZug6VuhJSKp6aq\nOKbPTL3Ek1NVDBRn1wYEccZ3rnYwhUGuJMenq8w3SnzrkuJqJ2Cq6qJQfPH0Ks2SfU2tsF6gNU17\n1OysCd6ZmT00XubShs/lVsBk1d0qCXsmzviNkys0POu6nb7R9R3L4I88N8vJq138OEWieP3sBp87\nMctCs0Q/SrdG24/qiM+uDohziWcahImk5ccIdimp0/YNHQRrj5RRjdmX3l3lxHwdQdEncpRdWO5G\noNQ1BzC2H6Tw44yvxhlPTtUAtRXkHp2q0gtjnp2t04szpJTkueJ3319DSkUrSDCFoB9lZLlEAp5l\nstyJeP3senHQTkEuFaeXeqS5pBNkLHVDvnp2Hcc0mKi6ZLni+GyV1V7Gt692qa77ABgIWoOEKM1R\nCg6Ol7e2EEeH6TRN0x4lNxpdPAqOB3HGU9NVnpgo89R0bWsd/9q5TTb6cTGufpe2ZtuvX3YMVns5\njp1xeSOg4dlUXIN3l/vUPYskVzwxWWG27rHYCWmWbOJU8hMvzvPtxS6uKa4JtHVf9v1FB8HaI0cC\njbK9tcUmYWsk5/ZDEqPWaPBhZni5E5JmRQYABRXXHB2fY9NP+dqFTSq2xVzTY7Mf0w1SFIp+mBaD\nN9KcNFeYQGBldIKcdpCQZorZhkeU5dhG0eh93U/oBhmWITBNQS6hHSQsdSMsAw6Pl1nrRzQ8ix98\neppff2eJMyt9VvsRIDgyWabiWFsB/fbFGdALtaZpD73ddrJGwfGoJngzSOlcam+1sQzTDMMQLHYC\nLNO4LlO7Pbhe60UsdiKSTHGpFfCvv32VDT/BFMUgpAsbPjMNF9MwODFf5/hMnbV+RKagWbKvKdUA\nbtm1Zzc6cH506SBYe+TstsU26itZ9WxA4cfZddmD0SGNxnASnEDgWoJ3FruYBkSpZKxkU/UcgiSn\nF2ckuSTNJGmuqJVsFGAbioprkUtJIoYDMZKEsmdhp4Ioy1ntJfSjBNcxsQyDfpSRZ5JG2QYBG4OY\nf/GNK4yVbY5O14iznDDJcR2D8Uox5rnq2VuPA7juUJ1jGddMTPqoC7BewDVNu99qnr1V1jBd8ziz\n0uVfffMKAsVXz7UYq1i0/JS5use/fPMKnz42RckxQQhqrkU/zkApZuvFQejzGwPKjkHJMXFjgyjN\nubgxIM0UB5plLmwU0zyb5Wv7C6/1I5Ks6APvxzdvv7mb22l3qT28dBCsPXJutMVWdS0ubRTlBdv7\nSo5s1aFNVAlSiQAqroUhBBNVlzgNWexENEsZwjCI0xzPMpisOkgFllEEoGmW0Q1jBCCVIJUS1zIo\n2QaOIZio2KwPEqqlEp2gKLcwRBEch70cFFiWQZJJumHKSjegUbJplG0WOwFppgjTnI1+xPkNH4Nr\nD5i8v9JDAc+M1bnc8netIb5degHXNO1BGSU0Lrd8Ti73kVKyMUjIlMIQBuNlh3eWesSZ5PUz6xyZ\nrGAbRecdyxQ4psHzCw1eOtikFSQ0Sw5X2iEtP6JZdii7Fs2y4NtX2gigWbZ5dq6+NbjoNc/aykaf\nXulvJRh21jDfzK361msPNx0Ea4+knVtsNc/mU0cnmW14VB3rur6ScG0GueoWP/qbgxjbFIxXHDb6\nMYfGSxhCUC3ZLDTGsUyDqaqDaRgs9UI6fo4fZxjCGN6mwVjZ5ZnZKk/PNljthrx+dpN2mBAlGYYA\nwzCoujaGAblSpDmoTBZZ5jzncktSsi1++OPzPDFZJUpTTi71mKl5WEbRW7jm2XSDlCjNqQzv+1o/\nIk4lniU+8gKsF3BN0x6UUULjzOqAKMm50ApY7ERUbBOpJKu9BIRiquax3o+QCmzLpNWLGCs7xLnk\nwvqAubrLbN1jouyQn9vg8HiZV54YR0rJWNnhrSsd5pslpFT0o4y5xoc7YCi1lY1e60c8O1u74VS7\n3dzo8J/2aND/W9pjYXs/ym6QcnSmet1ldmaQoeg1WXEtNv2EIxNlnp1r8OX3Vtm42kEpOLHQwHMs\n3r7cZt1PEQLSXJLmxW1mUpLlEUmWs9qLWelFpLlEKUWcKQwBkpw0l+SyKKOouiaubeHlOQYGlinY\nDGL+3bsrPDNTxTQMhBK0/RTXzjm91CORCtcSRJnks8/OUB2WgBgUk/A+6gKsF3BN0+6nneVXNc9m\nvuFxckkwX3cJojIlW/CNSx3GyxYrvYTZukfJschzSSeIsQy4sDGgHaZMlh3GKg4C+MoHG6SZwjAU\nTw4qlByLmbpHlEpOLfW40g5Y7Uf8wQcGQghaYUqeSQ6MlwGKTPBwHbzdZMCNdia1R4N+xdMeCzfr\nR7lzwd3erL3i2fzQszOsdCO++sEaX3h3mVNXu7QGCYYpuNIOeGKywpVWyCBOidNiu8wQxWC6JIMs\nzxhEGav9CMswhl8TCFHMrBMKBAoB+HFGnOYcnrAp2TaNkkOUSUxRBORZLpmsuBwar3B6pQuR4Mtn\n1qjYJn/kuVkGcYbk2kz4a57F2dU+fpIzuMNMrl7ANU27X3Yrv4LijbxnGcSp4FNHJ/jlN6+SZJI4\nVxyZrHBiocnTM1XeutzGtgwMIZgJU8I4o+o5WKZBs+TQ8Gzmx0pcbg24sBnw7GyNby92OTJZJkpz\nPljt882LbcIkox0kgCDOc54YL/Pnv+cJojTnq2c3qLrWNQerb0W3sXx06SBYeyzsltG8Wb3r9q+N\n6sCCTHJpbUA/ykgkuAaESc7GIEEqhRAGucwp2Qb9WGKoolOFAaQSyBWWASiFEoKxctGKRypwbAgT\nhVSKbNgCLc4ynpysEqY576/2MRAkqaQTpszWTUq2xUTVwTEES92Ik1c7PDVduy5bO4gy/s3by4Rp\njpSKz7/6JEdnarf93OkFXNO0+2G3ZIUfZ6wPYqarLqeXeqx0izKvumfT9tOiG49QfOHUKqYBzZJD\nyTVplmzyXJFkOZYhqLkmrSBmuR+x1A44NF6h7JgcHi8T55K1XkzLj3Esg0GUEaYZtmUQJZLFbsS/\nevMKMw2PmXqJSxs+Lxxs6nVxH9BBsPZY2C2judgJtya0+cm13SJGi3HNtfjORhcBdIOURIJlCASg\nUFiG4MnxEt9e7JFmOamENJao4fe1DXAtg1TKom1anKMEmIbEEoJKyaZkGnSCFKkUlilIMsk3L2+S\nJLDYjhivujQ8i1zCcjdmzijGKXejjMW2T5gpFholLm4G/MjH569bmJe6Eb0owY9zOkHKr59c5j++\nwahRTdO0B2VnssIA3r7S4dKGz6nFLo5p8NLhMc6t9Rl3bZplmxcP1hmrekSLfUqOwbvLXaZqHi8e\nbPKpo1Mg4OzagKudkKpjMujFhGnGpc0Bq72Ilw81eWKygmMbNMsO/TAlyRVKCaKoGHk/WXVxbQM/\nzmC0uit1s4eiPSZ0EKw9NnZmNA3gveU+uVSYhuDVY8XWWz9K8aOUXpjy1qU2SZYTpBLTEDwxWWG5\nZ1DyU2qexSeOTNCJUsYrNkopsmE9cA64tkChKLsmjukgpWS5l6BUsX4qoej4CWbFIcslphDYpoEl\nwDMtBnnMaj+mFaQ8P1/n8GSFIM2pejbfudqlWbYo2TaerXjliXHCJKcbZdeVeDQ8i8V2RDtI8GwD\nzxRbbdV0mYOmaQ+LncmKUYu0V49PcWa1j2EIHMvgU8emmKq5PDFR4TuLXX73vVXW+jF1twiin56t\nFYfZGt5WazPLEJxZG9CPM6JEUnEsWoOYc+sDrnQifvTjcxwaK9FyTWYUzDdKDJKMpU7IdM1lrOJy\neKxEquCp6SpzzdKDfrq0+0AHwdpjSwLPzFYpuzatQcRSNwLYOkDXCRJyJZlreCgUCJMj4yW+/H6K\nUzNwbBPLEpiGYL5ZoRemCMPAVBIlwRIKMChbJm0/Icg+zBDnChxTIJWiFaRkmaLqCiqOQclyyIEs\n/zBjPN8o8fxcjc1BzNVWSDtICOKMWslivOLSDRNMYRAlGV84ubLVI/i1p6couRY/+PQUH2z4KCkp\nOTZhnPHb767i2gYVx9KtzzRNeyhs340zKEba9+OMA2NlnpmtsdINi7VWFEHtWi9ivZ/gWoK1QTHm\n+NffWaLh2ZRsk26Ycmalx+VOSCYlFduiF6a0/AQFdMMUFab83pk1PvnEBL0w5VI7KO6La3FgrIQf\n51Rsg06YUvUsPNvc9b7rnuqPHx0Ea4+tumdRcW38JOPiZohnm5xa7OJagqmax7n1ASevdjEtg8mq\ny1/+9FNc2AyZaXiYQtD2Yy6tD7jciai5NmW3OMgWZ5JWkIACqRSbfgoohmfmgOIXq1Yy6QQZSVaE\nxmEmsRJJ1RGESYZtFqUXJdckl5LTK30GYcKVdoCUilQoHNPgc8/N0qjYbPQTvnGx6ATxQ8/O0B8O\n0qh7FgtjZZplmyhXfN+TE3z1/Cbn1gY0yzYLYyXd+kzTtIfCzrMao2E/o043V9sBZ9cGfPrpaTb9\nmE6QUvdMEqlQFP2BlzshizLkf/HP8dR0lapjEybFjl7VMXBNE8eGKFVcaYfM1D0cy+DIZIUL6z5P\nTVZJsqJ0rbuakUvFl99fZ6LqMF3zaJadXYct6Z7qjx8dBGuPre09KBkOybjc8okyyeVWQJxK5poe\nZcfGMATfuNjGtQQr3Yien9CLMqIsxzINkiynUXK2+kxOVhw6YYpjmbT9lCi9tn7Ms6EzyMiHnxaA\nZxskueJqt+gCocRwiEaa88bFNlJKSraJZQpqZjFZTiF44+ImShWH9J6Zq3FpM+CbF1s8MVXdGqSx\nfWpcL8rwTEGzbNMJUiarrm59pmnaQ2Hn4TgJLDRLnFntc259wGI7YKkT8sV3V/AsA6UUYSoZK1s4\nhsvVdggCqq5JyTbZGCRcTgOEAtc0cCyDsmOSSIlpAAqSPCdMMl4/s0acF997uu6x3itGNMdZMTyp\nZJt0wpS1fowfpSx3uGZd1T3VHz/6lVF7pN1qe6rm2RyfqW6Nx6w4Fq8eG6MfpaS55HffW6ftJ0zX\nHECx3EuZqjjYRjEw48LGAFMIBnFOyZF88sgEv39mlSiVhKkkSotuEVJKovzD75tKSLbFxQqwhEGK\nIkklyfCyFjmDCPpRBqo4ZAeKkmthGgaWAUudiDjLyXKJYwpWuxGtsRJjlYRf+84SjikQwuAzz81s\nPQcV12ahCRM1l888O6MXa03THgo36uTzxvlNvnZ2k06YMNdwmaq5TFVdjs3UOHm1w3S9xOYgxjDb\nRCsDDCGQQMkSrPZSKrZNnOSUbZNDE2U2/YRBlJHniiDOeetSh36YUXGLtXCy6vITLx2gXnZY60V8\n5YOUMM3JpMJA8dblNu+tDHhmrkbFsXj58Jjuqf4Y0v+L2iPrdrenduscMUeJmmcTpzl+klNxTE6v\n9FnrRVRci+max9m1PrmE3CgytFNVh36c4DomWaaYKFt0woyKYxFnEvIP6yHi/Lq7gWtBEORbATCA\nnw3/MfycyiUVu+h5OVGxEcIostaZJEkz3rraRSnFNy+12fRjPMckjCW2JVjrhfz09xxhrlnSvX81\nTXso1Tybl4cdICrbu/VIxbNzVc5vBNQ8i+m6x3jZYaMf0QkzECFXWiF/9Lk5Dk/0iOKcy22fy+2A\n5U5Ezc1QQlEp2dhmcRD6W1danF3LSDJJKOH8ZkDVtaiXbI5NV5BK8YnDY6wPivK2jUFMlOcsd2MO\nTVTpRSmXNn1cy2BhrMTx2RoohSEEZ1YHzDc8fYDuEaeDYO2RdTfbU/0oZakbMVVzeXmiytfPbxAk\nGYYBvTjlyESZw5MznF3rs95PqLsmx2brnF8fMFV1ObnUQw4nwJ040OBKK+D0cp/sJl11umG2PU7e\nVZ5DJCTdMKVedliouyx1QwzDJMslBmCZBhv9mGbZ4olyjfeWWlimQTdIqZeX+LOfPKR7/2qa9lDq\nRymvn93g1GIXgOcXGnzq6ORwHLzgwFiJIxMV/r2np5FKsdqPiTLJUidkqRPyG+8s4ac5Ncfm4mZY\n1PYqGCQZVcdioeGR5oqXDjYZq9icXTuPIYo8g20IBlFGK4j4f//uOebrHrZpkClFkua0/ISnpqvE\nqeTCxoB3Frt854pECIMPVvucWGhgGgYXNwJMozg0/flXn9SB8CNMB8HaI+t2R/7udhDjzUtt/CTj\nvZUBUSq5sBngJzl+lGNZxXy3sbJDw3OKAxeJpBMUtWJZVgzAUEqR5kUt2VNTVT5Y7ZPtkgEeCbIb\nfw2KX0bbgqpn04syljshcZIxUXHIFCRZxiDKUcrANIvHO1Vz8OxisEbJNpFS3fLNgD7hrGnagzIa\nkFH1iqB3NAXzcydmeeFAAz/JQSneutLBsQx6wxrdjUFM2bEI06IF2rEpl1OLXcIkx7UNUFByLc6s\n9jENg985s0aj5DBdtulnOf2wSHI0PYtj0w1OLnaIc4kEgiTlubkmar1Ps+xQckxsw2C65iAVxGnO\n5XbERLVIuFiGwYsHm3ywOuDtq12qei19ZOkgWHtk3e7I350Z46VuRK4Uh8YrADRKDi8JqKyYvLvS\nw7GMovsDiiDJqXk2S50+RkvQCRLaQUIuoeyYTNVcPrbQ4JuX2liWgS0l28/IGRQHK3ZTDOT4kGeB\n7ZjESU6eSdb7EZuDCNswOTBe4shElSjJEYbg+bk6B8dL1MsOhycqLHdDOmGCady8Vm30hsBPMuJU\n8pnnZnQWQ9O0+6bo2mNxccMH4PBE+cP1uwm/9/4664OYSxs+nzgyzrm1AWMVm36cY1tQ8zwWWy2+\neamNbRtMOx4Yilwq6p7Nhc3iHEeeS77vqUmOz9dZ7ERMVxVPTlboRxmbgxjTMLiyGRBnOX6ckeUK\nYQjSXNI0bb59tcNyNyKIcyzDoFmxECiqjkWaKz5YHbDcC1nthnzh5AovHGwyp4cUPXJ0EKw90m5n\n239nxni+4V1zUO6FAw1eP5syXXdZ7jp0g4RukDIIE3pRTsU1SXKFENAs2XSDFIUEBAtNj3aQcGa1\nTxhLdiaCb1b9sLNyophGl2MxPFQ3vDFhScJE4lqSWtlCKEHJMTm7HjBVzVDDgD6T6pZTjnpRhp9k\nLLZDOkGKEvAnX1rQC7emafdFzbO3sr4IwVzDAygmfMbZMEFR5tKGzwdrAwCOTtW4OlyzLnZ9QGAb\ngqmqy6ePT/H1C5tc2PS5sDHAj3NsU7CaR1ztBPzZTx7m1HKPyYrDl95doeLa5Erxxz42y7/99hKO\nZbI+iFjvx5hCcEEYuKag7Sc8MVFBCEGUFCOWL24GvHJ4nB84Nsmp5T5PRmUOjpf5ypl1BnHGVNXV\nrdMeMToI1h57u2WMXxu2vKl7FoMoox0kuJbJ0ekK37pU9P3d8BPGhlt20zUXKaETZpiGgW0ZPDFe\n5sdfOMg3L20SpDmGoCiT2Pa9TbguMIYiQ1x2DQaxxN52PZlDsuOyqVRs+hHCUMRZ0Rbo9z/YYLbu\nsdwNaYcJtjA4sVDHscxd+1ueXR0wSDLm6h5xWpR2NMv21nQ5vWhrmna/1Dyb2myx5mwvV0uyIm0w\nIOP5hQbzDY93l3ucXR8gFXzyiXHeOL9J2TExDUEvTOlECbWSzUKjxLl0UKyjStEsuzw5VaXkmCw0\nSyy2Q/pxRtWziymhcU7ZNbFMg+VOiGEIXMvgwsaAyy2f9UFCxSlGLc82PPwox08yTi/3aJRtHMtg\nuRtvJToOjZcZDHu36/X00aGDYO2xtr3+dWHbtv9okVruRvze+2tcbYWUHJNcQb1kMYhzHMvAtkzK\nnsWzczWCJGcQp0gFQVL0AH7zcosvnlplY5Du+v13C4A9s8gQp6nEgq3yiRsdmnMMQa4Uea6IlGSi\n4tANUzaChM1BzEzNZXMQc3bVJ8kVn31+dutxG8BvnV7lS++uglIcHK/wk68cQAnwTEHFtXWrH03T\nHpid5WrPztZACPwo4+z6AMcyOLXUxTYNLqwPqJVsDAM2BwkLTQ+B4OhUhbVejFICa9h/PU0lp5f6\noKBZshgvOyy2Q86t+6AUzVKx9g3inMmaS3N4FsO2TCwTnpwqM1ZycW2DLFPEecJswyNIi0N6rx6f\nBmCh4VFxLK60AiqupdfTR4z+39IeWzdroTb62vog5sxqH4Hgg9UBYxWLdpAigPGKyzNzVaJUMt8s\nkWSS82t9VnoxKMXJxS4nl7o37QhhUtT+bj8Tl+ZFu7Sc3YPkEQNwLYFtGcM+wwI/yQiSHCEU455F\nexBjmYI4y0lkzmLL5+RSl+VOhGsbRJlkpRviWSYV1yz6YCr47LMzLHUj5nUNm6Zp99HOg7k7y9Vq\nns2bl9psDGIubvg8t9DAsy2enKoQJsWOW5jkWIbPWMVhtRczUXb45JPjRGlO3zWRSuEnOec2+lzY\n6DM37DgxXnHIcuhGCRc2A5qehW0aHJuuMlVzsS2DKMk5vTIgTFLCOMS1DSYqLlEqWenF2GYxUOnr\nFzYo2yYvHxpjuRcziG9x8ll7KOkgWHts3ayF2uhrU1WXpXaEEIpYSp6bm0Ci8EwT0zRY7SecmKuR\nZBLPNjkwVuG95R6DKC8C25uX4O4a5OYUnSJMwDEgvkEGWAIyV8TkVFyLVEokw6DWttj0U9JcsdEv\nDuqNlR3CJOPLp1cZxDn1ksWhsTJl2yTKcqI04+B4BUvAl95dxbWLbcDX9MlmTdPugxslJraXq21f\nm99Z7HJxvc9yNwQUuYIT83Wen2+w2Al5Z7GLH2eEaU7NsUAoNoMEyzCIswyBTaYk64OEI+MV4rTo\nEjFI8yIYjzOOjJcpORZVz6ZZcfAsg7GKw8Yg5monREnFwniJuaaHBJ6brfP62XW+fbnDZNUFIaiX\nbJ6ZretJco8gHQRrj62btVAbfe1qJ0AJxVyjxNV2wOnlHmGcU6vZTDc8XFOAMAiSmFwqlAA/zdmL\n9/w5Ny6BgCKDLAVYiGLhjjJMA6SEsiOx6x4HxktIpchzyVI7Yn7Mo+XHXG6FJJnkyljAj3xsnr/w\nPYdxHZO5usdXz29ybm1As2yzMFbSi7amaffFjRITOw84J5nkrcUuhoBBnPPyoSZPTNVYagd0whTP\nipitu5xa6tEJMvwkJUpzGq7NWMlhruHxwdqANMtJpEJlkn6c8cMfm+NyO+APz7XoBSndKGO1HTBR\n9XjhYJMfmavjOibHp2ucWe3h2Ranl7q0BgkvHGzi2SYbfsxSN8IzBav9iKm6i2uZepLcI0r/b2mP\nrZu1UBt97dtXOlze8BmveiS5ZKFZ4sR8g/VBzEKzxC++cQkpFYmUPDVeYbEV0PBsMj+9aRnEXlAU\nQXIm1VbC2cjBEEVNci9MGESC8YrDWNXFFIqqY7LYicjy4vBbmGb88reucny6xl/+944iKWqBm2Wb\nTpAyWXX1oq1p2n1xu73dZxseS50Q1zbphilXOhGuZfCdxR7jZYc0y1FK4JhFo0lTCKJUkWUREgOE\nouSYeLbNIMqwbYu5uotrW7SDhDhJiaVCSjCMYlR9J4j5zVMr1FyLp6areLbJk5NlxqsOJ+bqTNU9\naq7FubU+7y31OLvuE8RFEP8nXzpAaVgPvFtCQfdmf3jpVz/tsXazFmo1z+bFg01WuhGDOGOm7uLZ\nJoM4RRgCpRSTVQfXsnh/ucfFVsByNySRCsuALC/qdhVgm1wzDvlGdvYGvpWdiWLJsAtaDnEumat7\nbPoxUaIoOwaZgpprEmeyyBBLQcM12fRjzq4PePFgk4prs9CEiZrLZ56d0Yuypmn3xfbEhEGRGR59\nHrb1MY9TFtshhhBM112qrsmZ1QGnFjt4toUhBLMNh7GyQ8tPsE0DAM92GCvbZFIhlSTLwI8z4lzx\npdNrvHiwyVo3RgpBnhflFXkqWepGSKWYa5RxLIOlTsgzs3Um6i4vN0q8t9Jnw0+2hi09NV3jcjug\n4roopehHKRXX2nWU8s3OpmgPng6CtUfe3bzLHvWsHF1/tRvxG+8s0yjbXGoFrPRikjRgbRACBp0g\nJkokhgBHQLVkEaeSRsmiE6REmbqj3sC3stuwDUVx0K7tZ2R5iJQShcCRBv0gReaKklO8UCgEFzYD\nZuoeFzd8jk5VOT5bA6WYa5b0Yqxp2n01WnO+cHKFQZxRdS0+d2KW2rA7gx+nlF2bo9MVwkwyW3Pp\nRBmtQUycSbphhGkWbdAmKjaGIbBMEBgkuWS1GxUdJAR0oqTo8Y6km0lOLnUxDYFtGqSmQkmFbRqY\nAuJMcnq5h2UKUqn4xsVNFppFH2DbFMw3SgRpzlI34rsONTi71mcQZQzijN9+b5V2kGIK47pRyjc7\nm6I9eDoI1h5pe/Eue5Qt7kcpXz2/ycYgIZMK01A8M1vDBH7rdMxmkJLlCqnAsgQyV0SZxLUMEODa\nJoqMcA8PCd8qoE6zfLilBy0/pmSb9OKM8bJDs1zUxk3WXL7niQkGScYXT6/SLNmYQuhJcZqmPRDL\n3YhTi12qns2lDZ8XDjapeTYG8N7KgFwqTEPw0999iJJrcXF9wBvnNohzRZBk1Es2oAjSnPGKgx9n\nSAUVx6Lu2VQcgw/WBljCQImcVEksYeCYRnGQLsmRw3IIicSyDKaqLjN1l7VeRJbDRhhjYHB5M8Aw\nwLUMhFGMZy67Fsemq5zf9JmquuQSwjTn+bkqlzYDlrrR1vp6uyUg2oOh/ze0R9pevsvuRdlWvexa\nPyJKJLYluNwKqJdtcgUbWVHzkGUKpcATMFP3UBKCJCK9z11ycgmWaVB2TdJUMtdwaYUZplG0TVsY\nK5FLGAzHJHuWuK3nStewaZp2z2xNtlTXfCyBZ+ZqCCFo+cUgirpncX7DpxdmuKaB8GwOjZdJMkmS\nKcI4pxenlGwbIRQVtxhwIVEkeY7Mh116DMkgTjFFUUssDYHIJJ5joJRiw09JckmYSvpRSpJKxio5\npoDpeqnIHucKhEBKyfcfnaJecnBtg16YstwN+WB1QMkxmR9OwYMbn03Ra+zDYc+CYCGECXwTWFRK\n/fG9ul1Nu5m9eJe9fbCEYRiUHZOJqst0zaVkm0TDcod+lHF+bcB6PyFIUnJAGIKNQUTVsZisOIRR\nkZG4WQb3bhkMO0cAQkEuJeOlMl2RsDZIyfKc1SRnbqxElOZM1VwWmiWemqry5qX2LZ8rXcOmadq9\nNNcs8fxCAz/OODxRuSZragjBqcUuAG9f6QBNMql4fqGBaxsM4oy6Z1N2LKZqDq0gZbMfUXUtVvoJ\nLT8hV1B2LKI0x0gkDNdk2xD0wow4k+Sq6LSTS0nJthkv24RpTppJ8lximIKyZSJRbA4SwiRDCPjO\nVYO65/Dq8WmOzlRZ7ka8faXDSwfH6EYZP3xi9rpdtp1nU/Qa+/DYy0zwXwFOA/U9vE1Nu6mbdYC4\nHTtHdkZpjmubVFwLzy6ark9WXeYaLoudkEMTZcqezXvLXQypEBSjlNt+VhxaA+xhG7N7xTQBWYxa\njoeH5M6uD2iWTOolm6emGpxe6REmOb/z3irPzzeYb5Z54WDzhs/V9qyErmHTNO1e2L7ObD+LMVpf\nap7N0akqi52QY1NVMqVAKaquRZpJJqsuLx0a44WDTb5xYZMLG8FwtLFLlEmqjoljG0xUHFa6IVGa\nIxXYoujHvtYvhtILimRCxTOZqXtEmaTsFuc6WmGClIqaa7IwUWK85LDcjTi7Vlw3SnIOj1vFsCE8\n+lGGlJKD42VUK0CqW5/80Gvsw2NPgmAhxAHgR4C/D/zVvbhNTbtdN+sAcSvbF6P3VnoI2Gp6fmis\nXGzPzdR4+2qX8YrDxQ2fubrLpQ0LhUJJsESO6RgkmSSVH/b+Hcaqd3wY7lYqtkmQ5qht3ShGXSPi\nTHFuzacbZChScqmKzHVcvPgs7HIYbmdW4uXDY7qGTdO0PbVb9nNhR8a0H6WcXR/Q8RO+4bd4fqGx\ndYC3EyTkUlFxLS5u+Jxa6hNmGabhcni8wvlNn05QnOfoBRmbfoJpGEhykuEinAxbTFY9k6pt0ii7\nTFRspJKMVVyCJKMdJGAookxhAut+wnI3pBumSAXvLPVY7Sd4tsmvdWOOTJY5tdQjznIqjkXFtW55\n6FjXCT889uqZ/1ngrwO1G11ACPF54PMAhw4d2qNvq2l3Z/tiVHWLX4e1fkQvTPl6r0XTs1jrx6z1\nYkqOiSkMNvyYhXEPJRXL3QghIEjkVrA7SgLfRse0OzJqr9aP8l1vuxfl2JZBIHMQAlOAIYqDIFfa\nEcYNbnf0RqDmWlxuBfSj9K6y69rjQa/Z2l66nexnL8pwLIMfOD7F5VawdWCuF2VM1z2max7vr/RY\n7kaUXYupmosfpZzfGCAQLHUjaq7B1bZPnIOSRcZ31Mpya23OFbNTHoZhEKc5fprTi3z8OCOVEts0\nsCgOHD81XiLLJRc3/aLjjpR4tkGcSTYGMWXXZK0bYpoms/USQZJxZnXA8ZnqTdtz6jX24XDXQbAQ\n4o8Da0qpN4UQn77R5ZRSPwf8HMArr7xyj8cMaNrt2bkYASx3Qn73/XUW2yGrhuCtKy2utEKSXFJx\nTI5NV3lhYYxzGwM6QYpRdVjrJKQ7btsUkO/hT7opIFMfBte2gHTb7Uug5aeYBmAIHFGEzYYhqHsG\nXzy9ymefnbmuXq3uWSSZ5CuX1gG2Mhk7szTa/qLXbG0v3U72c3SZQZwxVXWZGx4w237dimsx1/A4\nt9YnTjNKtknLT1jrx0Rpjm2KYt3d9hM7rBrDAGxLUPdsohR6UUSSSrJc4jkmjiEQCtJMkgHvXO1x\ntRPz1GSZynAsc5RKukHCl0+v0fJjvnOlg2UK5houl1sDrrYDwiTj/Ppgq/Xbbu5mB1PbO3uRCf5+\n4MeEED8MeEBdCPGLSqk/twe3rWn33M7FqOdlNMo2gzjjzFqPOJWMlx02/BjbNFj3U+r9kCjN6McZ\n3SDddYzyXgbAwHUT6gwDqqZBKiVJNuwfrIohHiWhODZdwzQNDjbLrPRSljoJPT/hpUNNnpquMdcs\nbdXoHZ2qMIgzDo2XGcSZrlHTNG1P3U72c7ekxGInpO5Z13x+EGVM14oR8SXH5PfPbJAraPkJUSox\nEJiGGnbPEZii+LchijK1MMlIpCRNJZlUZFLSjTIMUZSzCVGsr6ZRDNXoR0VbNssQdKOMEwtN3r7S\npuza+HGKZRi0/IxcgkLR8susdLtbmWzt4XXXQbBS6r8A/guAYSb4/6oDYO1Rs/3ARt2zqDgWC2Ml\npCoWyrPrPqlUxHmO380YxGnRekcWp4wVH5YrWLBrULzXTEMghCDLr687ziX0o4zZhsfZtT7dKGe8\nYvH+ao9TK13qrsOPvzjPUjfCsYp65qprMYizXbM0up2Ppml363ayn9v7tu9WQ9yPUl4/u8Fbl1pc\n7UTM1F0cy2Cu7hEnGeuDBGyDLJcIijVSobCGU+UGUUI/yZFRsadmCrBNQarUh4mGYer4zEofQ8AZ\nx0IBRybKTFYdrrZ9BnFGlOaEqaQnMhpliycny6z3E1a6ARgCfzgRT6+fDy9dja3te7sttq89PcXZ\ntQG9IOGTT0wwVnH55sUWm35MkMjhFCIARckxiFNZlCEgkPe6RxpFwJ3nqjj9vMvXHMsgjHPCJCfK\nFWGScSlKkEpQtk3OrPbJlCTPFS8fGce1DF46NEbFtXbtHLHz4Nyof6de0DVNuxe2T4/zhwd7R/XB\ngzjDtkw8y6TsFOURjbLDWMWh5cd8sNYnTDIGUU7NMTEMgWMbdPyUKP2wNMI0iiBYiesnfZoCHBOi\nrLgvhoBWkPDJI+P4cc58o8zVjs9Y2aHq2liWQT/OCfOcxXaEbcHvn12n5lm8t9LX7dAeUnsaBCul\nfhf43b28TU2713Y7sGEAv39mnaVuxHSt6Bm80CyDUMSdiDDNMQ3wjCK7UHctGmWbTx2d4q2rbd5Z\n7N/T+6woWv7sZAKOVYwA7ccZjTRnEKZkUpIpRZLmnFzsYpqCMyt9okRypVW0fnv50NhWHfCNWqZd\nbvnXTJ3TC7qmaffCzulxrx6fBoo331XXIogzulFKIzapuFWyXCKVYqkTkKQSQxgYhmKs4jBZdXhi\nusrvvb9OnOX0Y4kEDAnCEriWQZh+eNzYElCyDUxTkA0/nylIUkWrH7MepMw1XPzExnUsZK6K7hC2\nyUTZxjIMulHGB6sDfkMtM1N3OTRR5fLm4JaH5rT7S2eCtX1v54GNMM749ZPLXN4M8JNiO2uhWWK6\n7nK17WMaAoviAFma55AXWQQpFRM1h+97cpJLG3168f1/LJYFQhiAJM3zrcl3CoUhQKmi/i1Xgpaf\nYAhBSZrEWcZXz28yMzyIcqOWaXcydU7TNO2jGk2PKzsWQZJtZWprns2njk7S9hMOjJcp2SYn5huc\nWesz3/A4s2rRLAvaQUKzZLLpJzTKNpYodsEALAMMBa5TdHkIkhx7WAcsJcw1XI5OV9n0M95f7ZIO\nz1yEacJXzm1iGYJz6z6HxktMOiaXN0OaFYeSa7DcSdjwE9JMUrJNQLHaT4jSHhc3AxCC5U54TQJB\nl0s8ODoI1va90WGM5W7Eei/iV7+9yEo3xE+Kvo/zDY8//fIB/Djjn/7hRd6+0uFKKyDLFXFa1JOZ\nhiBTULaLyXIV18WP4z1vk3YrcQa2UfQrTiUEgwwLcByDim1hGpK6ZxPnOSiFn+T4UYprCqLhliNw\nTWa8H6Ucn62BUtQ8+7amzmmapt2N0dmMXCkqjnXNWiOBmYa3tUYh4A/PbfKty22iNGe+WaJetlG5\nohNGdIOUq+2QqmdRcmxcWyFQOJbB5iAmk0UAXHJMslzhJ5KTy136YcYoQWwKCFNFKsG1IMlz4kyh\nELTChHaQsNGPqXoWT89UWe6G+EnG+6sDPnlkjE6UcmSyzKHxyjUJBD097sHSr2DavrTbO++3r3R4\n4/wmS52QsmPRKFscmijzZ14+yFyzxGIn5OXD4xwcK/Mvv34FPyt6SqZSUTENHEPwxdMr9IKUNJMI\nUYw1vt+9pdIdZRJCgEAxWXcxhcAwoBUULdYUEKeS9UHM6ZUBPwZUt2XGk0zy9tUujmVsLdAvHx4r\npiU1PL1Ya5p2T2xPTvhRxnI32vr8zt27IM7YGMSYhsCxDPw4xXNswixFSsVKL6YfZzw1WcWzDaIk\n25oQGm47xSzSvNgNTDJyFGkGZccgHU5AksPFfJAoTAG9IOZ0lBAlOZZZHI1ulGwutwI2+jGOZRBn\nOT/49DSebRJn6roEQi/K8JOMsmPhJ7ozz/2mg2Bt39ntnXdxCCNjvOLQj4uG7YcnqvyZlw9cM9e+\nF6acvNrFcwwSaTBRdfHjlCyXxAacXRsMuyykW10jHjSlwETwzHSNkmuSZoqjM1V+9VuLbA4SFAJD\nCOabHpJr2xT5ccbp5d5WxmW5G3FmeMhjuRPymt6+0zTtHnr7SodTi10Anl9obPXeHa1RBvBvvrNE\nnOdEaU6U5EhpMlv3iNMM1zIZxDmDJCPOcjYHCVKCEsWI+6J4rFBshF27akepRClwbLCFgZUX9cTH\npqukUtILMyquiWmY1IZt1LJcIQyBUtANU7783io/+MwMn3lu8rpDxQbw3nKfMM3IFbx8aOy+PK9a\nQQfB2r6z20G4uleMu0wyyUTZ4chUhR/9+Px1gyU6QUKcK56db3C55bPRj2l4Nr0wY7zsAjHxcF79\nwxAAj0SZ5NfeWcK1TBzLwLUMDoyXiJIMP81RSlCyP9xy3N6m6MxKfyt7gVJ65r2maffF6I141bMA\ncU0P89GfxU5I07M4MddkEGZElsFcw+PJ6RpKwSDKSPMcIaDtF60tDbNIDiiK3sHyBou1QfE114Lx\nskMvynBtAcIkSCVJJpmqubQGCXNjJY5O1ag4JkkmWe/HxEpR9TyOTFZ44WDzutcTKALwIxNlLm4G\nhGnO184VZzP0unp/6CBY23d2m1xU82w+d2KWFw40QAjmdlmEljshy90IpRSX1n1yJQnijH6UEucK\nOayZdT2DIM2RibxuwMWDkMFWqiNXOamULHcjnpmt0g5SxqRkomLzqWOTwIfN6UeP//hMdes5ATiz\nOtA1wZqm3XOj5MTFDR+AwxPla9acfpTixxmGYTDdcDkyUcGxTVZ7EW0/YbLm0gpS1gcxSkE8bG2Z\n5sNxyhJcsxgwtJ0JIIbt0wAhioPESoFhm9gWrPVDDEPRC2NKno2UivGKxcXNkCDNqZdsDAHHpmvM\n1ktb6+d2o/uf5JJcKqZrLq5t6OTCfaRfwbR950aTi2qeTW3W3qoXHn0OisVqtV+0e5hreKz0Qsq2\nSSoVAoPxssmBcY9PHZ1BCLi4MeArH2zQC9Oip68E14Ysg/Gqw0o/eSCPPZNgCEWWZ1iWwXjFxhAG\nrmlgAF84ucKmH5OlOU/PNbiw6dMo2VSGvThrnq1rgjVNuy9ulpxY7oR86d1VXNvAEIKPzTe4shkS\nZRlVz+T7npoEAWXL5Oxa0bLSNqFZctgYBrQSEJZB1QQ/kcPe78PR9OrDqZ+uLbCFQZJLgjgniz68\njwrFIE5I0hxDiOI8ScnmmdkauVIcmqjwmedmtnbWRiUc/SjdOm/h2SYHxktba61OLtw/+pnW9qUb\nTS7arV4YipZhfpwiEJRckycmKqS5otwNEUJQdkwOjFX4waen+PqFTeYaJZ6aqvCNi52tsoggLQZZ\nbA6SrelyD4KU8M5Sj7MbAXXP4shkhRzFr751lbV+jB9lLHUjvNOr1Fybjx9o8MRUdeuNwZuX2rom\nWNO0+2KUnNiuH6V88fQq59YGNMs2E1WHfpwzU7e50s4pWRaXWwFZnvOVcxuYw/pczxFEWX5NsBsl\nEscUOCZUHItOeO28TwuIE4mwBXGmdi11k0CaSa60Ag6MlVFCUS+Z1EouP3JibmtE/e+9v46fZLy3\n3Gem7rLSjfiB48VrzHc/MU5leOhPr6n3jw6CNW2b3eqFgeE7+ioAYxWXXpjSj1IaJYfvfapOzbX5\n5JPjvP7BOt+81GK5G7HUiXYNdB/0gblcFX0ys0yx0o1pBwkHxytcXPdRKNJcgVCULAvLNFgbxMw3\ny9cNztA1wZqmPQi9KMMzBc2yzVo/ZrkbEac5XzvXJleSMMkJ0oyOnyAETNdLdMME2zDIRXHQbVQB\nkSnIM4UJRHmx3m8/LGdaw9IJIZDq+slyI1muUEAvTCm7JmdWfD7xhMtXz29ScS0kxetI2bHIpWKi\nWgTBl1sBU1V3q164F2UMokxP5bxPdBCsadvsVi8MYArB5c0BUa6Yqjocn6lxZqXPwlgJzzSoexZv\nXW7z628vkUpFJyg6RuykePAH5hSw1s+wzIyKbRElkl6QkciMZ2brXN4ICVOJUoqZmsvxmerWdh6w\n6/OjaZp2L/WjtGiTNjx7UXFtFppgmQYNz6Tk2oxVLOJUstkvevbmSuHZFlGaoRTM1D3WehGWCfm2\nOmAB2BZYwkAii6AXaJZMJqoul1oBvVhurd3bd/IcoyizqLg2tgm9pOgWEaaSN85vMlZxiJOcH31h\nHlMI/CTDNARSSp5faBQH5rYNKdr0Y04t9nh+vs5E1dV9g+8x/QqmadvcqF745cNjfOndVTzb4Oy6\nTy9MudIOsE2Dk8s95uol4jynHaQopQhSWRyueEgJisdadU0GYUYuFUmqkLlCojgwVqbiWfzESwt8\n/GDzmrrp3Z4fTdO0e6UfpXzh5Mo1rdI+dbRoN2YAr5/d4K1LLfxYYg2bs5ddk/VBysfm60RJxiDO\nSHJFmObXZXMlxWE5IYq6YAMo2XB8poZlGnTDlPVBunV5xbXZYtc26YQZjiFIpGSu4WEYikutiDCT\nmKLDc/N1npmt0Y0yXj40Rsm1rllDFzvFcI2LGz7L3ZCyZ+HpQ3L3nA6CNW2HnfXC/ShlqRvh2sbW\ntJ+nZ+tc2gxwTIMgySk5BsvrQXEwwrNIsxjLEgySB5333V0OSJmT5QLbEqRZjp/knFrpg1I0yw6W\nIfCc6wPdG9VTgx7/qWna3utFRRBb9WxA4cdFucDCsITghQMN/Djj+49OcWqpS8kxaZRckqyPbRoo\nx0IIg/eWe9iGALOYj5xuW56VgiQDzwLTMGmULJoVh0GYMkjSa3bwRgkOS4BjGziWCVGOMIoDdFGS\nY7smYZLTC1PeDVO+dnaDMJU8M1ej4lhb501G3XjqXpHFDhNJxbWIkowoV3q37R7Tz66m3cTWYYY4\n5b2VAVDUhh0aK/HCwSZ+nBKmGe0oJUxybFOQyRzHNoZteNRDUQKxm24oiZIExzaQSiCEIkly+klK\nP86YqLgkaXZdy7Qb0eM/NU27F+qeRdW1uLTVKq1C3bNY7oQsdSMansVk1WUQp5QciyNTVaJU4pom\nhhCsdGNqnkmY5WRKEeVyq/MDFK3QHLMYcpFmkIqclpJ8+1KbMJUEO5r5SIbZYAVRLBEUfYiDRNIo\nWUzVHHIpmKq5lBwDoAioW8U00tHB4revdvHjjIpr8bkTs3zmuRmUAKRECIPPPDuj19B7TAfBmnYT\no4Ngo0NxC80SFzZ8vn21i2UIvvuJSdJccWqpT9WzsW0DP8oxSemGCcaweGy0aAq44cGK+00CUQ5R\nLjFEgmcJenmGZYBrGszWHX7z1ArzzRITFXdr+/FGAbE+NKdp2r2w1SrtYBOUYq5ZYhBl/NxXzpNL\nhWkIfuLFed64GHK55ZNkkmbZZr7pUStZKKnohQlxmhMmObksAl/PFITDjg/JsKm7axctLQWCbpwj\nb3C2Y0QCUinKtkmcSSYqDrZhULIEvVDQ8Gym6h6uaWAagiDJMITg4mbAW5fbjFcczqz2mau7PDVd\n43ufGL9hr3pt7+kgWNNuYvtBuYprU3EtTi/1sC2DNJMcmawwXfdo+SlnV3v0opQkz0EVIzh3C3gN\niglEuYIk3+UC99FoMS+yIgrXFIxVXUwh2BgkpFmf1W5M3bNoBwkzde+GWd4bHSrUNE27WzvLsM6s\nDsil4vBEmUubAec3AtpBQmuQYJgGBClHp6vUPJv6MZuvnVsnzYphGaPsLAhKZk6SD4cKUbSyBHBM\nCBN506SFBGwBaS7JJSglSHLJt692qDk2woTvnZngJ185iFSK+abHxiChF6dsDmIW20VJ3WI74M3L\nbX77vXWema1Sce1dh2toe0+/SmnaTew8CHZ2tc9iJ8CxzaI5OkVvyZJj4FgGYxWHlW6EVEWmwaBo\nwWNS1OEqoOIIbNMkSrObfu/7Lc7AMouw2LYMXjo4TitMkAoGcYaUN8/y6kNzmqbdL/MND9MQXNoM\niNKM8xt9Lm8EXGkHTFYdKrbHobEyUPQIdm2DsYrNhq+wTGh4DqmUxKlBHKTX3X4/ufWenUFRXgzg\nmCZSqaKXvGUyUXMwRTE9tB+lnFzq8VvvrtCPMwwEP/HSAgvNMoYhWGiWmW+U2Bz0KLs2uVJ6J+0+\n0UGwpt3C9gxExbVYGCtjmwZpLik7FmXH5O2rHWzLJI5SDAFprnBtQc21WesnbE/4FoflHq4A2DGH\npRoK4lQyXnaolSz8NEMoxYkDTQDeOL/JRNW5Lsu7/UDc6LCKpmnanbrdw7VzzRKff/VJzq31eetK\nh/V+wljFpuxa2KbJcj/i3727wvn1AM8WdIMU1zaGU9lMPnlknN88tUqUZHzUDTkhwDENEIpm2SJK\nJSXHpB9KljoBuRRIFL9hm0RJTppLkkTSiRK+cGqF145P8crhMc6u+wRxSpjltAYxE1VX76TdJ/pZ\n1m656OgT/x+aa5Z46dAYflz0ejy7PmAQZ3SChJprst4LSXNFyTLIleLIVIXj0xX+8EKb+GEpBt7G\nogjHk3zUEB6SLKcVxERpznPzdQwEJ+br/NIbl4hTyVjV5YeenQHYGgE6miK3fcqe/pnRNO1O7Dxc\n+/LhsZueQ5hrlpDAYjcizRVXOwGHx8s8N9/g5NUumZJYpmC86pLkEts0mK2X8ByDS+0ApRSp+ujH\nlqWCRsWh6hTDMMYrBiXHpOxatP2YNJNYQnB2tcdiJ2IQZ/hRhmsbbA5ielHK0Zkas40SX3p3lRPz\ndQTF49br5v2hg+B97lYn+vWJ/2uNDmgsd0JW+zFL7YBD42VOLXYZq7g8YxmcWSkOyUVpzlyzzIGm\nx/lWwNV2/NB1idiej1YUpRuDKMcxDRzTYLzistwJ+ZU3r/LuUp9m2cZPct652iXJJX6cstKPaXo2\nx2frrPUjljthUa+nf2Y0TbsD2w/XXm75fPH0Ks2SfdN1xKDYvZqoOlQ9i5Jt4lgG9ZKNH6dkucKP\nMiyjyAYPwgzPMXlmpsZ5279uTPKdEEDbT1BKcWy6RskxWevFBElKkin8OOfchk/JFghhUHWHw5co\nEg6XWwHLnZCKZ9Mo21vlZhKdfLpfdBC8z93oRP/oF9CPUn3if4dBlPEHF1ogJRc3Q54BXjjYJEoy\npIL+8DldGCsxW3NZ6kQcn6qx0Y/Jcq7pTfkwUdv+lkJxdq3HqaU+/Tghy3PiPGe9X7zYbPoJSZaz\n6Ses9WIWVYhnG1RcG4S45mdmuRvpxVzTtFvafrg2TiWeJW762tOPUt681Ma1BFEOP/rxearD8e6v\nHpuiH2es9yLOrA34+vkNDCKyYTeJNT/GswVW0TL4mpKI0SAMQRGs5jdYsyXgJ5JBEtMexBimwUTZ\nwU9zkrS4RSmgHytqrkOc5cVgIqmoqlEphbjuULEBOvl0n+gg+DF3q3eTu53o3579TbJiD1+f+C/0\no5QvvbvKubUBzbLNkYkSR2fqzDc8+nEGSvHxAw1++701pmouCMFSJ2CxGyFE0S+tZgv6D2skTDEC\n1DIMNv0UUAgMwjRnvOzgxxl11yLJc04t9ciVpOY5zNUdjs7UOT5TtJI7s9JnrR+RZJK3r3RwLEMv\n5pqm3dT2w7WjMqudrz3bX9OWOyEbg5hD42X6wwEa289wzAE11+Jfv73EmdUB64MYzzJ4dr7Osakq\nSIWfSIIkxzEEuZJEqSSV4IoigBWqGKQhKQKmUbvL7UkDgDADkUmUSjCEKA7JiaI8Aoa9iC2TE/MN\nVnoxNc/i0Hi5uHG45lCxbjd5/+zviOYxdzulDLud6F/shNf8Aj47V6eyY8TjftUb1nM1yzadIGWi\n5jLf8LZqYnthWtQHexYG8INPT7Pei+hdbJPmilRB+hAHwFD0DlZSsTGI6Uc5VbfYXkxySdm1SKRi\nouLy1HSFN85v0vEzgjjjx178sK/la09PsdyNWOuGLHZCpmtlvZhrmnZL24PY14YB4ei1ZzQ+eRAX\n5Q0AFzd8Lm74PL/Q2PXA7ttXu4RJztFhuYJtGTw/36BZcjCFKJIXQDfIaIUx9ZJNGGeUXJM0VwRp\nvhUoZbIIgk2GO2bbvtfo31EiEQaUHYNcKjphQsW2KJVMZusOnSDDtQwqrokBfO3c5tawjO2HinW7\nyftDP7OPsdt9N7mz/+LO7LBu2v2humdRcSwWxkpMVl0+8+wMEsiVoupafPn0ClfaIVXXYqbu8cqR\nCY5N1cjyJVBFFwaZF6eKc/XwDM7YacNPmSjbuLaB5xiMVxxKjsXH5pu8u9zl7NoAU0CQZNiWyWIn\nZKUXMbdtET+z0sdPsq1JexXX1ou5pmm3bedr03I34tRil6pns9wNOTZd5QeOT3G5FfDCweau51k2\n/ZiVbshGP8EUitlahVwqpFLYtsHhiQoC+Gp3kyyTRSmEABB4jkGU5luHmkcBMKLI7NpA2bXohtnW\nWp4Btiomi+Yo8lwRC8lYxcUwTWZqNnONEr0w5czagIPjZS5u+LxwoAHNDw8bH5+p4g8D9OVutPV8\naHtLvyI9xj7q8ILb7fe6Hwv3d27XSYa9IoXgcisgzYvJQ60sJYhzvvzeCufXfeI0R6oiALYAyxII\nqZA52FaxlTa6vYdBrqATp4yVHGquzVjZwY9zvnWpzcJYideenuLyps/vfyBolGx6Ycp6L94asbw1\naW+8AsDR6RrHZ6r75udE07R7QH1YhOBaBoYhGMQZU1X3uuESozXowFiZqZqLKUAJgTAEb13u8OLB\nBoMo59BYiZPLPZBF+UI/KkYgS5khKIYebd+7G/UFNk2GhcOKYaXbNVzLJJcZSkCQ5lxpBzQ8m/V+\nzLtLfTzHxLMMZupF4sBPcn7v/fUicbDc58hEmTNrfZQExzJ4fqHB507M6jV0j+kg+DF2N8MLdr4D\n3+lBd414kAH46PvtbOXTjzNag5ilboBJ0Zg9SCUbg5Sya2JZBkIoKo5FkhW1Z70wIxkeTn7QAfDO\nIFyoIsP95GSF5xcarHRjlnoBT05VmK17nFzsYpuC1W7MgbESq/2I9pmYKFd8/5MTH07acywdAGua\ndtfmmiWeX2jgxxmHJyq7jnIfvTZsT040Sw5jFYfLmwFl18aPM+JM4VgGC+NlFjshB8ZKLHUj4ixH\nAJlUpLssyon8sKe6YwpsAdaOw3O2CRXHZBCnKAR5rgijFAHMN0qYtmCi5iAQlB2Tg+Ml/CjFTzLK\njkUuFQhBmObUXIuqZzOIM11Odg/oIPgxd6tg9qN6kIX7DzoAh+sfvwTmGh71ko0lDKQC1zbJMkkm\nhyvpcL58mktagwQEH7lJ+15zDVASkm2fMwRkuRxOPMrIpOL4dJ3pusdSN6JesvkT33WAd5d7vLDQ\nIMpyFjsRa72Yrp/wwx+bo6RryTVN2yOjFpU7EyD9KGWxE17Xs3yUnKi6FkGc4scZ800PA0XZMag4\nFt+61OZKJ+LyZlBM9zQgy4sg90YURdAbZoooy69rfRlm0ItTDGEgVbH+G5aBaxn0o5QgzenFKWNl\nG8+u0wkSzg27DR2ZLGMaApSiZJukmWIQpRyeKOtysntAP6PaR2IAnTAlSrL7Xuv5MJycHZWaXN4c\nEOUKY3i/bNPguw6P0Y8ygiRjvOYyW/couwZXN0K6cYZrC3L58ATAwK6DPLK8GKN8tV28uBybrVN2\nTAwhmG94nF8fcGqxC0AvzoiSjLVeTCdMCJKUf/GNjJ/6xEE9QU7TtD0zSuzsFvh2whTPMjg0XtlK\nThyfqTHX8FjuhCS5ouUngKBRcmj5CWEiOTJZ5vxaHwNJtK1t8O2UqI1aqW2nKFploorDdApIU0lq\nS9K8qDteH8Ss92MubQY0PIcnpis8PVPlyakqH19oUHEtPvv8LP0oBX02557RQbB2x0a9GT3LIE4l\nrx6/v9NtPmqt816qeTYvHx7jS++u4tkGb15q8/LhMSquxSDK6IYJFcfiY/MNXNOgG6WUbJNvX+5S\nsS3aVoLKdg+EdykveyBSBSqW5EpxsR3i2RbPzteI0pyVbkijZDPb9Dg2XWMQZ5xYaBCmkiBJudQK\nWBsk/M9fSfmrnzl+zYE5TdO0u7F9N7AbpLiW4NBElSjJiFO51Z7Rj1L6UZExXhYRZ1b7DOKMzUHC\ndx0e460rbT5YGZDLIpQVYlToW7hZADxM1gK7r9dZ9uH1PVvg2ALPMYmTHD/JCZMM27TI8px+FLAR\nxCx1QkqOxXTd29rl1GvnvaWDYO2ObT/0tNaP6EcpsnPj0ZawtzW8d1PrfDd2PgYJ1035+dTRSTp+\nTJC6rPVj1vsRE1WXfpySZJJm2caxDA42yyS5ZKkbXVN3ZgDu8KDcwyADFtsBYDAIEwxD4CcZXzmz\nTrNkFb2PFVRcC5Ti5cNjLHdDTCGYrBYtiJa6kV7ItftuPx7c3S+27wZGaU6UFYFvxbV59XhRAvH2\nlQ6nV/q8fbXLCwcaXNoMeOdqD0MoOkHGH5zd4FuX2hgC4lRhmUX51604BtiWwESQSkk6PDi3c9iG\nawvSXCElWKbANU2mKi5rKmYQ50QZJHmx0NdLFlNVl7JjsNyLeGqqSl/XAN8XOgjWbtvOAwdbwxCu\ndm86DOFe1PDeq1rnG9ntMeyWke5FGdON0tbYz6PTNRqexTcutghiScUxOTReIcpy4jSjF6aESU4y\nXHuFANMwEMiHIhsMkKSKaqnoevGVD9ZwzGIy3EzNpVmx6UYp76/0+ObFFo5ZDNYwBLQGMY0pm/kd\np7Y17V57GM4NaPfO9rW34li8emzsmgNyshPiWMWY4t+/tI4fZ2wMYhqeSdWzMY2ItUFEmhddJlxL\n0Kw4CCCXAUEitwZijEoiXAMME8ZKDqZpkElVlDwMw99Rhx9DFEFvmikwwLYFJ+abnJivc6kdFrtl\ncUbJcXFMg36cYQqBbQiSTLHSCfnNk8scm6lhPKDndz/RQbB2W3a+qLx8uFh0/Djj9HLvpvW5D0MN\n793a7TEsNEu7ZqR3dkU4szrAs0y+96kJ/uDcJp5jsDGIKLkWjm2QSIWZSjxbFC18FNgGW4Hx/SQA\n1ywGZoykCrpBjmPl2IZBlmYESU4/Sni5PM5Y2eFrH2xQdi1s06BRsvnxFw+w6Se8dnxSZ4G1++5x\nWHN20pntD91qN3DrzEYrAODQeBmBYrLusTaIMEyDMM4xBfTCopzCMV3KtsXR41Nc2vRZ7EQMkozh\n9GMSCYaCMJWQSsI4I5HXD8ywDZioWPhxUf9bdixePNRktl6iVrI5NF7m/ZUeG/2EIMlolh2mqi4T\nFRvbNGiWXU6vdDkwXubNS21e0//f95QOgrXbsls3hIVmieVOSDdIidKcimPtWp/7MNTw3q0bPYad\nGendFuf5hodpCK50AmzLYKrqcmHDZ9CP8OMcUwgcS1D1bPw4JcrVAwmAodjqi3cUKrsmpHmRFclk\ncXDEFDlxmpNmOd++3MJPczKlqDoWZsXBsQ2OTlc5OlPbuh39Iq7dL4/DmrOdzmxf72a7gaMzG+fW\nB1hGMRVuourxH3zyEN+41MYS8G/eXqJesjFMwZGJCj/2wgLfvtLh2EyVp+cafOvSJuuDhLVeyCDJ\nkRLyXJHlklxJMsAYpokVxRCNnGJS3IddIwRRKlEKjk1X+CdfWUVKRZDlHJuucqUTsDmIMYUiSHJs\nU2KaAlMI5usefpxyZnWgW0zeQ4/2yqDdN7u9qIwOyLmWIMokrx7b/YDcg6rh3Ut38hh2Ls5zzRI/\n/d2H+MbFNl89u86lVkiUSizTwLONYhSnKnpCmoZJ1YHOtglE91Murz/kUTRrL/7Pu2FajAtVRbB8\nYSPg+GyN73ligm6UcGi8wp94ceG61mj6RVy7nx6WcwO3+vztehwz2/fS6LUpVwrPNnl2rr41TKMd\npJxb6+PaJs2ywyHbpFkqegcfmSjz5ESFJ6eqNMs2f3BugzjNCeIIhQIBUSaxjaKPOgwDYAHZ8GM/\nlpRshVRgGYI4l/z624t0/ITJqstk1eVrZ9e50g5IshyZw9ogoe5a5AIMw0AYgnaQsNyNQQiWO6Fe\nM+8RHQTvI3ezEO/2orLYCYsDchPVrezwzb7fo/4L/FEew3In5Oz6gIsbPn6c0fYT5pslXNMgyYuB\nGaYBuZTYhkEOpNmDqwfeeR7PBGolC882sEwTiSIbZFuHQNJc0otSjkxUODxR5pXDY8zs0spHv4hr\n99vDcG5g1Mrrbt8APm6Z7Xtt53pTcT98zXv58BgXNgbMNjxafsx0rcTx2TpRKrm8GXBxM+DFgzHf\n++QEnSDBsw0QgiSTbAxiHFOQZTnKACXAM0ApgZ8Wq3YiwcoUlmmQZcWrYpDlvHWlw3yzRDdMWO3H\nKKkIM0nVsbCVYqLmUvMsjs/UiZKMqVoJ1zIoOxZ+nLLcCel5j24i6WGlf5MeA7cT3H6UhXi32/Wj\ndGue+c0W5v2e+etHKWfXBvzym1cIk2Lx/IFjk5imKOrGLAPHBIUik4Js2De47FoIV+KHKb3kwbdL\ny4HNIMME6mWLMc8msDPitDgAsumn1Eopl1s+ZcfkKx+s8xvvLPPpZ6b5+IHm1v+5fhHXHnc3eqO3\nF28AH4fdtPvpVq9Nm4OEJyYqlC2TVw6P4zomJxe7rPZjUIqvvL9GnudcbgUYwiDPJK4pyHNJkBWB\nrm2CiSCXiihTW4foBIAhmK7YrPZjpAKZQzeMma05SCkYK1n4icRPcnphjMJmpRsCJc6u9qi4NhU3\n4sJGgLkekCtJkivqJXtfvp7eS/qV6CFwNxna2w02b7UQ77wPux2Ee/3sxtZwhNEc8xstzPs58zd6\n7s6uDbjSCnjpUJONfkQrSDg4Xma65pHnikGSUis5xIkkl4o8V/TDhLGSzYsHJzi73ifKJONlmyud\niDRTD2y0cg4EcUbFsRgrOUS2pFl2SKXik0fGWR8kvHmpzdogZrOX8LWzm3z/sUn+2IlZjs7U9Iu4\n9ti7UeC1V28AH4fdtPvlRutNP0pZ68ckmaTqFe0q//BCi1xJ3rrcARRpDp5lMEgyVroRYxWH/nDI\nkVQgRu0iFIT5tSkKk6J0TCGIckXJsTCEIEhyglRyZs3HtU2klPTCBCllUTZhmqz1I6ZqJVKp+MSR\ncdYHMQcnSiw0yyy2A/y4OETnJ7p12l7SQfADdrcZ0+3B5uWWf8Mi+hvV9I5anm0fNTlaPLYHsUvd\niE0/RgGOZWzNMV9olna9v/s58zd67o5OV3nrcosr7ZDZhsdLB8d4crJCybUI44zfeW8V1zJ4f7VP\ny1dEiQSl2PQTBnGbTIJtGgghGCtbdMKUOH1wmeE0h04QU/NsbLvoAmEYBkGaYxnFzKQwzonznJV+\nyBdOLrPai/jUsSk+d2JWv4hrj7UbBV76DeCDsXO9Gb3W+nGKMKDqmqiGx0o3JIwlhhDEqSRTRb/g\n9iAhziTdICVMc6Q0QYCUH45N3jlRzrKgUXboRxlSKZRSuLZZHI6TIKUizovGwpZZNEBLckU7SMgy\nydWWz1jF4Uo7YKLqUnEtpFJUXIv3VnosdSJMQ/Dqsan7+lw+zvZPZPKQup0M7XI3AqWY2xFw9qMU\nPyqGMJxZ7XFysUeUZLsW0e9ciAG+cHKFQZyR5pKGZ23V9o4usz2IbXgWV1oBV1oBgqLlzM0C2/28\n8I+eu1wpfui5WWZqHpdaPoudkG6Y8rkTsyw0S8w0PF45MsFvvrPEb51eZSWJQA37BAsDw1BU3WLh\nbXgufiwxLUn4gDLCkqJXsD9sGzRTVTwzW+HjB5s8O1vn9z9Y54O1AUkmMQzBeNmk4lhbb5i2Z2P+\n/+z9WZBcV5rnif3O3X13jz0QAAIbQXDJJJnMKnZnVmVW1VRmV7dqNKq2VmukHplMD2q99INMetOz\nzKQnmc3jtGlMNpJ6JE2PWl2qruqyzNorl2JlMklwA4g99vCI8N3vfu85ejjuTo9AAAQIkATJ+JvR\nCMAj/Lrf5Tvf+b7/9/9/He+LEzx7eNr34oM2eicbwC8Wg0irLPhJxtnZMgCXFqvUPIv/6m/v0AtT\nHMsgl5IslbTDjE6Y4pkG3TAhThVxKkGAaQhsEzzbIkjSQzbLBcfENCCROVamCwO2KSh7Bu1Bzv4w\noeAYCAQLFZe9YYQ5cp5TwN4gIs21qdLvvbwE6BzBj1IcU1B0bYI4/cI6gl9FnCTBXzA+ibv0p+/v\n3kdBOEpXiNKcvUGMacB2LyJMJTu96L6gOx2IbzQHfLDVo+zZtIcx5+dLhz7D0SR2pxdxZqbIlcUK\nfpLzxvmZTwzqX9fAf9y5+9ntA8qezc3dAcs1j1fOaL7sQs1juVHkH1yY42d3Duj6CaYhiJKcOFek\nmcQxBQtVD6UUca4T4EfxtH/aEKP/wkSSS7h9MEAIXckwDYMrS1XOzhQpOibDOKPoWSCg7H4snfd1\n54qf4PPHwxQbTu7Frz6mK8DXd4cAlFx70jH9X//mBf7kvR36Ucov77VBwF4vRhhaEm2QTGW5CmZK\nDrlUJLnENk2iTI8JC7RqTqVgE6aSTCo8y8CPM5JcoYRWlCi7FnGeE6QZ+aQ6rEafNUeqhD98Z5vV\nmSKzZReEoOLZlFybXClKrv216qx+1jg5k18wHlYx7UcZwzij7NmAwp+qqE1XkDt+QsU1yXOHD3d6\nLFQ8Zssuy8dM6U8wNj1H4VgG315tsFAr3NfGGyfcVze6rLcC4kzy6pn6pzJA+Kzkg55FTG8Adroh\nAEmWs9UNeH+rRzdIJ65zZdfCsQxePVNnfxDT7Ed0jRQZpTiWIJda1scwwLZgwbORQuh23eeYCSsg\nlVoM3rJ1pVqhKLs2d/aHBElO20+wTcFsyeEfv7jIN87UmS+7k/f4OnPFT/D542GJ7sm9+PXA+DpP\nKsALFS4v6j9vdUMWax7/y984z629IYaAX4ycL1MpcW0DxzSIpKZJGAIGcYZtCIq2Sb1qs9kJ8RPt\nkqmLBJoelklJ0baJ85woy3AtgUT/kGuaWKbAEiBNgziXusigXejZ7AT8H//jNZ5frFJyLV5aqfHa\nmTq9KKM2ciYFTu7Xp4AnToKFEGeA/xuwhC5O/Wul1H/5pO/7dcKDKqbjBGntwAdgdbZ07LBFybUo\nuRYQs1Dx+O3nF8iUemBQH0QpCMHFhTK5VKzOlibDS8dhpxvS8mM8W+96wzQ/9ucehp1uyI+uNUFK\nhDD4wYuLLNcLhxapJJO8crp2H+3jy47leoGXVmpsdUJWGkUuL1bYH0TcaA45VfN45XSNSwtlSo7J\nvVbAH13dpjOMeGu9S5RKbNMgzTOSTPPR+lGOYxs4toFMdHD+PHjCFdcgTuXIQlThWRY11+LuwYB6\n0SHLFYsVl1Qq4iwnloo/+3CPc3NFBIIfvLj4teaKn+Dzx8MS3ZN78auPwUjNKMnkaK3UFeBhlPHj\nD5u4tkHJsXh9tcFWJ2Sm5DBbdlmoeMRZThDnWIbBwSAmTHNdkFIK0xBYhmC7H2FZBlaek0mIkpxW\nHlIvuERCsNuPUAiEkqQKPAuWKi5Xlmu0g5S37rUJEz2XY5m6kiyltnJOckWcSxY9m9Yw4me3W7i2\nwfWdAVeWyhiGwStn6g8vdp3gE/E0nvoM+N8ppX4lhKgAbwkhfqyU+vApvPfXGhVP84JeOVO/jxN8\nHMd3pxsyW3bJRlWPo9SKo0Nwnm0em3ROV2YBrm72uNkcsj+IeHG5Sq1gP1bVZBCl/PjDJte2+3TD\nhHrRRgn4p6+tTBapaY/3ubI7sWX+KlSHx9dxpxdxdaPL/iDi+u6QKJP8h6vBxwHtdI0LcyWqns16\nx6fkWVpnUgj6YYYhxr70BiuNApvtQFcf1KgV9xl/jyCWGAI8B1CCM/UCUQ6LJZtfOzfDh9s9LEuQ\npJKyV+BU1WO9FfD2WodcQZjl/M9+/ezXlit+gs8fD0t0n/bcwlexo/VlxnSBBeCFpcqkg/mja01u\n7w2pF21WGgW2exF+nFJ0bbrDBGEIagWbiifY6UfYlkGY5SgUaa6Y9SyEYZDlCs8W2KZBlktCCWEO\ngySm6pkgBCaKHIFlKOolj9mKi2EIio7BxYUi270YP0pRCG2egaI1SKiXbPb6MQJFreCyUodGqUQu\nFYYQfLDVYxhnzH/F1svPG0+cBCuldoCd0Z8HQohrwApwkgQ/BTyMV3v0tcqSzXK9MBmkG2M6GOz1\nI3KpeG6xwpCM0gMmaMftw8uLZRzL4LefX+CvPtqjXnQeaI/8IPSjDNc2KDgGW92MubJDOBrgW64X\n7vN43x9E/PjDJrXiV0cTcXytlmseN5pDEIKiY3F7z0cYBh9s9bR9piE4O+Px0Z7JYtljfxhjGYJu\nqCeKcwVRlrPZDuiF+efKC87RlYpBDCaSOwc+SirWWhZrLS0F9/tXFpmruNzaGxLEKestn66f4dgC\nKXN+/dwMlxbKn+OnPsHXGZ+U6D6tuYUTfvGzh/sMM0bXeqsb4pmCetGmG6TMlV1qnsX13SG9MMUy\nTc7OFgnTjEGUcX62TBBn3Nwf0Cg5pJnkVL1Ay0/xbAOlIJNq4hgHI+rYqIARZwoxGqireiaZhJmi\ndqi7slil5ARIBdd3BiilKNgmAN+/vECc5qy1fNJccaM54BsrMS0/5m5Ld4fPzhQ5GMb86FoTz9Sy\nbD98YfFT0RW/rniq/R8hxDngNeDNp/m+J/hkTFd6b+wOyJXiRnN4SO6s4lr8ZHeAn2SstwJeW21g\noHlR4wVipxex2QmYKelEtVm0STKJYxm8cWH2vsrxo1Q/qp5FybE4N1eiE6TEqWS3G3F1s8dyvcD3\nn59npxdRdi0GcUaUKzzb+Epy9SqebsftdEP8JMM0BO1hRJJL9gYxH2x2aQcJ/SilWnDwHIP5ssP+\nMCYbS/Nkiogcwcd+9Z8nDPTn0EMcUDMkd/aGFG2LMJH8y+9d4PdeXuJGc0izH/PORpdemLI/SPnJ\nzQNu7Q2RSk9bj2kxJzjBZ4XPY0D3hF/87OFhus0l12alDrMVlx+8sIgErixXSNKcXEpWGgU8xyRN\nJT+7fUAriHEsg5mCzUzJ5eWVCn9944AoNbGEQKAI08N+m6lUGEJhAGXPIsolQZKzfhDQDVJs08Bo\nePiJxEBRKVgQa/c5xxSst312+xFhkuMnkiTP+dtbLZ5frLDTCXlxpcYwzrRqhVJsDWK6QcqPFfzB\nt1ZO7r9HxFNLgoUQZeD/A/xvlFL9Y17/l8C/BDh79uzTOuxXAk/aRpuuQvSCFNcSx8qd3dgbsDeI\nOD9XphMkyFzx3/79GnmuqRa/+8Iib95p8fPbB6S5QgjBD0cVy3Er6dNMV09XY765UuOdzR5nZ4qH\ntIY16qAUFc/WxgtfUa7e9Pn43nPzDOKMv/5oj3c3e/SijFwBQlD2LM4UPFzbolIYMgikfs2AJP/8\nk1/Qye/YGQk0BcOPM4TQ1s87vZA/fn+Hf/76GSqexXK9wFY3JMsVL5+uYVuClh8TxDndIJ3QYk4C\n9rOHk5j96Pi8+cUn1ItPxuPoNg+iFEMIbu/7lBwLQ8CvrzaoeDazZZcPd3oMo4y7B0NSmfOXHx2Q\n5noAruhqFZy2r5PgHHANsC0TzzIYJFp+rWAb2IZBfaQu0R5G+FGKRLFQcVmpF9jtRZoHXHGRQL1o\n0xoktP0hRcfCNQ2Wax5BInlhqcL5hQoGmt7RDVLqRRvXNk42YY+Bp/KkCiFsdAL8b5RS/+64n1FK\n/WvgXwN8+9vf/iKdYJ8pPCyRPM7F7ZPc2aI0JxoNARyVO7u63mH9IMCxDfaHMX/4zga39wMaJYeZ\nssNixSWTiueXquz2I4Iko2CbOJZxH21i+rgV12K9HbDTDaksHT+IN/7cVa/CVjdiGGeHTDuOnoOH\ntTC/CgvAtPKGBH77+QW6YUqzH+GPBiVqnk3RNjEMQd1zyfMEmUNwZDBRoC08k88hKxZAyYFsVPSQ\nSjNvXMsglpJZ18UzjQmdBeB3nl9kvRNQ9SySXBKl+SRge6aYTDp/2a/pVw0nMfvR8Xnqop9QLx4d\nj6rbXPFsXjlTn3Bsf3mvzZv32jR7MUtVl2GUMYx1Misw2B/EFB2TTOqizVzRYaMdotDduYsLlZEG\nsKDq2QgEYZoTpDH9KMWyDJRUxJkkyiQl16LsmJiGwXzRYRhlFB0LobTKRK4UrqUH0++1A5arBS4u\nfMxx/uELi/xYMRn0+6oVjj5LPA11CAH818A1pdT/+ck/0tcLD2qjHWdbfNTV7bgp55Jj8b3njifJ\nL9QKvHCqSstPqBdstjtamNtPUtzYoB0kWIZgGGccDGMEgnfWu7y22jj2oap6Fkkm+Zu1fZJMkuRS\n816n2tuPkuBudcP7zsGDnOi+SgvA0e/yB6+uUC/YBElOluecapQYhAk7vZh6KcSxTNp+TJTnKK3b\nPqEmjOUhBJ+tUoQChslhnWKpoO7A+ZkSL56qYAgIkozZksPtvSFLdQ+BGlE8bKIkp1awKLomhmFg\n8LFxS9m1JlrYJzjBlwlPk3ZxdDh5Ol6eUC+eHqbP83LNY77ssj+MAZgtOtw78NntKzKpo93lxQpX\n1zv0opRcShzT4Pxskf1hRNWziLMMgaBWMJmvVBlEGZ0goeunxHmOaQgUo6LBSDs4SnNQH8tgorQG\ncZhkHAwTHMvAsUzmqy71gsX3n1vgynKF8tSavFwv8AffWjkpJHwKPI3twneB/znwnhDindG//e+V\nUn/yFN77K42x41s/TGn7ySFTgeNsix8U+D6pCjGdbHm2yfefm8cU0BomFF0TocTIMjKn6Nr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xEzjDKiJGOY5syXHN7b1tV1P8ko2iaD6NMnwI9KhRjPUxdHn71esgnijJ1ehB9LChZk6IrJfMVh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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10_000\n", "key, subkey0, subkey1 = jax.random.split(key, num=3)\n", "samples_gmm0 = gmm_generator0.sample(key=subkey0, size=N)\n", "samples_gmm1 = gmm_generator1.sample(key=subkey1, size=N)\n", "\n", "fig, axes = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(12, 6))\n", "axes[0].scatter(samples_gmm0[:, 0], samples_gmm0[:, 1], marker=\".\", alpha=0.25)\n", "axes[0].set_title(\"Samples from generating GMM 0\")\n", "axes[1].scatter(samples_gmm1[:, 0], samples_gmm1[:, 1], marker=\".\", alpha=0.25)\n", "axes[1].set_title(\"Samples from generating GMM 1\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "Peg4TOVUiMe5" }, "source": [ "## Fit a pair of coupled GMMs" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "msmkcryDhrvC" }, "outputs": [], "source": [ "# As a starting point for our optimization, we pool the two sets of samples\n", "# and fit a single GMM to the combined samples\n", "samples = jnp.concatenate([samples_gmm0, samples_gmm1])\n", "key, subkey = jax.random.split(key)\n", "gmm_init = fit_gmm.initialize(\n", " key=subkey, points=samples, point_weights=None, n_components=3, verbose=True\n", ")\n", "pooled_gmm = fit_gmm.fit_model_em(\n", " gmm=gmm_init, points=samples, point_weights=None, steps=20\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "executionInfo": { "elapsed": 126893, "status": "ok", "timestamp": 1643139254464, "user": { "displayName": "", "photoUrl": "", "userId": "" }, "user_tz": 480 }, "id": "Nq6_t9bsuj0U", "outputId": "f2652b55-cc5f-4df6-bad6-b72f8d66b4c9" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0 -3.862 -3.877 transport:0.011 objective:-7.739\n", " 1 -3.835 -3.848 transport:0.041 objective:-7.683\n", " 2 -3.814 -3.822 transport:0.129 objective:-7.637\n", " 3 -3.794 -3.802 transport:0.262 objective:-7.598\n", " 4 -3.775 -3.781 transport:0.448 objective:-7.561\n", " 5 -3.761 -3.763 transport:0.676 objective:-7.531\n", " 6 -3.748 -3.746 transport:0.954 objective:-7.504\n", " 7 -3.737 -3.731 transport:1.259 objective:-7.481\n", " 8 -3.725 -3.717 transport:1.628 objective:-7.458\n", " 9 -3.716 -3.704 transport:2.050 objective:-7.440\n", " 10 -3.704 -3.694 transport:2.502 objective:-7.423\n", " 11 -3.694 -3.683 transport:2.773 objective:-7.405\n", " 12 -3.686 -3.675 transport:3.313 objective:-7.395\n", " 13 -3.678 -3.667 transport:3.388 objective:-7.378\n", " 14 -3.671 -3.661 transport:3.730 objective:-7.369\n", " 15 -3.664 -3.654 transport:3.836 objective:-7.357\n", " 16 -3.659 -3.652 transport:3.993 objective:-7.351\n", " 17 -3.652 -3.646 transport:4.349 objective:-7.341\n", " 18 -3.648 -3.644 transport:4.494 objective:-7.337\n", " 19 -3.643 -3.640 transport:4.606 objective:-7.329\n", " 20 -3.638 -3.638 transport:5.005 objective:-7.326\n", " 21 -3.635 -3.635 transport:5.146 objective:-7.321\n", " 22 -3.629 -3.633 transport:5.559 objective:-7.318\n", " 23 -3.626 -3.630 transport:5.715 objective:-7.314\n", " 24 -3.622 -3.628 transport:6.157 objective:-7.311\n", " 25 -3.621 -3.625 transport:6.335 objective:-7.309\n", " 26 -3.617 -3.624 transport:6.571 objective:-7.307\n", " 27 -3.616 -3.620 transport:6.952 objective:-7.306\n", " 28 -3.613 -3.620 transport:6.986 objective:-7.302\n", " 29 -3.612 -3.617 transport:7.067 objective:-7.300\n", "CPU times: user 2min 4s, sys: 3.74 s, total: 2min 8s\n", "Wall time: 2min 6s\n" ] } ], "source": [ "# Now we use EM to fit a GMM to each set of samples while penalizing the\n", "# distance between the pair of GMMs\n", "%%time\n", "EPSILON = 1.0e-2 # regularization weight for the Sinkhorn algorithm\n", "WEIGHT_TRANSPORT = 0.01 # weight for the MW2 distance penalty between the GMMs\n", "pair_init = gaussian_mixture_pair.GaussianMixturePair(\n", " gmm0=pooled_gmm, gmm1=pooled_gmm, epsilon=EPSILON, tau=1.0\n", ")\n", "\n", "fit_model_em_fn = fit_gmm_pair.get_fit_model_em_fn(\n", " weight_transport=WEIGHT_TRANSPORT, jit=True\n", ")\n", "\n", "pair, loss = fit_model_em_fn(\n", " pair=pair_init,\n", " points0=samples_gmm0,\n", " points1=samples_gmm1,\n", " point_weights0=None,\n", " point_weights1=None,\n", " em_steps=30,\n", " m_steps=20,\n", " verbose=True,\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "height": 281 }, "executionInfo": { "elapsed": 2966, "status": "ok", "timestamp": 1643139257645, "user": { "displayName": "", "photoUrl": "", "userId": "" }, "user_tz": 480 }, "id": "oW4yprDmTRV6", "outputId": "226fe01e-57dd-4ab5-b77b-171a24165c53" }, "outputs": [ { "data": { "image/png": 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ixeRYBwboPNyL8jzqJ3se8MlPEos6ikgm89//Vr2sIFBlM9bX1QkheXksx0zF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\nPWZds64sO+0kI1vKvZ3tQL/GV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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colors = [\"red\", \"green\", \"blue\"]\n", "fig, axes = plt.subplots(1, 2, figsize=(8, 4), sharex=True, sharey=True)\n", "for i, (gmm, samples) in enumerate(\n", " [(pair.gmm0, samples_gmm0), (pair.gmm1, samples_gmm1)]\n", "):\n", " assignment_prob = gmm.get_log_component_posterior(samples)\n", " assignment = jnp.argmax(assignment_prob, axis=-1)\n", " for j, component in enumerate(gmm.components()):\n", " subset = assignment == j\n", " axes[i].scatter(\n", " samples[subset, 0],\n", " samples[subset, 1],\n", " marker=\".\",\n", " alpha=0.01,\n", " color=colors[j],\n", " label=j,\n", " )\n", " ellipse = get_cov_ellipse(\n", " component.loc,\n", " component.covariance(),\n", " n_sds=2,\n", " ec=colors[j],\n", " fill=False,\n", " lw=2,\n", " )\n", " axes[i].add_artist(ellipse)\n", " legend = axes[i].legend()\n", " for lh in legend.legendHandles:\n", " lh.set_alpha(1)\n", " axes[i].set_title(f\"Fitted GMM {i} and samples\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "executionInfo": { "elapsed": 3530, "status": "ok", "timestamp": 1643139261545, "user": { "displayName": "", "photoUrl": "", "userId": "" }, "user_tz": 480 }, "id": "1VR4eAHQaQ1d", "outputId": "076d1564-8719-4df6-c6ba-fc906ce40403" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitted GMM 0 masses [0.54755753 0.2253582 0.22708425]\n", "Fitted GMM 1 masses [0.26321912 0.374353 0.36242783]\n", "Mass transfer, rows=source, columns=destination\n", "[[0.32590222 0. 0.22165503]\n", " [0. 0.22536384 0. ]\n", " [0. 0. 0.22707897]]\n" ] } ], "source": [ "print(\"Fitted GMM 0 masses\", pair.gmm0.component_weights)\n", "print(\"Fitted GMM 1 masses\", pair.gmm1.component_weights)\n", "print(\"Mass transfer, rows=source, columns=destination\")\n", "cost_matrix = pair.get_cost_matrix()\n", "sinkhorn_output = pair.get_sinkhorn(cost_matrix=cost_matrix)\n", "print(pair.get_normalized_sinkhorn_coupling(sinkhorn_output=sinkhorn_output))" ] }, { "cell_type": "markdown", "metadata": { "id": "J1WkqSYVgNg9" }, "source": [ "## Reweighting components\n", "\n", "In the approach above, we can only change the weights of components by transferring mass between them. In some settings, allowing reweightings of components can lead to couplings that are easier to interpret. For example, in a biological application in which points correspond to a population of featurized representations of organisms, mixture components might capture subpopulations and a component reweighting might correspond to a prevalence change for the subpopulation.\n", "\n", "We can generalize the approach above to allow component reweightings by using an *unbalanced* variant of MW2 as our measure of distance between GMMs.\n", "\n", "Recall that \n", "\n", "$$MW_2^2(\\mu_0, \\mu_1) = \\min_{w \\in \\Pi(\\pi_0, \\pi_1)} \\sum_{k,l} w_{kl} W_2^2(\\mu_0^k, \\mu_1^l)$$\n", "\n", "We use the {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` algorithm to obtain a solution to a regularized version of the above minimization:\n", "\n", "$$MW_2^2(\\mu_0, \\mu_1) \\approx \\min_{w \\in \\Pi(\\pi_0, \\pi_1)} \\sum_{k,l} w_{kl} W_2^2(\\mu_0^k, \\mu_1^l) + \\epsilon KL(w, a^T b)$$" ] }, { "cell_type": "markdown", "metadata": { "id": "Hd5ysiRIqXOG" }, "source": [ "## An unbalanced Wasserstein divergence for GMMs\n", "\n", "We define $UW_2^2$, an unbalanced version of $MW_2^2$, as follows:\n", "\n", "$$UW_2^2(\\mu_0, \\mu_1) = \\min_{w_{k,l} \\geq 0} \\sum_{k,l} w_{kl} W_2^2(\\mu_0^k, \\mu_1^l) + \\rho KL(w_{k \\cdot}||\\pi_0^k) + \\rho KL(w_{\\cdot l}||\\pi_1^l)$$\n", "\n", "where $KL(f||g)$ is the *generalized* KL divergence, \n", "\n", "$$KL(f||g) = \\sum_i f_i \\log \\frac{f_i}{g_i} - f_i + g_i$$\n", "\n", "which does not assume that either $\\sum f_i = 1$ or $\\sum g_i = 1$.\n", "\n", "As above, we add a regularization term to make the problem convex and solve with the unbalanced {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` algorithm." ] }, { "cell_type": "markdown", "metadata": { "id": "kZQ2SAKdxjer" }, "source": [ "## Interpreting the results\n", "\n", "The coupling matrix $W$ we obtain from the unbalanced {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` algorithm has marginals that do not necessarily match the component weights of our GMMs, and it's worth looking in detail at an example to see how we might interpret this mismatch.\n", "\n", "### Marginal mismatch\n", "\n", "Suppose we have a pair of 2-component GMMs:\n", "\n", "* $\\mu_0$ with component weights 0.2 and 0.8, and\n", "* $\\mu_1$ with component weights 0.4 and 0.6.\n", "\n", "Suppose the unbalanced Sinkhorn algorithm yields the coupling matrix\n", "\n", "$$W = \\begin{pmatrix}0.3 & 0.1\\\\0.2 & 0.4 \\end{pmatrix}$$\n", "\n", "The first row of the coupling matrix $W$ indicates that 0.4 units of mass flow out of the first component of $\\mu_0$, 0.3 units to the first component of $\\mu_1$ and 0.1 to the second component of $\\mu_1$. However, the first component of $\\mu_0$ only has 0.2 units of mass!\n", "\n", "Similarly, the first column of $W$ indicates that 0.5 units of mass flow into the first component of $\\mu_1$, 0.3 from the first component of $\\mu_0$ and 0.2 from the second component of $\\mu_0$. Again, while 0.5 units of mass flow in, the first component of $\\mu_1$ only has 0.4 units of mass.\n", "\n", "### Reweighting points\n", "\n", "Our interpretation is this: points from $\\mu_0$ undergo two reweightings during transport, the first as they leave a component in $\\mu_0$ and the second as they enter a component in $\\mu_1$. Each of these reweightings has a cost that is reflected in the KL divergence between the marginals of the coupling matrix and the weights of the corresponding {class}`~ott.tools.gaussian_mixture.gaussian_mixture.GaussianMixture` components.\n", "\n", "Suppose we transport a point with weight 1 from the first component of $\\mu_0$ to the first component of $\\mu_1$.\n", "\n", "* We see from the coupling matrix that the first component of $\\mu_0$ has mass 0.2 but has an outflow of 0.4. To achieve the indicated outflow, we double the weight of our point as it leaves the first component of $\\mu_0$, so now our point has a weight of 2.\n", "* We see that the first component of $\\mu_1$ has a mass of 0.4 but an inflow of 0.5. To achieve the indicated inflow, we need to decrease the weight of incoming points by a factor of 0.8.\n", "\n", "The net effect is that the weight of our point increases by a factor of $2 \\times 0.8 = 1.6$" ] }, { "cell_type": "markdown", "metadata": { "id": "HoZgA_qZ4glY" }, "source": [ "### Unnormalized couplings\n", "\n", "One point that is worth emphasizing: in the unbalanced case, the coupling matrix we obtain from the Sinkhorn algorithm need not have a total mass of 1! \n", "\n", "Let's look at the objective function in more detail to see why this might happen.\n", "\n", "Recall that $UW_2^2$ penalizes mismatches between the marginals of the coupling matrix and the GMM component weights via the generalized KL divergence,\n", "\n", "$$KL(f||g) = \\sum_i f_i \\log \\frac{f_i}{g_i} - f_i + g_i$$\n", "\n", "In the divergence above, $f$ is a marginal of the coupling, which may not sum to 1, and $g$ is the set of weights for a GMM and does sum to 1. Let $p_i = \\frac{f_i}{\\sum_i f_i} = \\frac{f_i}{F}$ be the normalized marginal of the coupling. We have\n", "\n", "$$KL(f||g) = \\sum_i F p_i \\log \\frac{F p_i}{g_i} - F p_i + g_i \\\\\n", "= F \\sum_i \\left(p_i \\log \\frac{p_i}{g_i} + p_i \\log F \\right) - F + 1 \\\\\n", "= F \\sum_i p_i \\log \\frac{p_i}{g_i} + F \\log F - F + 1 \\\\\n", "= F KL(p||g) + (F \\log F - F + 1)$$\n", "\n", "Thus, having an unnormalized coupling scales each KL divergence penalty by the total mass of the coupling, $F$, and adds a penalty of the form $F \\log F - F + 1$.\n", "\n", "In addition, the transport cost for the unnormalized coupling is simply the transport cost for the normalized coupling scaled by the same factor $F$.\n", "\n", "The result is that the cost for an *unnormalized* coupling $W$ that sums to $F$ is $F$ times the cost for the *normalized* coupling $W/F$ plus $(\\epsilon + 2\\rho)(F \\log F - F + 1)$.\n", "\n", "For $F \\geq 0$, the function $F \\log F - F + 1$ is strictly convex, has a minimum of 0 at 1 and is 1 at 0 and $e$." ] }, { "cell_type": "code", "execution_count": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# @title x log x - x + 1 { display-mode: \"form\" }\n", "x = np.arange(0, 4, 0.1)\n", "y = x * jnp.log(x) - x + 1\n", "y = y.at[0].set(1.0)\n", "plt.plot(x, y)\n", "plt.title(\"y = x log x - x + 1\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "PY9XNDodC2C6" }, "source": [ "We should never get an $F$ larger than 1, since such an $F$ will both increase the cost of the normalized coupling as well as introduce a positive penalty term. If we use the balanced Sinkhorn algorithm, we will always have $F = 1$. \n", "\n", "The case of $F \\in (0, 1)$ can be interpreted to mean that all points are down-weighted for transport to reduce the overall cost. We can shift the transport and reweighting costs into the normalization penalty, $(\\epsilon + 2 \\rho)(F \\log F - F + 1)$. \n", "\n", "The net effect of this flexibility in allocating costs to the normalization penalty term is to bound the total regularized cost to be less than or equal to $(\\epsilon + 2 \\rho)(F \\log F - F + 1) <= (\\epsilon + 2 \\rho)$, something to consider in setting the various weights used in the overall optimization." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "executionInfo": { "elapsed": 134199, "status": "ok", "timestamp": 1643139396720, "user": { "displayName": "", "photoUrl": "", "userId": "" }, "user_tz": 480 }, "id": "ijP5fyNoKRMX", "outputId": "b185ba51-8214-4d25-916d-ada70a1846ec" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0 -3.862 -3.877 transport:0.011 objective:-7.740\n", " 1 -3.835 -3.848 transport:0.019 objective:-7.685\n", " 2 -3.814 -3.822 transport:0.042 objective:-7.640\n", " 3 -3.794 -3.801 transport:0.061 objective:-7.601\n", " 4 -3.776 -3.781 transport:0.093 objective:-7.566\n", " 5 -3.761 -3.763 transport:0.117 objective:-7.536\n", " 6 -3.749 -3.747 transport:0.152 objective:-7.511\n", " 7 -3.736 -3.731 transport:0.182 objective:-7.485\n", " 8 -3.725 -3.717 transport:0.220 objective:-7.463\n", " 9 -3.715 -3.704 transport:0.265 objective:-7.445\n", " 10 -3.704 -3.694 transport:0.296 objective:-7.427\n", " 11 -3.695 -3.682 transport:0.346 objective:-7.412\n", " 12 -3.687 -3.675 transport:0.372 objective:-7.398\n", " 13 -3.677 -3.667 transport:0.427 objective:-7.386\n", " 14 -3.671 -3.661 transport:0.454 objective:-7.378\n", " 15 -3.662 -3.655 transport:0.500 objective:-7.368\n", " 16 -3.657 -3.652 transport:0.522 objective:-7.361\n", " 17 -3.651 -3.647 transport:0.563 objective:-7.354\n", " 18 -3.646 -3.645 transport:0.566 objective:-7.348\n", " 19 -3.640 -3.642 transport:0.603 objective:-7.342\n", " 20 -3.637 -3.639 transport:0.608 objective:-7.336\n", " 21 -3.632 -3.636 transport:0.643 objective:-7.332\n", " 22 -3.629 -3.634 transport:0.639 objective:-7.327\n", " 23 -3.624 -3.632 transport:0.674 objective:-7.323\n", " 24 -3.623 -3.629 transport:0.684 objective:-7.320\n", " 25 -3.618 -3.627 transport:0.711 objective:-7.316\n", " 26 -3.617 -3.624 transport:0.731 objective:-7.314\n", " 27 -3.614 -3.625 transport:0.734 objective:-7.312\n", " 28 -3.613 -3.622 transport:0.745 objective:-7.309\n", " 29 -3.611 -3.622 transport:0.748 objective:-7.308\n", "CPU times: user 2min 11s, sys: 4.29 s, total: 2min 15s\n", "Wall time: 2min 14s\n" ] } ], "source": [ "%%time\n", "# here we use a larger transport weight because the transport cost is smaller\n", "# (see discussion above)\n", "WEIGHT_TRANSPORT = 0.1\n", "RHO = 1.0\n", "TAU = RHO / (RHO + EPSILON)\n", "\n", "# Again for our initial model, we will use a GMM fit on the pooled points\n", "pair_init2 = gaussian_mixture_pair.GaussianMixturePair(\n", " gmm0=pooled_gmm, gmm1=pooled_gmm, epsilon=EPSILON, tau=TAU\n", ")\n", "\n", "fit_model_em_fn2 = fit_gmm_pair.get_fit_model_em_fn(\n", " weight_transport=WEIGHT_TRANSPORT, jit=True\n", ")\n", "\n", "pair2, loss = fit_model_em_fn2(\n", " pair=pair_init2,\n", " points0=samples_gmm0,\n", " points1=samples_gmm1,\n", " point_weights0=None,\n", " point_weights1=None,\n", " em_steps=30,\n", " m_steps=20,\n", " verbose=True,\n", ")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "executionInfo": { "elapsed": 3048, "status": "ok", "timestamp": 1643139399942, "user": { "displayName": "", "photoUrl": "", "userId": "" }, "user_tz": 480 }, "id": "ehNGVodMREjW", "outputId": "3f0b10a1-bbf2-4101-d15d-229fcbf95bd6" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitted GMM 0 masses [0.56643116 0.19865721 0.23491158]\n", "Fitted GMM 1 masses [0.255262 0.39326635 0.35147163]\n", "Normalized coupling\n", "[[0.4567368 0. 0. ]\n", " [0. 0.25642195 0. ]\n", " [0. 0. 0.2868412 ]]\n" ] } ], "source": [ "print(\"Fitted GMM 0 masses\", pair2.gmm0.component_weights)\n", "print(\"Fitted GMM 1 masses\", pair2.gmm1.component_weights)\n", "cost_matrix = pair2.get_cost_matrix()\n", "sinkhorn_output = pair2.get_sinkhorn(cost_matrix=cost_matrix)\n", "print(\"Normalized coupling\")\n", "print(pair2.get_normalized_sinkhorn_coupling(sinkhorn_output=sinkhorn_output))" ] }, { "cell_type": "markdown", "metadata": { "id": "BTL8luL4wphM" }, "source": [ "Notice above that neither marginal of the fitted coupling matches the corresponding GMM masses. One way to interpret the coupling is as follows:\n", "\n", "Mass is re-weighted at two points: first, as it leaves one component, and second, as it enters another.\n", "\n", "So we see that the heaviest component above has its mass downweighted by a factor of ~2, and the two lighter components both have their masses roughly doubling." ] } ], "metadata": { "colab": { "collapsed_sections": [], "last_runtime": { "build_target": "//research/biology/diagnose_a_well:notebook_py3", "kind": "shared" }, "name": "GMM pair demo", "provenance": [ { "file_id": "/piper/depot/google3/experimental/users/geoffd/contour/clustering/ot/normal_demo.ipynb?workspaceId=geoffd:clustering::citc", "timestamp": 1624308540124 }, { "file_id": "1oH9ypL40aZ5J0sCRxw7OCnigqvhwbtlY", "timestamp": 1616035411138 }, { "file_id": "1lVlIwla1ox6KGQ3oZfs880a2v0ABOwar", "timestamp": 1616034396680 }, { "file_id": "15f03x6Cc1Y_GTVM-FicXBcxhQFgDxMra", "timestamp": 1615496973043 } ] }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 1 }