{ "cells": [ { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "151ace28-1df8-4b52-baf0-4f792e91d5ff" }, "slideshow": { "slide_type": "slide" } }, "source": [ "$\\newcommand{\\Reals}{\\mathbb{R}}\n", "\\newcommand{\\Nats}{\\mathbb{N}}\n", "\\newcommand{\\PDK}{\\mathbf{k}}\n", "\\newcommand{\\IS}{\\mathcal{X}} \n", "\\newcommand{\\FM}{\\Phi} \n", "\\newcommand{\\Gram}{K} \n", "\\newcommand{\\RKHS}{\\mathcal{H}}\n", "\\newcommand{\\prodDot}[2]{\\left\\langle#1,#2\\right\\rangle}\n", "\\DeclareMathOperator*{\\argmin}{arg\\,min}\n", "\\DeclareMathOperator*{\\argmax}{arg\\,max}$\n", "# Reproducing Kernel Hilbert Spaces in Machine Learning" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "nbpresent": { "id": "aa569eb6-ea77-4a63-89bf-c6e50dea77f7" }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/ischuster/Documents/university/Promotion_NLP/software/python/distributions/distributions/linalg.py:35: UserWarning: warning: caught this exception:module 'numpy.core' has no attribute '_dotblas'\n", " warnings.warn(\"warning: caught this exception:\" + str(e))\n" ] } ], "source": [ "from __future__ import division, print_function, absolute_import\n", "from IPython.display import SVG, display, Image\n", "\n", "import numpy as np, scipy as sp, pylab as pl, matplotlib.pyplot as plt, scipy.stats as stats, sklearn, sklearn.datasets\n", "from scipy.spatial.distance import squareform, pdist, cdist\n", "\n", "import distributions as dist #commit 480cf98 of https://github.com/ingmarschuster/distributions" ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "facddd6a-d4b1-4885-bade-ce2aae8a72be" }, "slideshow": { "slide_type": "slide" } }, "source": [ "# Motivation: Feature engineering in Machine Learning\n", "In ML, one classic way to handle nonlinear relations in data (non-numerical data) with linear methods is to map the data to so called features using a nonlinear function $\\FM$ (a function mapping from the data to a vector space)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "nbpresent": { "id": "65cfcee8-427f-45f2-8825-5251c9ee0763" }, "scrolled": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/jpeg": 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\n", "text/plain": [ "" ] }, "metadata": { "image/jpeg": { "width": 200 } }, "output_type": "display_data" } ], "source": [ "display(Image(filename=\"monomials.jpg\", width=200))" ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "39211b06-42c0-4c68-bbc0-eb5c00376df0" }, "slideshow": { "slide_type": "fragment" } }, "source": [ "In the Feature Space (the domain of $\\FM$), we can then use linear algebra, such as angles, norms and inner products, inducing nonlinear operations on the Input Space (codomain of $\\FM$). The central thing we need, apart from the feature space being a vector space are inner products, as they induce norms and a possibility to measure angles." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Simple classification algorithm using only inner products\n", "Say we are given data points from the mixture of two distributions with densities $p_0,p_1$:\n", "$$x_i \\sim w_0 p_0 + w_1 p_1$$ and labels $l_i = 0$ if $x_i$ was actually generated by $p_0$, $l_i = 1$ otherwise. A very simple classification algorithm would be to compute the mean in feature space $\\mu_c = \\frac{1}{N_c} \\sum_{l_i = c} \\FM(x_i)$ for $c \\in \\{0,1\\}$ and assign a test point to the class which is the most similar in terms of inner product. In other words, the decision function \n", "$ f_d:\\IS\\to\\{0,1\\}$ is defined by\n", "$$f_d(x) = \\argmax_{c\\in\\{0,1\\}} \\prodDot{\\FM(x)}{\\mu_c}$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "nbpresent": { "id": "9cf40433-1214-467e-a61d-1e15c8ca2f2a" }, "scrolled": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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zoy7XT9b6y4jFLjhTOD5u925uCGL1nRf2hPGyPyC5M0EL+t80jtrB3S737OXn1j/4gOdVNFZu7wq0HhqF5nfGxnJnk5TpTcYdwtKlnCN/5IhZ/GTdJmjmStb6y4jFXsm4CfYV+sqrq1nczzjD3MaLMLutZE0CBQHgRSvGYGOuB0bVnADAFL3qamBiwPMqEpYeLwMjJ6K6u6WAMMI7myA+/zBSB43/okbRk25rOmv9ZUTYKxW3wb7CQqIJE/ixupqbgbkRsMILyLRp7GtPemGSRaybd9Vh/eaewKFDqJ85ChhqKdw5403g3eXc/2bzZv5O6+s9nVeRsNTUoHF/e/QTpSz4DSbqTh1sazNF3SDN1nQUiLBXKm4KiAwKfeVWoS4nzHYXkKefTm4WjBXLRa36je2Y1aCAj38crXuHAuyNwdi+29H4yv18fqedZl7ogqZwJuDOxu/0Jp0ZPs3NnHw1a1bxRSKNhUNRIcJeqQQJ9nmpGPVyAQmJQK6BrnO1btba1Ztl1ChgzpEngG4hnF/AlgtB3SFegol2xwL45mXYMPvPuCWKPPksIsKeFZYt47E1b74JDB3K42tmzCi9fVTDo8OsQHVZEKTTNVBkxa6sQuNkmwEjOs6vxAXUjWgHPWcvgmp3LMNNZV2fH3HPmu87KkTYoyaMqstly4Bbb2XLuLaW29/eeiu/V0rco7rVL3cB8ft9eCgI0uUasLVinxsLrNmKxgkH7c8vBNyIdtBz9iKohccyCpoK3SdO+/BC1vq6hIGkO0aJm4HPfli0iAWuf39OjTN+XrSo9GdKFRDpdo8YI/b27OFg6549pg86yPfhsSCoqPjHh8DYpsTNHIXqg7vtzy8k7Mbo2Ym203Mvo/Tcrsmge3dT1AH+3pTKt/aDHCspqZhJRiz2KAnL3/zmm2ypW+nbl18vhVtLOegdRl0dZ8EUuonq6ria0u/34dHF4zcQaMXWiv3cUOCMCyJvP+wmY8XpnJ2sfieL2Phs4XttbeZzw69u0NHB3SYN4Q2aJZOk9gtJRYQ9SsLyNw8dypZi//7ma3v2FB/LwK0bI2D/kw/38fTT3CPmrLPMrJjhw4N9Hx5iBKFXFcbQfrjcharcOTuJY+G2hUJcyp9eyvViWOzWYxVa8F7JUl+XMBBhjxJDjDo62MTZvZv/dxeW0nllzhzTp963r+kO+NrX7Ld3e+eg4w7DaR9BArhGjGDXLmDrVmDnTvYB3Hhj0aZZy6xwc6Fyc86lxNGNRWx9b+xYnnta6liGxW5MdDIeg7hOdNyBZRkRdh24dVdMn86dEdevZ7EzqjhzOd6HX6vPCJAa7o4hQ1jUSwVO3VrKOu4wnPbxxS/6D+AaLp677+ZE50GD+Ls37gYs36VjIDBhLYTdBAbdiLab4KeTODpZxIXvzZnjfKzGRh60ncuZ/3Xs+sW7JWt9XcJAhD0oXtwVdXXc7nbnTv7r7duXS/Orq4P72WfMcE5vtGJnKW/cyJbvLbeYAqcjJdJpH25ztUuJ74YNLO7Wfe/Z4/671OFq0oybjBcdKYDlxNFJ9L1ay83N9oO2/VrZWbsDCwMR9qB4dVd0dgLnn8+ZHAZHj4bfA8Qqjt27A2+9xX9lffrwX9rzz/MsNavATZvGFjDgPyWyXFplOf+0k/gGvaNIQPFUIVEFBkuJ44EDwAsvAK+/bi/6xtq8WMuGj91oCTBqVDAfu+S2l0fSHYNS0AEQgHO3wzi6GxamFfbqxX9Zhw7x+rduZVGvq8tPHdywwX1K5G9+A7z2WvHrQdMqndIag36Xbn937dH2RdeRmlmOiRPN/SrFAn3XXcAFFwBPPmkKt7UfenV1ceqimy6Iho/9w86V9flZMoJ+xGIPild3RRw9QOws09GjWWTnzmXBKmX5usn4OHoUuPJK/ksdP54DmJdeav61B8kaCctHD7j73bW3Az/8IQdpOzr44vXKK8C//3toVn1UgcGODuDRR4HvfY+/zoMHgZ49gU98ojgt0ujNYrhVrKJcbm1uXSdSeKQPsdiD4lSAY0dUhUFW1qxhMVq6FHjuOWDHjnzL1Gr57tjB2zz2GFvsbqzTqiq2+Ds7+ThXXw0MHAj8278FdzE5WeVBv0s3v7vFi4E33mA169ePH994g18PgaK+7BonBFk5fJjDPddcw6dz4ABb4p2dwJlnmtu5LYZywnp3YN1voVhL4ZE+xGIPip9mTWHkPZcKMLa389j6bt1YmA4dAlasYMt65Ej+rDV1cM0a3vbYY9lSdhtM/NSneBLCwYPAe+/xa//xH7yfu+7yf15BffROuPndrVzJ31uvXvzccGOtXOn/nBwotG5LVW0GtWKrqoBzzgH++Mf81ydMKLako8oZl8IjfQQWdiIaCuBhAIMBHAWwUCn146D7TRUxFKjk4RRgXL4cOPVUzjd7/32+137/fRbwpiZz/VddBdx2G5tsAwZwYvKgQe6zTM47jxXIoLoaGDfOzK/3S8Auh672X25fRMXPC1/ThJ0VS8QjZg3L1bCa3Qq8nYtj5UqeH7pmDd+YAcAxxwAzZxZ/PsqccSk80oMOi70TwA1KqZeJqDeAFiJappR6XcO+BTc4ZXfkcmb2S1sbC3XfvmyFFg7UGDWKq0OtGTtus0xGjOBtDx3irJuODuD++4Hjjgt+fnFeOCdPBp55htW1Rw++KL77Lpu7IVAowkYO+HPPAX/+M9+MzZrF77ktyy+VQtmnjynqvXrxr33atPzPRp0zLoVHeggs7EqptwC81fXzfiJaB6AGgAi7F4IUyjgFGA0f9aBB/A9gce/du3g/fvLWreseMYJz9EeM4NcbG7kAy7q/tHHZZRyL2LnTrBQeO5ZfDwE7ESYCBg/m13I5724KOxfH6NGmiB8+zDdBTz9dbP1HmTMuhUf60OpjJ6LhAE4HEI4DMqsELZRxEmQvWTheM3ba27nyc+dOtmS7d+eg6X/9F9DQwM/79eMJxFUhxuntLoqAnorSujrO8lm+nAXe+E5DuoOwE2FrDnguZ5bkexE7q4tDKVPUP/iAf01PPMGnuGZNvrhHmTMuhUf60PbXRkTHA/hvAF9VSu2zeb+JiFYR0apdu3bpOmw28NiCtgin7A4vmSNes0yWLOH2CEar4JNOAj76UY7IdesGvPMOb3fssf6+FzcU5uhv2gT88z8Dn/0s8NRT7Dj22B65qKVtXR2aT5uLlk/dwemhEXRuNDCqNOvr+V9NjSnuTpkyhefQ3Myf2bwZuPNOfu373wdeeol//tvfgC1b4s1AcZs9I5RHi8VORMeARX2xUupxu22UUgsBLASAhoYGZbdNxeK2grKUu6ZcgNGLj9rLti++yILesyc/79mTnxsZI/37c/rj6adzVO63vy2/T68uKetFcccOdkjv3s1maFUV8Ne/AlOmmBdKF+emexizV6yC3L27GZNubTX9621tzm4K6zkAZgfG7du5Hu266/hmKmkZKJLLrgcdWTEE4EEA65RS9wRfUgXitlDGyV0TV4BRqeLn1tcmTAAeeQS4/HLgnns4t70UflxS1otiWxsHa4nY/WNccNraOM/eZU59nGl3pfzMbW3Fbgprj3Snc9i8mX8eMgT4wQ+Ab3wD+OQn+bPWYRc6zi+oMPu5qMrFoBgdrpgpAL4A4FwierXr3yc07LdycFMoE9RdEwaTJrF1fPAgi/nBg/x80qT87WbPZhfGDTdwhkkp/JyjtYBp927OXOnenV0wAD/fs8dz24YoyvrtsJ3SVA+cdpp3N4Wx/bBhwIknAtdfD4wZwy6YxsZit4uOIii/RUaG68haEHXTTfntDXQfM8voyIp5AUA4Sb2Vgptc7TCHQvtl9mwOKO7aZWaMjBnDrxfy05+yz/vcc9mZO3Ro8TZ+ztEa8O3bl9dhZPwc7JpDeuyxxUHgMi6fuNLudAYrjXM4coRFEjAnHYWVgeL3bqfQUl+61PzVlPusFDYVI5WnSaGcK0VHC13d1NVxzxS3GSPt7WyJ19ZyvnuPHvnv+zlH60WxXz8O2E6eDBx/PPDqq5yxc955nJ5orKuMyyfJaXdu3Q7Wc5gyhV/78Y855FBdXezaAfhGR0cGip8iI6s4W0V91Ch3F1UpbMpHhD0txNE8DCgfzCx1QSr1uUOH2Pfdsye7nawVnH7P0boG47jbtrGg211oyrTrTVranVXMDct27VrOKLU26bJinIPRzeG119gjVV3Nn+nsNLe1XgR0+KT93u0UWurz5rm/qEphUz4i7Gkh7NJ6O/zm15f73ObN7PgdO5Y7UOk8RzdB5DIun6T1+y50U6xdy+3zN21ii9bO7TBxIrBgAfC733FZwbhxxft167rwEpwMcrfT3Mx3DXaWutNFNcl3WHEhwp5k7KzeuXOjO77fQRTlPldby2WO06YB114L3Hef+Vk7YdY9vi6Jbi0HCn3I1mlE1vetvPwy8KUvAV/4Aick2e3TrevCS6aK37sdY58XXeRdnJN2h5UEpG1vUiksvPFYZKMFr0NEvHzu3HO5avX++7nQqRRhfA9lspCKCpTAz62pgWFid3zATFvcuJEt240bzbVZ17h3L1vSxxwDPPyw/THszq/U8RsbOenpySfLt+71W2RUKhvIjThLYVMxYrFHRZDCGyCesW1Wy3bHDo64vfUW95xxGr7t1iI20h9nzwY+9jHO6SskjO+hjMsn7gIlu+MbBUYbN5pLHj2aBdfwuRPx12h8Re+/b79/J9dFdTWwapUZ+mhsZJfOli35fnndLo6kub/Sjgh7FAQtvDGIOr3Rb592L0HQ3/+eVWTCBM5o6d8///2wvgcHX3yQ9DkdxTKFxzcs81mz8oVXKX40LPiLLuLBVQAnA5Vqz+PkujDaBBsXDCOYaVxIrOckwptcRNijwI/VmQQ/sN8+7V6DoEeO8EXjxBP5ON26me/F9D34TZ/TZe1bj2+ItrEGY0SdUTlq+NqXLOGWAStWcC+2UrixjltbeW6KwejREpxMEyLsURC08Cbs9EYnN5HfPu1eWhxUVXFhUb9++c1RgNjSPIOk7AHBi2Wsxx82zP441m1eeQX42c94PGtQsTXSDq3HV0qCk2lCgqdR4DS3sxRRzUZ1E5z0s36v9O3LjmIAOP988/UYZsQGnTsatB2Bm+MvWsTiW1/PyUU/+xn/+go9WX5YsMC8xv/jP3ISE1FxQLWSg5NJRyz2KNBReBMWbtxEUVnN9fXAr34FfO5zXJ1i1MFH3OAsaPpc0GIZL8fv6DB93zpmfzQ3c6B06lSeSW5cZArnrgrJhlRhd74IaGhoUKtWrYr8uLFirYgMeViDJ265hU09q5vl6FE22e64w3wtyvV/9atc/75sWX4jtBRQKuMkjN4lzc1mu4D77uPuyEGPIZ0Skw0RtSilGsptJxZ7VMQ98LoUboOTUa7/3ntZ1GfMAP7+d2D4cPvtdBcuaSDKYpkbbuDH736Xc9adRN2tYFt/FpFPL+Jjr3TctAwuRXs7MH8+W/3z5+stnjIijyNGcH8Zu2PHUMBVrngpqmKZu+7iOSdf/jInKxnrKIWf1rbSDje9iMWeFsKyTo3g5OLFZq/0yZPdrSfInNZyEHGFTY8eQK9exQ3DYirgirt4qaWFB1R985v8X8DokFxuopKfbB1ph5teRNjTQNgiCrCInnOOGRwtt/8ohLW6mue4DRnCOXdbtpjvlUshDelCGLfYbd8OXHMNf/W3326uxbiwOLl8/LbTlXa46UNcMWkg7OlJfvbvt4+MV2pquFLmzTc598/6eqkUzJDdNHFNVzpyBLj4Yv75e98zLy7GhaWcy8epP4zOzwjxI8KeBsIWUT/7jyK33WDqVM6SeeAB4KGH+DWn2EDIF8Koxc7w63fvur/eu5db9hpNwdxcWPzk5gfN5xfiQ4Q9DYQton72HyTo6ofrr+e8+SuvZKVzKlwK8UIYh9h1dPDpA8Dq1cAvf8mnaDTlcnNsP90Tg3RcFOJFfOxpIOwCIT/7j2Pwx+OPczC1oYEbk5VKwQyxv0wcvb/Xr+dr2Re/yDHuXK64gMi6Fjv8dE+UjovpRQqU0kLYBUJJLaAq5OhRs0nY4cOmf8KKNdhsvVCF3IrALV7yw9euBU49FfjMZ/hXsnkzW+rz5pX/bFKR/Hj/SIHOnVBAAAAQ6ElEQVRS1gi7QCipBVSFVFWxk/mEE7gqx84wieNuwgNuUyb372dRB7gYt7XVbAhmbVNQaEUnXTjjThmNkrh+F1qEnYgWAbgYwE6lVAZ/PUKi2LEDuPVWbnkwZgyP9ikU7QRfqNykTCplhgkeeIAbfs2alT94o60NmDOneP9JF864U0ajJK7fhS6L/RcA7gNQYhBXxkhSKXuS1hIFVjdLUxPPapszh9sd6jjvEL9Pq/Vm5IcbQzKsmZyA2WN9+3a+bnkhDcJZKfnxcf0utGTFKKX+AuBdHftKPEmYRZrEtUSFNZVx4kTgvPOAF17gdMigLFvGw7V//WvOJ9y0Sev3aS3Rb242x9x1duZnttxwA7fIefZZnmkyZw5b662t5szRWbPsrXWDuHLt3VJJ+fFx/C4k3dErYRcLpXUtUVGYynjppcDQoTwU25gh54f2dh6u3a0bcPLJrMJr13JVkKbv00gXXLoU+OlP+bUvf9kU7eZmnhR4zz3AnXfybBPrZwv3ZaWwh41x4TBy3ZMknJWWHx/HRSyy4CkRNQFoAoDa2tqoDqufJMwiTeJaosIulfHaa7l3++jRwHvvAccd532/y5eb4/+IgJ49+fVcjlMsNdHYyK6Vmhp2t1gF+p13gJkzgTPPBG6+Of9z5Xq8W325AF88tm83LybW99wG7sIK/MWRMhoXToPDw7TcIxN2pdRCAAsBTneM6rjaScIs0iSuJSpK5dwbfz3HH1/cMMwNuRxw0kncSbJXL36tRw9Wx6lTtS2/uTl/1J0h0A0NprCtXFn8mXLiYPXlWitSja+hvp6DrZ2d7gN3YQX+Kik/Pq6LmKQ7eiWmGZyJX0tQ3AYtnVIZjRz8wYM5c8YLNTWm+wVgi333bo5saqqmdRJoY2CGXYdit+JgBCSNC0dTU/4xAG+BuzQEYZNOXBcxLQVKRPRLAGcDGABgB4BvK6UeLLV96guUklTMk6S1+MWpoAjwlqVijBW64grgF7/wvoYjR7ij5M6dLOo33sgDPzRQyrVx/fX8Xnu7OebOD6VEfOFC87XC7Bs3BP28oA+3BUpSeZoFkpjy6GVN8+dzRo/VpbRnD5uvhw55ryCdP5+jkgsXAv/6r97XHOFF8p57OAvmN7/hOLBfrHcD1dXAqlXshlGKH420yosu8mYxBrH4Bf1I5WmlEEWvdq8XDq9rKhUEfvZZ4Oyzvfd8nzsXeP55Ni9PPRWYNMndeUZc1PTXv7Koz50bTNSBfHdNczOL+YYNXJxbW8uBWqW8Be7iCvx5JemVtnEg6Y5pJ+yURz+58l7XVKq7pLX80sBtl8YlS7jtwOTJ7FZJGG+/zUI0cKCZ+hgE60g+IxPm7bc5kErEz6++mr/STZvc7TMt3R1lhF8xYrGnnbBTHv1MSvK6plJB4EmTgmX97N7NF5ZBg4APPmDz1S0hureOHmVBB7zHeN3S2Mgpj7kcu2GMQCoRMHKku32kJXtFgrzFiMWeBpyGRofdqz2KIRyleqvPnh2s5zuRuY5jj3X3GcDxLqXcMGs3GGn2u3d7z8p0S3Mzu19qavgrvemmfLdK1kh6pW3UiLAnnXKuEGPgRXs7D6P+1a+Ap58Oll5hJaohHHV17Gy+4w5+NPzdpYZpuKV3b25oDrgb0g04upKC3vZfcQWPl21pyb8R0YnVNz5vninuGzdmV/D8VnfquFAnEXHFJJ1yrpC6OmDaNC6H7+xkt0NNDYv78OHB3QdxD+HQEdAcMwb47W+5rPPmm4Hvftd5ewdXUuNcfurntn/xYuDhh/mm64wzvJ+GWwoDqUZDse7diytWs0CQIG/SO2H6RYQ96bjxV2/YwOJemC5YLnvEDX5FOmltcz/5SVPUJ01ikS9FmYpeP50J160DLr+ch1F/6Us+z8Elhm+8sCdLUrNaghKkujOr/nkR9qTjpm1A2AHUpIm0X+68E/jzn7nr1vr1bMnbUeYupVzflkIOHADGjeOff/c798sNmsZXKT1ZggZ5s9hCWHzsSceNvzrsAGqWMFR57FiOV9jh4Nv32plQKW5fA/AkPy8E9edbUyANGhsrN7e7FFlsISwWe9Jx4wqJs2dMEqtey/HBB5wl06dP6YZhJe5SvFrBhqWey9mPZ3WipJtgYDswP2XfeUJJSxGWV6SlQFaIo2dMwodGO7JzJwea+/ThGaoh8K1vAd//Ps/vCNJHLK9Xyzkp/s4TSNqqVqWlQKURhx/cT/FSUjjpJO6PO2kS8PnPA48+qvXu409/YlG/9dZgol7kJliwFo0npfQ7TyBpKcLyigi74B83Qdsku2rOPBP4+c+Bf/kX4CMf4QRzDT13tm4FLrgAGD8e+M53/C/P1k3w/6oAqkNj310AgJbNA9DxwUA07n8573NJtTidSJv1nGQkeCr4p1zQNg0zWa+6CrjySuD2283sowA9dw4f5kl9ALB6dbCl2fZqGXcU1R3md97R2Q2tm3qh+dDpANLdJ0V6vuhDhF3wT7mMnbTMZP3P/+SpSfPn5/vb3TYcs2B0LjhwIHi7ANuslqvHY2KvdR9+540nrkd9z41oPWHKh4Ou05qHbR3jl/ZziRsRdqE8pXrVlCv599NnJi5++EN+/PrXuYIX8JwyeuGF/NjWZk7X047Nd9747RkcCO4izUIoPV/0ID52wZlly7hdweHDPHKuoyPf9+wUtE3TTNYZM4CvfQ340Y+Aa67hJiseUkbvuw/44x+BX/6SU+RDpeA791owlWSydC5xIha7UJr2dhb1bt2Ak082Z4IeOeLOneKnGVhcGE3Ibr+dn//kJ64Dpy+9BFx3HTBnDifYRInXgqkkk6VziRsRdqE0y5ezW6JfP3YY9+zJPWdzOXfuFB3dGaOkrg647TbgD3/g1BZrAnkJdu/m5JrjjzdrxKJE5zCMuDsdpmWwRxoQV4xQmlyO870PHTKdxj16ANu3A1OnuttHGvvMXHghW+7f/jbwD/8AfPrTtpspxbFgILQap7LozMOOu9NhVnPK40CEXShNTY3pfgHYYt+9m2vjk+hO0cltt3F/+0svBV5/HfjoR4s2OfFEfnznHU76STtZ7XRYiWTgv6MQGtOns399/Hi+H96+nf3rN97ozwp3mgSVRJ55hh/HjSsyyZua+Br34oum1Z4FJCslG2gRdiK6gIjWE9EGIvqGjn0KCcDwkY8cyROZ/umfOP1jxgzv+0pDsZIdRkvGvn05AAzg178GHngAuPde7kiQJbLY6bASCeyKIaJuAO4HMAPAVgAvEdFvlVKvB923kAB0+cjT2leme3dg1y6ePt2zJ9pbO/DZz/LNzFe+Evfi9OKn06G0AUgmOnzsZwLYoJTaBABE9CiAWQAqU9iT3BslTsIeBhImAwYALS34YOLkD2dzLFsW75LCwM9gjrgDroI9OlwxNQDetDzf2vVaHkTURESriGjVrl27NBw2gaTV3RAFaR8GcsYZ6HjkN/ji5Dcy27vEz2AOaQOQTHQIu11HjKIm70qphUqpBqVUw8CBAzUcNoGkpTdKHKSpWKkEvWfPxEN/HfNhPxiBkYBr8tDhitkKYKjl+RAA+puBpMHFkWZ3Q9j4HYotJB5pA5A8dAj7SwDqiGgEgByAzwO4TMN+TayTegL2yg6VNPVGiYM0FisJjmR1tFzaCeyKUUp1ArgWwJ8ArAPwmFLqtaD7zSMtLo4MuBsEwQvSBiCZaKk8VUr9AcAfdOzLlrS4OMTdIFQY0gYgmaSjpUCaXBzibhAEIWbS0VJAXByCIAiuSYewp639qyAIkRF3u+Ekkg5XDCAuDkEoQMr5Gal+LSY9wi4IQh4iaIy0Gy5GhF0QUooImkljo/kdGM8rmXT42AVBsEXK+RlpN5yPWOwCk4aWDUIRUs4v1a92iMUuSFfKlGIVtKYms8tipVmrUv1ajFjsQnqHYFQ4fvqnZxGpfi1GhF1IT8sGIQ8RNKEU4ooR0j8EQxCEPETYBWnZIAgZQ4RdkJYNgpAxxMcuMNKyQRAyg1jsgiAIGUOEXRAEIWOIsAuCIGQM8bEL0SFtCwQhEsRiF6JB2hYIQmSIsAvRYG1bUFXFj/378+uCIGglkLAT0WeI6DUiOkpEDboWJWSQXI7bFFjp0wfYti2e9fhExrAJaSCoxd4K4NMA/qJhLUKWyUjbAmNqkSHuRofFjo541yUIVgIFT5VS6wCAiPSsRsgu06ezTx1gS33fPm5bcMkl8a7LIzK1SEgD4mMXoiFDbQtkapGQdMpa7ES0HMBgm7duVkotdXsgImoC0AQAtbW1rhcoZIiMtC2QqUVC0ikr7EopLS3+lFILASwEgIaGBqVjn4IQNTKGTUgDUqAkCB6QqUVCGggk7ER0CYCfABgI4EkielUpdb6WlQlCApGpRUIaCJoV8wSAJzStRRAEQdCAZMUIgiBkDBF2QRC0IZW5yUCEXRAEbUhlbjKQrBhBELQhlbnJQCx2QRC0IpW58SPCLgiCVux87EK0iCtGEARtSGVuMhBhFwRBG1KZmwxE2AVB0IZU5iYD8bELgiBkDBF2QRCEjCHCLgiCkDFE2AVBEDKGCLsgCELGEGEXBEHIGCLsgiAIGUOEXRAEIWOQUtHPlSaiXQA2l9lsAIC3I1hOHGT53IBsn1+Wzw3I9vll4dyGKaUGltsoFmF3AxGtUko1xL2OMMjyuQHZPr8snxuQ7fPL8rkVIq4YQRCEjCHCLgiCkDGSLOwL415AiGT53IBsn1+Wzw3I9vll+dzySKyPXRAEQfBHki12QRAEwQeJF3Yiuo6I1hPRa0T0g7jXoxsiupGIFBENiHstOiGiHxJRGxGtIaIniKhv3GsKChFd0PV/cQMRfSPu9eiCiIYS0TNEtK7r7+wrca9JN0TUjYheIaLfx72WKEi0sBPROQBmAThVKfUxAHfHvCStENFQADMAbIl7LSGwDEC9UupUAG8A+GbM6wkEEXUDcD+ACwGMA/B/iGhcvKvSRieAG5RSHwUwGcA1GTo3g68AWBf3IqIi0cIOYC6Au5RSHQCglNoZ83p08yMAXweQuUCHUuoppVRn19MXAQyJcz0aOBPABqXUJqXUBwAeBRsdqUcp9ZZS6uWun/eDBbAm3lXpg4iGALgIwM/jXktUJF3YxwCYSkQrieg5Ivp43AvSBRHNBJBTSq2Oey0RMAfA/8S9iIDUAHjT8nwrMiR+BkQ0HMDpAFbGuxKt3As2oI7GvZCoiH3mKREtBzDY5q2bwevrB749/DiAx4hopEpJKk+Zc/sWgPOiXZFenM5PKbW0a5ubwbf6i6NcWwiQzWup+H/oFiI6HsB/A/iqUmpf3OvRARFdDGCnUqqFiM6Oez1REbuwK6Wml3qPiOYCeLxLyP9GREfB/R52RbW+IJQ6NyIaD2AEgNVEBLCb4mUiOlMptT3CJQbC6XcHAER0BYCLAUxLy8XYga0AhlqeDwGwLaa1aIeIjgGL+mKl1ONxr0cjUwDMJKJPAOgBoA8RPaKUujzmdYVKovPYiehLAE5RSt1GRGMAPA2gNgMikQcR/S+ABqVU2hsUfQgRXQDgHgBnKaVScSF2goi6g4PA0wDkALwE4DKl1GuxLkwDxNbFQwDeVUp9Ne71hEWXxX6jUuriuNcSNkn3sS8CMJKIWsHBqiuyJuoZ5j4AvQEsI6JXiehncS8oCF2B4GsB/AkcXHwsC6LexRQAXwBwbtfv6tUuC1dIKYm22AVBEATvJN1iFwRBEDwiwi4IgpAxRNgFQRAyhgi7IAhCxhBhFwRByBgi7IIgCBlDhF0QBCFjiLALgiBkjP8PoLtkq2kv54EAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = np.vstack([stats.multivariate_normal(np.array([-2,2]), np.eye(2)*1.5).rvs(100),\n", " stats.multivariate_normal(np.ones(2)*2, np.eye(2)*1.5).rvs(100)])\n", "distr_idx = np.r_[[0]*100, [1]*100]\n", "\n", "for (idx, c, marker) in [(0,'r', (0,3,0)), (1, \"b\", \"x\")]:\n", " pl.scatter(*data[distr_idx==idx,:].T, c=c, alpha=0.4, marker=marker)\n", " pl.arrow(0, 0, *data[distr_idx==idx,:].mean(0), head_width=0.2, head_length=0.2, fc=c, ec=c)\n", "pl.show()" ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "e0cfa942-49a8-4265-87a0-c004b554b3fa" }, "slideshow": { "slide_type": "fragment" } }, "source": [ "Remarkably, all positive definite functions are inner products in some feature space." ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "80bb4b95-6e30-469a-b2cf-ffd1b507805d" }, "slideshow": { "slide_type": "slide" } }, "source": [ "**Theorem** Let $\\IS$ be a nonempty set and let $\\PDK:\\IS\\times\\IS \\to \\Reals$, called a *kernel*. The following two conditions are equivalent:\n", "* $\\PDK$ is symmetric and *positive semi definite (psd)*, i.e. for all $x_1, \\dots, x_m \\in \\IS$ the matrix $\\Gram$ defined by with entries $\\Gram_{i,j} = \\PDK(x_i, x_j)$ is symmetric psd\n", "$\\FM$ is called the *Feature Map* and $\\RKHS_\\FM$ the *feature space*.\n", "* there exists a map $\\FM: \\IS \\to \\RKHS_\\FM$ to a hilbert space $\\RKHS_\\FM$ such that $$\\PDK(x_i, x_j) = \\prodDot{\\FM(x_i)}{\\FM(x_j)}_\\RKHS$$\n", "\n", "\n", "In other words, $\\PDK$ computes the inner product in some $\\RKHS_\\FM$. We furthermore endow the space with the norm induced by the dot product $\\|\\cdot\\|_\\PDK$. From the second condition, it is easy to construct $\\PDK$ given $\\FM$. A general construction for $\\FM$ given $\\PDK$ is not as trivial but still elementary." ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "df9eace4-d45b-4d9a-bf16-1eaa70581162" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Construction of the canonical feature map (Aronszajn map)\n", "\n", "We give the canonical construction of $\\FM$ from $\\PDK$, together with a definition of the inner product in the new space. In particular, the feature for each $x \\in \\IS$ will be a function from $\\IS$ to $\\Reals$.\n", "$$\\FM:\\IS \\to \\Reals^\\IS\\\\\n", "\\FM(x) = \\PDK(\\cdot, x)$$\n", "Thus for the linear kernel $\\PDK(x,y)=\\prodDot{x}{y}$ we have $\\FM(x) = \\prodDot{\\cdot}{x}$ and for the gaussian kernel $\\PDK(x,y)=\\exp\\left(-0.5{\\|x-y\\|^2}/{\\sigma^2}\\right)$ we have $\\FM(x) = \\exp\\left(-0.5{\\|\\cdot -x \\|^2}/{\\sigma^2}\\right)$.\n", "\n", "Now $\\RKHS$ is the closure of $\\FM(\\IS)$ wrt. linear combinations of its elements:\n", "$$\\RKHS = \\left\\{f: f(\\cdot)=\\sum_{i=1}^m a_i \\PDK(\\cdot, x_i) \\right\\} = span(\\FM(\\IS))$$\n", "where $m \\in \\Nats, a_i \\in \\Reals, x \\in \\IS$. This makes $\\RKHS$ a vector space over $\\Reals$.\n", "\n", "For $f(\\cdot)=\\sum_{i=1}^m a_i \\PDK(\\cdot, x_i)$ and $g(\\cdot)=\\sum_{i=1}^m' b_j \\PDK(\\cdot, x'_j)$ we define the inner product in $\\RKHS$ as\n", "$$\\prodDot{f}{g} = \\sum_{i=1}^m \\sum_{i=1}^m' b_j a_i \\PDK(x'_j, x_i)$$\n", "In particular, for $f(\\cdot) = \\PDK(\\cdot,x), g(\\cdot) = \\PDK(\\cdot,x')$, we have $\\prodDot{f}{g} = \\prodDot{ \\PDK(\\cdot,x)}{ \\PDK(\\cdot,x')}=\\PDK(x,x')$. This is called the *reproducing property* of the kernel of this particular $\\RKHS$.\n", "Obviously $\\RKHS$ with this inner product satisfies all conditions for a hilbert space: the inner product is\n", "* positive definite\n", "* linear in its first argument\n", "* symmetric\n", "\n", "which is why $\\RKHS$ is called a *Reproducing Kernel Hilbert Space (RKHS)*." ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "9d0c7200-6f4a-4d8d-9fd9-f5039b6d05dd" }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Inner product classification algorithm is equivalent to a classification with KDEs\n", "The naive classification algorithm we outlined earlier is actually equivalent to a simple classification algorithm using KDEs. For concreteness, let $\\PDK(x,x') = { {{(2\\pi )^{-N/2}\\left|\\Sigma \\right|^{-1/2}}}\\exp({-{ 0.5}(x-x' )^{\\top }\\Sigma ^{-1}(x-x' )}})$.\n", "\n", "Then the mean in feature space of data from distribution $c$ with the canonical feature map is \n", "$$\\mu_c = \\frac{1}{N_c} \\sum_{l_i = c} \\FM(x_i) = \\frac{1}{N_c} \\sum_{l_i = c} \\PDK(x_i, \\cdot) = \\frac{1}{N_c} \\sum_{l_i = c} { {{(2\\pi )^{-N/2}\\left|\\Sigma \\right|^{-1/2}}}\\exp({-{ 0.5}(\\cdot-x_i )^{\\top }\\Sigma ^{-1}(\\cdot-x_i )}})$$\n", "which is just a KDE of the density $p_c$ using gaussian kernels with parameter $\\Sigma$. For a test point $y$ that we want to classify, its feature is just $\\PDK(y,\\cdot) = { {{(2\\pi )^{-N/2}\\left|\\Sigma \\right|^{-1/2}}}\\exp({-{ 0.5}(y-\\cdot )^{\\top }\\Sigma ^{-1}(y-\\cdot )}})$. Its inner product with the class mean is just the evaluation of the KDE at $y$ (because of the reproducing property). Thus each point is classified as belonging to the class for which the KDE estimate assigns highest probability to $y$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "nbpresent": { "id": "1a23e96a-8352-4ecc-b47e-af3593998d40" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "class Kernel(object):\n", " def mean_emb(self, samps):\n", " return lambda Y: self.k(samps, Y).sum()/len(samps)\n", " \n", " def mean_emb_len(self, samps):\n", " return self.k(samps, samps).sum()/len(samps**2)\n", " \n", " def k(self, X, Y):\n", " raise NotImplementedError()\n", "\n", "class FeatMapKernel(Kernel):\n", " def __init__(self, feat_map):\n", " self.features = feat_map\n", " \n", " def features_mean(self, samps):\n", " return self.features(samps).mean(0)\n", " \n", " def mean_emb_len(self, samps):\n", " featue_space_mean = self.features_mean(samps)\n", " return featue_space_mean.dot(featue_space_mean)\n", " \n", " def mean_emb(self, samps):\n", " featue_space_mean = self.features(samps).mean(0)\n", " return lambda Y: self.features(Y).dot(featue_space_mean)\n", " \n", " def k(self, X, Y):\n", " gram = self.features(X).dot(self.features(Y).T)\n", " return gram\n", "\n", "class LinearKernel(FeatMapKernel):\n", " def __init__(self):\n", " FeatMapKernel.__init__(self, lambda x: x)\n", "\n", "class GaussianKernel(Kernel):\n", " def __init__(self, sigma):\n", " self.width = sigma\n", " \n", " def k(self, X, Y=None):\n", " assert(len(np.shape(X))==2)\n", " \n", " # if X=Y, use more efficient pdist call which exploits symmetry\n", " if Y is None:\n", " sq_dists = squareform(pdist(X, 'sqeuclidean'))\n", " else:\n", " assert(len(np.shape(Y))==2)\n", " assert(np.shape(X)[1]==np.shape(Y)[1])\n", " sq_dists = cdist(X, Y, 'sqeuclidean')\n", " \n", " K = exp(-0.5 * (sq_dists) / self.width ** 2)\n", " return K\n", "\n", "class StudentKernel(Kernel):\n", " def __init__(self, s2, df):\n", " self.dens = dist.mvt(0,s2,df)\n", " \n", " def k(self, X,Y=None):\n", " if Y is None:\n", " sq_dists = squareform(pdist(X, 'sqeuclidean'))\n", " else:\n", " assert(len(np.shape(Y))==2)\n", " assert(np.shape(X)[1]==np.shape(Y)[1])\n", " sq_dists = cdist(X, Y, 'sqeuclidean')\n", " dists = np.sqrt(sq_dists)\n", " return exp(self.dens.logpdf(dists.flatten())).reshape(dists.shape)\n", "\n", "\n", "def kernel_mean_inner_prod_classification(samps1, samps2, kernel):\n", " mean1 = kernel.mean_emb(samps1)\n", " norm_mean1 = kernel.mean_emb_len(samps1)\n", " mean2 = kernel.mean_emb(samps2)\n", " norm_mean2 = kernel.mean_emb_len(samps2)\n", " \n", " def sim(test):\n", " return (mean1(test) - mean2(test))\n", " \n", " def decision(test):\n", " if sim(test) >= 0:\n", " return 1\n", " else:\n", " return 0\n", " \n", " return sim, decision\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "nbpresent": { "id": "1681f63f-4290-4335-bd75-0a261ec26735" }, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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CJr+G2VrU048Wdo0mDD966C6qx40GBi1oMynp9ttvZ8SIEQmNH8kiDrTcY0n0sSspKJx46xowmYkWdo0mDLPOOcP3c2BrvFNOOSXh8eOJXokl0ceOpKBQ4t3Q0MT69Ym7ezT2o4U9iWRDXRVNeDau38D4qZM46SMzhkTJPP/881RWVnL66acndIxMdmdE8tUXFekaMJmIDndMEnZVGNSkl199/fu8+H/PAEPDH1euXMmaNWsSPkYoizgTkohC+err69soKnJzySWtfm4Z833d7i69aIs9SWRLXRVNBAQ8yvCpBzbasGPx1K7olWQSzFdvhjqar+seppmFbRa7iDhFZKeIPG7XmNlMttRV0YTHKt6ChHwv/vFDW8SZ5M4IDMU049d1uYLMxE6L/avAG0CZjWNmLXZVGNSkFzHNUWMDsD/cMdtK2uoeppmPLRa7iEwAPgncY8d4uYBdFQY16UUcDjye0B2U7KrHnm0lbXUP08zGLov9F8CNQGJBvTmEWVdl8n2rcH1wiK6J49i3eKmt/vVsj7rJhvnf9sg9lFVVAINiawr7z372M4qKipJ27EwurqXj1zObhIVdRC4DjimltovI+WH2uw64DqC2tjbRw2YFyayrki3djEKRLfOfMnP64EaAxT516tSkHTfabNR0kA0LvsMdO1wxHwMuF5F9wEPAx0XkgcCdlFJ3K6VmK6Vmp6PrTK7hF3XjEAZGlOAudjH5vlXpnlpUxDL/qi3bOXPpjZx36TWcufTGlIaMPrNqPbu27gSGFgF76qmneOmll2w/ZqbXUs+WBd/hTMIWu1Lqv4H/BvBa7F9XSl2T6Lia8NjV1zNdRDv/dFv2v//hL6lvuJhZ55wxxMd+7733MmnSJD760Y/aesxsWJzMtgXf4YZOUMpSsqWbUSiinX+gZS8DAxQfPMLsJTekxnqX8PXYwxGqhnlUh82CxclsW/AdTtgq7EqpF5RSl9k5piY42R51E+38rfkA+a1tjHhnD+J2I8qTkmzeYHHs0YQ4JtqAIpOzUTWZj7bYs5Rs72YU7fytlr3rwCGU0wkiuIuLU7KuYK3HLgE+dofDETTcMVEfeeDi5IoVe6ivb/MbT6MJhy4pkMVkezejaOa/b/GVnHrTrZS+u5f81jaU04nKz+PElElACtYVrBZ7lAlKifrI7aqlrhm+aGHXZDwKBQpwOBBfozqDZK8r/HTt7yn2uoIC49hXrFhBXl7wP6FEKzbqxUlNImhXjCajmXzfKvpqajh+5kc4ftos3MVFqDwnrgOHUrKuMKZ2POUjDb94oCtmzJgxVFdXB/2cHT5yvTipiRct7JqMxrp42l9ZTseHpuEuKiKvozMl6wp/uf9htj3/N2CoK+bxxx/n2WefHfIZ7SPXpBvtitFkNIHF1Pory+nMy6O3upIdd96e9OM/fMfvOX3uOcy+4GNDomJWr15NRUUFF154od9ntI88PjK5hEK2oYVd4yMTa7fsW3wlM3+wAjAWSvM6u7zul6VRfT7RcxKHZfE0hnrs2kceG5lcQiEb0a6YYUiwFP1M7fiUSFinHeckQaJigr0X/LPhtzUGmV5CIRvRFvswI1SK/oCrOO0dn0JZ1/GGddrWxSrJ9diHO9lQQiHb0Bb7MCNU8a2yN95Na8enZDwx2NLFSsSi66YrRgt7KOIto5ANJRSyCW2xDzNCFd8CIyY8XR2fktEj1o4uVp/60mO4+wpRqs/nY3/uuTLee6+SlStXhqwXU7p9OzWrV1N48CC948fTuGgRJ+qyN5ksGhLxk+v67vaiLfZhRqjiW+0zP5TW2jPJ6BEbbT2aUGWBlQKno5qdmyfy9J9HYlYB27GjlO5uJ2Vl5ZSVDe0EWbp9OxNWriSvtZX+6mryWluZsHIlpdvTu16RTBLxk+vwUPvRwj7MCCV2by9fmtbaM8moVhnNwms4F5AI9HT/mpGj/8TWZypY/euxAJxxxgkWLGhi/fp1rF+/fshxa1avxu1y4SkpARE8JSW4XS5qVq+O+1wyHWtN9k2bylm+fJpfI45wVreu724/2hUzzAjVsg9Ia6hjomGNoYi08BrJBfTk/Y8wddbJwGd8cezz5rUgMoa//OUvADQ0NPiNWXjwIP0BGakel4vCQ9lRKz9eEimjoMND7UVb7MOQljl17Ljzdl584gFfkk+4hctUdDAybzjKAZXbX2PEm+8w4Cq2/TiBRHQBCRx+P9/7s6EyL7xQ7hWh4IunvePH4+jyf/pwdHXROy72p49EarqnmkTLKOjwUPvQwq4J26Yu1fHteZ1ddHz4Q7TWnYYoSXosfTgXkFLQ1Z5H85F8zvnEcT791SMA7NxZwrp11SGFvXHRIpxdXTg6O0EpHJ2dOLu6aFy0KKa5JVrTPZVkmp88m26IyUALuyas1Tqkg1F/P8UHktPBKB19XMMtsIqAw+mgalQvF13VjMNp/Lmcfnq71/cbXNhP1NVxYNkyBioryW9uZqCykgPLlsUUFZPspJ1kCJ/VTw7p85Nn0w0xWWgfuyZsWKBr/yE8eU7K/7mfvI4TOPr7cRcUgMMRd//RUIlI6ejjGmrNwTyfkjIPoyb0IjIYxz537nFOO62Vxx4LHcd+oq4uofDGZCbtRApLjLVmi3U8E3O8VPvJrTdEML5D65PEcKk/o4VdE3bhcvrPf0vFP9/EU5CPDAyAAmdvL/2lpXHFmodrTm1H3Hk8hFtgXfH4H3GIYakPCoIh5itXrkzqvBKt6R6MYMK3dm01mzcbwvfkk4ZIL1wYXSx6JCFNNTqL1UC7YjThwwJFfI0txKOMUG6FT+UCLepIC62mu0X6+ynf9SZlb7xN8YEjTP/5bzOyj2thURH5hQXGRkBJgcLCQgoLC207VqDx7/HY3/c0MCzxmms+zOrVNcyd20ZDQxPd3U5Wr67h1ltro3L/JBLmmCx0Fqu22DVeQlmteSe66Tj5JFwHD4PqAA8gQv6JE+S3HEfl5/ss6nDWuDm26doZsWcfyunwPQlUvPYGQFi3SDpYc9cfKSkbwcVXLfRZ7qawr1mzhu7ubj7zmc8kfJxA94jHA7fcMpk9e4q44oomP0sYEhMqU/g2bizH7RZaWvJ9r5vs2lXCsmXTEInO2rU+WSiVXiHVWaxa2DURMN0jXePHGj723j4AFELZW+/SPbqat74+GAcfqSxAV+04Rr68HeV0oPLykL5+nN3diMfDGf91Mzt/dWtK6qxHy8Z1G6geO5qLr1o4pNHGCy+8wPHjxxMW9mDujPXrq9mzp4hp03poaIiupnu0vnFT+ERgzBjj97l6dQ2bNpUjAosWNfp+NucTShA3bKikq8vpN/aRIwXcemstN9+8H0itTzswOsfOG2I2kbCwi0gRsAko9I73iFLqe4mOq8kMTP978YEjeAryUQ4nzt4eVH4e7qJCekfX+FnjkRY/9y2+klHPvYinsADp6yfvRKdvv/z2E3EtxiYVGRRyAnqe2naIEH7hK65ooqGhCW9HvpBJO0rBU0/5L2AqBevXD10QDSZ8a9dWc+edxlPX6NF9vmOZhLJ2lYKuLsN1AzBrVid9fQ6OHDEs/rVrDavZ5UpdTXXd5MTADou9F/i4UuqEiOQDL4rIk0qpLTaMrUkzpv999pIbEI8Hd0kxHSdPo7+yHDyKwqZm377RLH62zKnj+OmzGPH2XvLbO1BOB+7iYiO8sbjIF96YKcLuEAdKGY01HAE9Tx0Oh6/pRqJEu1AauG21mDdvNhKnXn/dxfvvFzFihJt589rwePxFPjAsEaCqqh+HQ3H0aAGrV9ewaFEjCxeGt3ZFYOHCJl5/3cXu3SW8/noJra35nH12O2eeeYJdu1y0tOSnPBpFZ7HasHiqDE54N/O9/4ZZOkBu0zKnjqbzzqZ95sm0fWSGIeoMFe1oFz/fXr6U7vFjcBcUMDCi1IiPd3voGj82paWCo8JStjeZ9djjydo0XTibNxu/j7lz21i9uoZnn63inXdcjBjhpqHBcOtYF0Dnz2/1ifq6dUZEzKJFjfzpT28ya1an3zEixaI/9VQlp5zSxejRfYwd20dlZT/vvlvMI49U+0Q9HaI63LNYbYmKERGniLwKHAOeUUptDbLPdSKyTUS2NTY22nFYTQqJRrSj7XZk7jdQNgJnTx+eggI6TppCf1VFSksFR4PT6bBYfv7C7nA4QpbtjYV4szatESmbNxsunJaWfMaN62XcuF46OpzccEPwKBUjLn/QbWGGN958834WLWr0CbkINDQ0cfHFrX7zNf83XTFHjxb4xj10qBCPR9K+iDqcsWXxVCnlBk4XkQpgrYicopR6PWCfu4G7AWbPnq0t+iwjUiKPdb/A10IlJO381a2+KJqBEpflZpFY4S87+dn6P/h+Hmy0Ybhffv7zn9tyjET8wtYIlyNHDHE1F0SPHClgzJi+sK6IYG6L4mI3PT1On+/edPW4XG4uvrjVF9duFXuT9vY8QPnEPxnRKLrpdWRsjYpRSh0XkReA+cDrEXbXZBnxtKiLFAKZaeGN4bDDOg9FvH5hpWDt2mqOHCmgpSWfqqp+5s5t49VXS9m92whjHDOmL6zABopkT48RoWOKs7k4umhRo18yExhib0bRHDlSQH+/MG9eGx/9aJtvHLDPck9m0+tcumHYERVTA/R7Rb0YuBC4LeGZaXKCSCGQ8fYzTRUP3/G/5BXks/C6a4e4Yh5++GFaWlq4/vrr0zI3U9Q2by5n1qxOZs3qQil4+OEalIJzzmmPWWADI3SsbiAzBNL6ZHHxxa2sXWuETjqdipEj+znjjBN+ImtXNEoyywUk84aRDuyw2McCfxARJ4bPfrVS6nEbxtXkAOmo/2Inr/z1RQqKCg1h90bFmK6YV155hX379tki7PEIS6ALx2T3bqOg27e/vR+HY9AnHq3AWiN0rLHugXHt1huLNXRy8+Zy3xh2WeqmaJvnuXGjfeUCcrG+TMLCrpT6B3CGDXPRZDCh/OSRCBUCOVBSzJlLb0xbY4+oEWsUTMBbQaJi4ul1moiwBCvaFZgYFGu4nzVCx0w4Anz+eqtbJ3BtwFyEtTNmPPCm19DQxKpVNTidilGj+hO+eeRifRmdeaqJSDA/+ak33UrPqJHkdfaEFeZgBcYKG5tQKMRDyNIDmUL+iU5KG/dz3qXXsLFnHuAf7tje7mDDhkrmz2/19Tp1u1x+vU4jlexNVFiiCe2LVdQ3bSpn7lzDj2762E2/uvUGlOyYcTPyxgzpbGho4nvfm+xbTzDna5e421lwLZ3oImCaiAypyT4wQOHRRka8/V7E5hvBQiB7Ro2kr6YmpXXX46Fqy3ZK9h9E+vrpqR5Jf6ch6K+s60EpOHiwkK4uhy8+PJFep1ZxN7lm4lNM/eZNfPiaa5hy000paYYdaIWbi6NmCOTChUPj2pMZM/7UU0YN9blz29i4sZyrr57Bxo0VTJzYw4MPvsG8efY080i0+1OmoS12TUQC/eSuA4dQ+Xk4BgZ8wgyhy/cGLpCed+k1WeF3n3zfKkry81F5TsQpzB+/lV8eht3bHSxfPo2WlgrKywt9ll0ivU4DhcV5vI1nbznAtWNbY7L+7WD+/FaefLKS9eurh5QoeOqpypRZstYELPPpoaPDCSguvbTFtnIBuVhfRgu7JiKBfnJndw/KIbiLi3z7xCLM6aq7Hiuu/Yd44MxTwWH8VTtMC7WvF4Dp0+9gxYo9vv17x48nr7XVsNi9RNPrNJiwvHjtRp7ouhB3RymfLXncN2bN6tVJF3ZryCMMFiWLpca6HaGDpnArZbiDzCqUY8f22er6ycX6MlrYNREXRgP95J78PJw9vZyYOtm3TyzCHK6xRyYx9AZk/IU3SjUur1BZC11dsWgRE7zNNzwuF46uLpxdXRyOEDUTTFiWqN8howZwOXt8whKt9Z8oifr8kxE6aPrUx4zp82Xa2unPz7X6MtrHPsyJpll1oJ+8Y/pUukdXo/Lzo26IYW3AMfm+VRz4109GLD2QbvYtvpKV7+/np2+8g3IrnjpwLgADLpfXz/wrfvObn/DIH0px3b+O8StWGgXNIOZep2b9FlNI+iaMZ/GIVfzbqGd9+0Rj/dtFMJ9/tAlTdvdq3bXL5RN18/hz59rfSzWX6stoi32YE00NdRhqnXEDAAAgAElEQVTqJ/dZ+VFkjAaLqpmw5omUi3ms7oGWOXU8NaoG9cEhbm5upmCEAw7Dued3s3lzOW++uYuuE1s5l4/zhVF/YqCk2melx+MLt86l0Wv9uyU26z+R8w38bCzNKsyxre6TREMHzTm0tOQPqTY5d25b0JIGGgMt7MOceBOIYskYjfbmkUxeWFdJb5eDi65q9rkHnv7zSApdHs5fEFogBirK6M7P48V19zHujXfg4js455w2Hn/cCHd0qj5+OfUnqFLjnOzyhZ+oq+PAsmVGTPyhQ/SOG8fh66/3jRlJtBNxh8S6mBh4LJNjx/IZNao/6GeiIRd936lCC3sOMfneB5l21/3kH2+nv6KMPddfy75/vzrsZ1KxkJnM7NNoEqeUgt4uB1ufqQDgoquaefrPI9n6TAXnfOJ4WEvW4XCgPGY9dmOnrVtLzXdBubmv40o+W/K47b7wE3V1QW8OkUQ70UzKWAQ1VHNsM/bdPFa8sebBfN/W5iPWY2gG0cKeBuLN4gzH5Hsf5MO33WF0NnIVkdfZyYdvuwMgrLinYiEz0s0j3u8jmh6rYPzRX3SV0RBk6zMVPoE/5xPHfRZ8SMRSj927eLp7dzGf+lQb5eUneHFDHxuOzQHgs2MMcU+mLzxa0Y5m8TOc1R/tYmLgsaxVJq3uk40b/a39WMTYrieR4YRePE0x0SxWxsO0u+5H5efhKSwEhwNPYSEqP49pd90f9nPR1lBPhHC13BP5PgITp8IlOlnF3SSiqAPlVZWUj6zwjmHsPGNGJwsWNFFeXsbE8RV80vUspQNtCApHZyfOri4aFy2K8tuJDVNIzXrty5eHrrcebvFzw4ZKvwQcUyA3bKj0bYcS/WALoOaxRIxiYKaoi0BRkZuyMjdFRW4/MTaPFS3JWJjNVbTFnmKS5W/OP96O21Xk95onP5/84+1hPxeNtZzoE0bLnDoO/Osnh7iJWubUcebSG+P+PmJx8Zg+dStP/3lkRHFf/ovv+342hb2urg0RWLZsGSxbRsm27Yx6eDX5h5qH+MKTQTTp7+EWPyG81f/kk5X09AS3is3PWt9bu7aaXbtcvuOYfnVzHj09TtranL4a76YFP29ebAW2crGmS7LQwp5ikuVv7q8oI6+z07DYvTj6++mvKAv5mWhcGdG6O8JRtWU7E9Y8QVftBAZmGO6eCWueoH3WyQl9H9GuD5iibvrUrT52iM5yBxBH8J06Z9fx3uzURveEi1iJZvEzlEBaW+mZ+wbWjjHrtgT60wMjV0whLipyU17u9lVkVAo/Cz4Wcq2mS7LQwp5irGKU39qG68AhnCc6GSgbQdWW7XFb7Xuuv5YP33YHDgxL3dHfj/QPsOf6a0N+JpqnBzueMMKNkcjirbk+kNfeQWFzC3mdXXjynBxe5h8SKAKFLo+fT910yxS6PGFF4c8r76a99TjXf/9GAuuxP/TQQ7z++uvceuutUX0PsRDKFRJtxEo0i5+hBDKcVQzGPKzvmbXgTdeL9VhgWOzt7U5fRyfDB9/ns+DjCYG0kowuTdmOFnYbicZlYRUj14GDxlXtcNBXUZ5QhUNzgTSWqJhorGU7njDCjbH7O8viXrw1XTzTV96NDAwwUOKid2SV72nA+j2ev2DoYqAp8uF+b+/+8w2aDh/1fsZf2Pfs2cMrr7wS9fcQLZEWCKMR7UiLn5EEMpxVHPhepDLBDQ1N7NxpdHQyywJMn95NQ0N8ce25VNMlWejFU5uIdhHQXKwsON6GeMBdXEzHh6bSM35MwhUO9/371fz170+y4e2/8de/PxlVqGNeZ5ffa0WHj1LY2Mx5l17DmUtvZKCkaMg+sYZDBjuOOUa0i7fWzNUzl97o+16rXnmVjg9/iJZzZ9N26syw32OwiI5IvzdxiK+xRmDPU4fD4fvZLqJZIAzMUjWFNDAqJFQmZaTm2R5P6EqHoW4IgViPtX59Ne3tTqqq+pk5s5Oqqn7a252sXx9b9cRQTyKB1SY12mK3jVhcFi1z6uitHkn7jOmDlaVITYVDq3U6UFJEYWOz79hFh49Ssm8/nZNrfSJX2NiMQvn2iSccMlJIZaRkp3B+/kSfKCL93sQ0mRna8zRYo41EiXaBMJH093CumqIit1/BL9OPbm2Tt2mTsfAZjcVsjYoBoyTAmDF9cfvYc62mS7LQwm4TsQpMOiocBgpkXmcXCoVyQGFTMwXH2+icXEvP+DHG/L1zUw7oq6qMu+F0ok2rk+Wjh8i/NxHB0dnFmUtvpPHdfQAUvPee7z27hd0YN/kLhOEEcsOGSp+oW+uhu1zuIQufkTJBzaiY9nan381g48byoD72aMogJHJTGy5oYbeJWAUmHRUOQwlkX1UlW1b/LmSd9MKmZras/l1Cx06kaXWyfPQQ+fc2QYTy4+2U7N1PR5PxdFPz0EPUVFczcuRIamtr4zqncKRqgTCUQJqiD/710C++uJV16wy3ilWUw83LfDowRT3czUAnH9mH9rHbRLgknGCkIjEokBG736Hkvfep+vtOyv/5Bvktx/2sU6svPL+1jfJ/vkHV1u0UNjYnnECVCHb46EMR6ff2CxEeGj8W18HDRmMRjMXTcXffzdfOOIPf//73tp5rMP/33Ln+XYJSkYgj4p8MtXnzYDKUVaTNfcMRzZqATj6yF22x20Q87oZErNhQhIrwqNqyncKWVkR58BQU4OjrY8S779E1fiydUw2rM1kRO4mSqI8+HJF+b679hyhsbkE5HT4FU3l5MDCQlKYXgf5vqyukqMgIHzSt2Isvbo3ago+30qNdbqFo3Ck6+cg+JBk+wkjMnj1bbdu2LaExHv9gh02zyR2sPnSrAJrCVbJ3P66Dh1BOJ8rpxNHXhxJh2z0r/BKSzvivm8lvP8FAqYuu8WPpr6ogr6OT3upKdtx5e9rOzV98E6+vEw3Pf/wKDr23n/sqyjjgUZzUepzfFhXxhZISfpWXx5qpU/n1r39t6zGtf5KmP7qqqp9TTjGeWqyt4lyuyG4Kuyo9miRTbJWC5cun+bZXrNiTlaJel6TMYxHZrpSaHWm/hC12EZkI/BEYA3iAu5VSv0x0XE3shFtkdO0/RM/Y0bhdxUZSVHcP7qIiBkaUDKm7nq6InXAk4+kmGv4xqpp9e/fh6OtDnMafi/J4GKisZG9vL6+99pqtxwsU4YaGJnbsKGXr1jJefLGCqqp+Fi1qBAyBj1StMZFKj6mOG9fJR/ZhhytmALhBKbVDREYA20XkGaXUbhvGHlYkWpMl3CKjuUjYX1lOW6Xxh2la4YHEE2mSjIqVmUBfTRV9FeWoATfOHqPX6UB5OSovj+7Jk+Gll2w7VjARXr++mo4OJyNGuFHKTUtLvi9dPxrLOZyLIzBBKFDko81gtevcdfKRfSQs7Eqpw8Bh788dIvIGMB7Qwh4DdtRkCSfIsUThxBqxU7VlO6fedCv5be04+vopPnSYsjfe4R+33ZwycQ92YwESutkYQif0jyhl20+/S9Fv/wjPv0hfVRUHli2jf9MmW8Mdg4mwGV4IfQC0tub7UvOjbVVn9ZOb22a8eiT3TKrixlN5ExkO2BoVIyKTgTOArUHeu05EtonItsbGRjsPmxPEUoI2FOEiPGKJHok10mT6ijspPNqIeDx4CgsQj4fCo41MX3Fn3N9HLFizRz35eYzcsp2zP/Nlzlr8VUr27o+rPPIL6yp5+s8jEXHg8Siaz6njNx81GlU3LljAibq6pGSeWgVNKThypID2dif19W3U17dRVdVPS4sh7mvXhs/cNEvzmpmk5njHjuXz8stG7fRoIlBSFTduRs9Yj7NgQZNugRcHtkXFiEgp8CjwNaXUkFqxSqm7gbvBWDy167i5QrQJTuFcHpEiPGLxU8eyb9nud1D5eUa0CN6oEaUo2/1OVJ8PJFa3jnlTlIEBRry7F+V0IkohfX24Dh7C7Sqm3+t+iqZ4mX/HpQ8xeUYnT/95JDs2GeVoPR7j8h09ejQzZsyI6xzDHdv0M4sYtc0NNwy8+GK5z7++a5eLzZvLQ1rQpltn48Zydu4spb3d6bP8y8rcvm2z4iLYtyiaSK/Vp54a2mYvmoXeRI6Zi9gi7CKSjyHqf1JKrbFjzOFGNH7taNw16VpktIt4XFLmTbF815tGxE9eHuIN+FZOJ64Dh2irLI96AVjE2nHpf/C4YeszUDdvD69uBrwlFj796U/z6U9/2q5TD+ln3rixnN27Xcyd28bChYZFu3DhoOAFEzCr5f/II9W43QL0MW/eYGneoiI3Tz9d5fuMHaIebwSONSHKdBlZSwCHW+jViU1DSdgVI0YBjXuBN5RSKxKf0vAkmgQnO9w1yaB9xkk4+geQgQFQChkYwNE/QPuMk2IeK55zNBOYnN09KKcTAOUQlMOBcjpxdvcAsZUasIq7yQVXHDfGTlKIcCg/87x5bZx1VoevLK41eSiccJn7jBrVz5gxfb5th8OItunpcfrtb+2oFA/xJhmZLiMw5jd3bhurV9dwzTUfDtodyo5j5jp2WOwfA64F/ikir3pf+5ZS6i82jD1siCbBKZlNoRPh7Ru+xEdu+gEFxztw9PXhycune3Q1b9/wpZjHiucczcVeT36ecXMR8bmFHH19uIuKLDfKwQXgcC4fsznHwb0/4UTbK5x8xqO8sGak9z1DLVatWsXjjz/O/feHbz8YC9EsVprvWysohhI9q1sHjO2GBsMSNsMlrYW+IH7LPZ4ko2CRQAAtLflUVfWjVOSSBTqxaSh2RMW8iNnlV5MQkdwo6SgcFg0tc+r4523fsSWBKJ5zNG+K01fcScWru3AXF9N+8kk4e3opPnSYgREl9FZX+t0ow7l8ms+p83VYKh+5l97uf3LOJ47zt78YHZdMH3tTUxNvv/12zOcYiWCLlaZ4m26HhgbD8g7ldggXPvj660Ybu7lz2/wWK6uq+hOOQIk1UzVQmM1m2FVVg08ZkWLZU1E0LdvQJQWyiHQUDjOJtKAZ7KYUT2x7vOfYMqeOLat/55eh2jm1ll3f/0bQY0Yq12t2XHprZy9HP1BcdFUzvT357NwESiWvHnswrGJuXRA999w2enqcQX3Qodw6ShkLr2bDC8BnvZuFvoIR7eJkPElG5txMUW9pyWfp0kN+PnYILdY6sWkoWtiziETL38ZLPAua8cblJ3qO0S4eR3L5mB2X3n7VMJdF4F+uaOV3twzun6yyvVYCXRVmN6ItW8p4++1ixozpG1KUyySYW2fhwibfwuumTeW+/qXhXBfRLk7Gm2Rkfs6MAqqqGmyGHU1ZYJ3YNBQt7FlAurM64+l7mkivVLus/3BE6/LxE2+zCFiIxht2YvWjm5a2NWmpqqqf0aMHF0St7hr/+QffjuS6sPZYNZ8SzP1CRarEk2QUTJjXrq32C+WMpiywTmzyR5ftzXCibbmXTIxuSy6/1yItaMbzmVAk4zuIFIVkJihNOGkKM886HaXguUcMC990v4wfP56zzjrLdqvdjBIJHPbYsXxfkpHDoTh6tMAnjGYS0oYNQ0tEBBLKdWEe78knB48vApdf3kRZmZtHHqn2le4NZeFH27bPJJgwL1zo3+4ukjjHeszhgLbYU0y8yTfxWL52YVq3MjDgKyDmyc+jY/rUiJ+xY6E3Gd9BOJePNUHpnE/8Fzf9tpmn/zySbc8XAIMW+2WXXcZll10WdPx4E2aCRYmsXVvN6tU1ABw+bPigx4/vpaKi35dkZCYhzZuXWGGvwkI3W7aU095uhEI2NDTxP/8zmT17inC7JermGuG2A7GjbEGqsmOzBS3sKSSR5BsrqQ5x3Lf4Sk696VYKjzYaGaYOwdnTS+HRRqq2bA86dzsXepP1HYTyx/snKFV4M1Dh7H85wo4XIo+bSMJMqCgRgEWLGikudvPyy+W0tTl9GaRHjhTQ2Ki44orwbgtz/HD9Ts02duYNY9WqGpqbjRtJdXW/X9iknf5rLcz2ol0xKSSR5BsrqQ5xbJlTR8+okXgKCxGPwlNYSPvJJ9FXUxNy7nZ2iErHd2CK+8G9P2HX388H4MJFLX77PPzwwzQ0NDDg7awE9iTMWMXWXFBctKiRhQubuOSSVm65ZR/nn9/Guee2IWI0hx41qj9qoQ3lurjkklZfQlR7u5Pdu0tobs4nP19RXj7A+ecbHZ3q6/07OmkyD22xp5BEkm/MfZMZ4hjOTZTX2cPx00/xq9GOR4Wdu13lDdIR5mkmKA30N9PbvQ+Avz7s72Pv6Ojg4MGDfiGPdiTMBPrAR43q93vfzBxdv77az4VhJh85ojDXQlnIIsbYq1bV+LYrK/spL3f7yvzqxcnMR1vsKSQeyzNVvVEjLVCm88kh1f1hTVHf+kwFY2r7KXK5OecTx/n7Xyu97/tHxQQunlrFzyRWUbf2PDV7jlp7nq5fX80jj1RTVubm5z839tm4sZxbbpnMk09GXkANhccDt9wy2Zf5OXNmJ9Om9dDe7vS7kQz3xclMR1vsKSSR5JtkL5RGWqBMZ3IUpLa4mQi+BKX33+phz+tGgpLb3c/25yMLeyIJM9GG7xUVuf0E14xv37OniDPOOBFXdUPzhrFnTxFz5rRzyy37WL/eKEJWVuamqMjtZ9lrMhct7CkkXQlG0RDJTZTJc08GZoLSPd836rEbPvdWfvvt8EXA7EiYiSZK5JJLWrn44lbWr6/2i2+PtIAaLlrHvKlccUWTz6XT0DC4sHrJJa1x3TA0qUcLe4rJ1LK60YQnZuLck5m8JQKTTp7G7As+BoDDMWihKwW1tbXU19d7k5gGE4rsSJiJJkrE4fBPNIoUJhhNtI71phJtXRpN5qF97BogurLBoajasp0zl97IeZdew5lLb0xZ8lQqkrcu+vQCbvzNj4FB18s77xSxbl01F1zwcVasWEFBQaFfclAqEmZMX7vp8jEfIkJFqsQSrWPNON20qdznW9flcLMHbbFnGcmyUFvm1HHgXz/JtLvuJ/94O/0VZey5/tqIY9vRqzVeUp28ZQp7fz9+rpVgKfbJjMvesKGSri4jgcgs3gVGca9QLp9Yo3XsiO7RpA9tsWcRybRQq7ZsZ8KaJ+iqnUDzubPpqp3AhDVPRBw7nc0/IpUtsONJ4qFf/o4vnPtJ37aIMH16J/X1baxatYaPfnQ+zz0nKRM805LevLmcXbtcPlHfvLmcWbO6mDu3LaquSibRltSNZn9N5qCFPYtIpojGO7adNWFiJVwIpl03wZ7Obo43DSYmGVa7YsGCJjyebvr7m3zbyRQ8ax0ys8tQS0u+r0JjfX2bt3JjaJdPpBoxie6vyRy0sGcRyRTReMdOZ3x7uHUB226CEhAF4632aAje4GJqMgUvXFEwa7XGcAWzQsXHh8ogjXV/TWahhT2LSKaIxjt2IouuiRIuccmum6DD4UBZMksdDuGtt4rYtKmck07qBeDcc48nTfCCLXqaRcHMolwQ2ZIOFa1jraKYyP6azEIvnmYRyUwSSiR5Kp3x7aFCMG2rLiniL5giOJ0e6uvb6O3t5Omn4dJLm3G5KmMWvGgqQEYqChZtlyGIvYqiHVUXQxFv9UtNdGhhzyKSKaKJjJ2J8e123QSnzpzOvIb5vm0RYcqUbhYsaGLr1slccskl5OfnxSx4sVSANAV106ZyX1GwT33K8KeHipMPJZyxRuskI7onkeqX2Ua6bmBa2LOMZIpoJgp0vNh1Ezzvsk9w3mWf8G2bHZVEYM6cOcyZMyfmuQWruR6qK5G5v7XxhVkULLDLkvmZTBbOWM89m3nwQejshCVLBnMD7rkHSkrg6quTe2xbhF1E/he4DDimlDrFjjE1mnBEE8+fjBuVXX1OA90rIsFjxE1RfuSRaqZN6/Gr3/Lqq0ZD60suafWz1DNZOIdLfLxShqg/9pixvWSJIeqPPQaXX558y90ui/0+4A7gjzaNlxWkuxdpps4l2SQ7Kcr6Xf64r5dfvPcBj+7ZAvgL+7p16/jpT3/K+vXrqa6uDjekD6s1vWBBk89n7nQGD5kUia3gVzYIp9W1ZJIpc7MLEUPMwRBzU+Avv3zQgk8mtkTFKKU2AS0Rd8whMqEXaSbOJRUkNZ7/3geZveQGal54iaKjx3C0HKevv5+Kl14BQBwOX/11j8dDb2+vXz32cFit6bVrq1m7tpojR4xWd263sHZt8MgWs7nGvHlGuOENN0yjvd0ZtOCXtayuuQ2ZJZzDJT7eKu4mqRB10OGOcZPOjMtMnksqSFY8f9WW7UxfeReiPHiKi3D091PQ3gHApD+sBvz/KEOV7Q2FNblo9eoa7rzTiNBZuvQQixY1+tVcD8Qs+BU4lnU+Zry72djabHx99Gi+37ixCGiw+PZEGE7x8aZP3co99yT+HUZDyhZPReQ64DowquJlO5nQizQT55IK7GyUbWXyfatwDLhxFxcZYY55eYi3HVFxkO8yVmE3PgMLFzbx6KPVVFX1M2ZMHwsXDrbBCxUyGanGu/k0YG1sXVbm5tgxRUGB4oUXDLeH2XkpmoXUZCzC2lX9MtMxRd30qVt97JB8yz1lFrtS6m6l1Gyl1OyamppUHTZpZEIv0kycSypIVlKU+SQgbvfgi96/vhMTxno3E1s8NcVx1ChD1EUGBTtUBchorFxTIOfNa2PPniKOHCmgrc3JSSf1UFExQHm50SjDrN8eqUKjHb1bQ5GK6pfpRsSIfrH61JcsMbZLSpLvjtHhjnGS7o5CmTqXRIh2AThZ8fxdteOQgQFcBw8DAyink9kovpifz/7PLQJAZNDHPmXKFD71qU9RVFQU1fjRNOEIRrRWrnVR0hR7axTN009XAdEtpCZ7ETaZ1S8zhauvHtrIJFU+drvCHf8MnA9Ui8gB4HtKqXvtGDtTSXfGZabOJV7CRboAQQXf7vMzb5Bd48dS2NxCXmc3F+XnM/nG69n3sbMBf4v9tNNO47TTTot6/ETcENFkgQZz15hRNBs3xh6BMhyiV5JNum5gtgi7UuoqO8bJNjIyoSeDFp9iCcEMVVt9+oo7yevsSkm9d+sNUuXn0TVxHHs/+280n30GDqUMn7qfkCrcbjdOp9Pnb49EImn64UTC+jRQVdXPrFmGa27jxnJ27Cj1hVSOGtUfdf/VRHq3phJdnmAoOiomB0hVuGMs9c1jnVOoSJey3e+kNOKnZU4dO+68nRefeIAdd97Ova/tZsHUc+jt7gGMomCmK+aJJ55gzpw5HDx4MKZjJMOKM58G5s5tY9asLjZvNqzs0lI3O3aUAvCpTzVx3nnRRaBkS/RKYOVLc95mN6vhihb2HCAV4Y6xCnWscwq1AAykrd47DI18sbpi4omKSSbz57f6arLX17fx6KPV7NxZyogRbhYtavRZ2lVV/RFdP6HcRplU3TGZC7zZjhb2HCAVzS5iFepY5xQq0qV9xklpi/gxu0oBnPbVm42bmFfYjcf9QWHPFBExa8c0NDThdgv9/caf+IIFRpij2Wnp4osjR6BkevSK9WazaVM5y5dP81uYzoSbT7rQwp4lhHODpCLcMVahjnVOoWqrv33Dl9JS7918Qsnv7AYgv+k4M3+wAufAAPv3Gwk/Isafj9vtyajHf6WMRdMxY/qoquqnpSWfq6+ewcaNg52WohW9TI9esS5Am8Qi6nYnYGUKWtizgEhuEKu1m9/cSsWOf1L+j10UtLTa5mePVajjiTUP9G+bi9OhmmkkE/MJRRUVAtBf6sJd7CKvq4eBAWHTpnK2bx8BwLPPVmTM47/VHTFvXhsPPviGT9yPHCmgoSG3LNlEyhPksn9eC3sWEMkNYoqfEkXZm++CQPuM6YgH2xZRYxVqOwU5mOAnG/MJ5bQRpfxH7QQKHMJAiQun282kSd3U17fx/vtnMGHCf/Lqq7UZ8/hv9Y2bWaam5e50Ktavz5yFz0RJZIE31/3zOkEpC4imZEDLnDr6RlbRdupMv1R7MG4MiYphPLHyGRkOGiVm2YI5leXMqTQiTPI6OiHPiVLKG9/9EUpLPwLAggV7kiLq8YTyzZ/fiseDL8t03rxBkY+m01K2kEheQDZUwUwELexZQLS1UZJdMyabhTpWzGSlXo+HE0VFVPb24uzpxl1agsejvMW2+vB4unE6S5MS351IrRaHY3jUZEk0LyBXE7C0KyYLiNYNMtxqxiQT8wnl911dnPziFo6WlxrurqJC9u8vYNOmckaPfpSXX57MjBnbbI/vtsNVkOlRLXYR7wJvLpcP1hZ7FhCtGyRdNWNytclHy5w6Pvj0Avju7bz20+9RPrLSr5l1WVkHa9bABRe0MmqUvfHd4VwF10x8ilHfXE3hwYP0jh9P46JFnKgL/n1nelRLuoimbk82f1da2LOEaNwg6agZk+xuRulGHMZft5lt6hBh7NheFixo4oUXjAdepTxJEYJgroJrJj7FxF+sxO1y0V9dTV5rKxNWruTAsmUhxV0zlFwvH6yFPcdItR88VI0X64JtNln0gXPdOG608UZA5qmRCDSYoJSshdNAV8GGX5zg88UuVInxPXtKSlAKalav9gl7NtdKSWXdl0T885mO9rFrEiJS4lI2te0LNtexf/krYCkbkGA99mgJFcr39AdncF/HlT4/8MPHLuS+jispOHjI73PZGIudjrjyXHVVaWHXJESkBdtsatsXbK6nV1by9Q9Npch787LWipkyZQpLly6NupF1LIRyFVw0cSelA22+KJkudxEbjs3hHpZkdSx2rseVpxrtitEkRKQF22xq2xdsrrNGVXNmUzMvlhquD6uwT5o0iSWB3YptJJirYP7XSpn4i9/h7nThcblYPGIVzhMneDT/31mzPHtjsXM9rjzVaItdExWhatVEyjDNphDMYHPtbe/gneoq3AMDxgsWgent7eXIkSP09fUlbU6BgtY5u44Dy5YxUFlJfnMz7qpKLrxlAu6K7I/FTrTui2YQLeyaiEy+90FmL7mBmhdeoujoMUr27vfzk4dL+U9Wf9JkEGyujx05yvDuRTcAAA18SURBVNnP/43mI40AOCyt8bZt28Zll13GW2+9ldJ5nqir473bbuPN++9n709u44EPLvZ7P1tjsXM5rjzVaGHXhKVqy3amr7wLUR48xUU4+vtxHTyE9Luj8pOnq4hXPASb6+HLDdEMtnia7nrsyWiGka5qh9nS2CNb0D52TVgm37cKx4Abd3GRIWp5xiVT2NyCyo/u8smmUgSBc+18+DEgfKONdGF3LHYiJQwSJdfjylONFnZNWMxwRkd/v0/UldOJM0P95HYjplPdJ+ZD90lnByW7YrGtUSmAXyZmfX1bSmLjczmuPNVoYdeEpat2HDIwgOvgYWAA5XTi6OtD5eVlpJ/cbsRheCs9prBbep6m2xVjYkcsdqZEpeRqXHmq0T52TVj2Lb4Sle+ka/xYPPn5OLt7USK8vey6uNwrsTTEzgQ+dOpMlnz3BsoqKwB/V8zkyZNZvnw548blxpOLjkrJHWwRdhGZLyJvici7IvJNO8bUZAbmgmLn1Fp6xozi2Pnnsu2eFez796tjHiubslBNJn5oCg1Lrqa03OiWZBX2MWPGcPXVVzNq1Kh0TtE24o1KydX2ctlMwq4YEXECvwE+ARwAXhGRx5RSuxMdW5MZ2LX4GU1dmUyjq+METYePMXbSBPILC/yEvbu7m8OHDzN27FiKi4vTPNPEiLfaYToXXDWhscNiPxt4Vym1VynVBzwENNgwblaTbS6HVBBrQ+xMYNvzf+PLF/4bR/YfBPwt9l27drFo0SJ27dqVzinaQqiolPr60OWIdRmAzMWOxdPxwAeW7QPAOYE7ich1wHUAtbW1Nhw2c8n1UrbxEm0nqEzCjIrJxDh2u4k1KiVTFlw1Q7HDYg/26xtypSul7lZKzVZKza6pqbHhsJlLNhW+SiXZlIXqwxftaFzSDodYfvZGzHijZHKBWKNS9IJrZmKHsB8AJlq2JwDJfbbeuDGj3RzZ6HJIBdmUhWoymIQUOkEpVyz2eNBlADITO1wxrwAfEpEpwEHg00DsIRPRsnEj3HADhU6VsW6ObHQ5pIpsykKFIOKdonrs2UCut5fLZhK22JVSA8BXgKeAN4DVSqnkrSbdcQeUlGS0myMrXQ6aoEz7yAy+ctvNjBxjhDQ6xOET9okTJ3LzzTczZcqUdE4xbcSz4KpJDbZkniql/gL8xY6xIvLeezB6NPR2+F7KNDdHOnqPapLDmNrxjKldOPiCDFrvI0eOZMGCBWmaWWagywBkJtlXUmDKFDh2DPIHX8pEN0e2uRw0wTlxvJ2D773PpJNPoshV7Odj7+rqYu/evUyaNIkRI0akeabpQ5cByDyyr6TAV74CnZ3azaFJCbv+vpOvNyzmwJ59gH9Fx71797J48WJee+21NM1OY6KzX/3JPmGfNw9+/vOsiqzQZC++xVPP4OKpGd6YCeGOWtDS0wQ708k+VwzAvHnsmDp8H301KcSMY8ca4pgZ4Y46nT8zyg1nItkp7BpNivC5Xiz12DMhjl0LmoHOfg2OFnaNJgy+euweU8wdeDwD6ZySdx5a0EzM78L8DkBH5mSfj12jSSFTZ07nxjt+zLgpRnK1NSpm3Lhx/OhHP2LGjBlpmZtO5zfQ2a9D0Ra7xkfVlu1G7P3+Q3TVjmPf4iuH/aJ01ega5l5+kW9bRHyFkMrKyrjooouCfzAFhBK04STuOvs1ONpi1wDZ2QQjFXQcb+PVzVs50WYkxIljMCqmq6uLrVu30tzcnPJ5BQraihV7qK9v8yuhOxzQ2a/B0cKuAXRFylDs+eebfOcz/8H7b74L+LtiDh06xJe//GV27tyZ8nlpQRtk/vxWP8vc/C6GS2RQMLQrRgMYFSl7a0b6vZZppRrSgS/yhcE49kyIigGdzm9FZ7/6oy12DWBUpMzr7PJ7LRNLNaScgHrs1szTdAu7MYfw25rhiRZ2DaArUobCzC5VXr+6ZFjmqUYTDC3sGiA7m2CkhACr3Opj12gyFe1j1/jQFSmHMunkaXzvvl8yZeZ0wF/YR48ezS9+8QtOPvnkdE5RoxmCFnaNJgxllRXM/vh5vm2x9DwtLi7mvPPOC/VRjSZtaFeMRhOG9tbjvLzhOY43tQD+Fnt3dzfPP/88R44cSecUNZohaGHXaMJw4N19/Oi6b7B391uAv7A3NzfzjW98g23btqVzihrNELQrRpNSsq1swWBUzGARMFPYdVSMJlPRFrsmZWRl2YIhUTHWt9Ifx67RBEMLuyZlZGPZAp+QW8RbKeXN+BS/bY0mU9DCrkkZrv2HGChx+b2W6WULJMDdIg4HHR3iraoo3vfUsG/FpsksEhJ2Efk3EdklIh4RmW3XpDS5STaWLZgwbTI/efgeZsw+DTAzT43mFps3n8Tdd/+Ozs4GNm0qp7vbqS13TUaQqMX+OvCvwCYb5qLJcbKxbIGrtIRZ55zBiAqjvreIUFo6QH19Gy+9NIr777+CHTs+NCw7F2kyl4SEXSn1hlLqLbsmo8ltsrFsQcfxNp579AkaD3lj1b09TxcsaMLt7ubo0Yfo6npXi7omo0hZuKOIXAdcB1BbW5uqw2oyjGwrW9B48Agrl32Xb939U2rGjcHhcODxeFi3rhq3u5233/4S06b9jHXrrtDirskYIlrsIvKsiLwe5F9DLAdSSt2tlJqtlJpdU1MT/4w1mhQyGPnie4XOTgebNpUzZ47RVemkk7qHXeciTWYT0WJXSl2YioloNBlJkOqOoKivb6O+vpVf/hJOPbWDgoLh17lIk7nozFONJgwOh1fYfeGOQlHRAAsWNNHW5s1KVR7thtFkFImGOy4UkQPAucATIvKUPdPSaDKF4PXYdeciTSaTkMWulFoLrLVpLhpNxjF20gR++eSDjJpgxNpbW+OVlpbypz/9iVGjRqVrehmJtQ9rsG1N8tGuGI0mDAVFhUydNdhIQxyDrfHy8vJ0k40ANmyopLvb6XNNKQXr1lVTXOxm/vzWdE9v2KBLCmg0YTjR1sETf1zNwb3vAyAMlu3t7+/n4Ycf5q23dCoHGCLe3e30ixBat65aZ+WmAS3sGk0Y2ppbuPPm23jnH7sB/3rsvb293HbbbbzyyivpnGLGIAILFjRRX9/Gpk3lLF8+jU2bynVWbhrQwq7RRINpblrUSZftHYop7la0qKceScdFOXv2bJVo15nHP9hh02w0mtAopfC43YjDgcPhwO12M+aoh7y8PJRSuN1uHN73NPi5X0yGo8VeV5ec7GoR2a6UilhwMWsXTy+beGa6p6AZrkxO9wQyE6Xgnnvgtdfg2mthyRJj+7HHKpg0aRJLlujomFSRtcKu0WgyCxEoKYHLL8cn4kuWGO+VlGhRTyVa2DUajW1cfbV/3Lop7lrUU4t2DGo0GlvRWbnpRwu7RqPR5Bha2DUajSbH0MKu0Wg0OYYWdo1Go8kxtLBrNBpNjqGFXaPRaHIMLewajUaTY6SlVoyINALvR7l7NdAUca/sRJ9bdqLPLTvJhXObpJSqibRTWoQ9FkRkWzRFb7IRfW7ZiT637CSXzy0Q7YrRaDSaHEMLu0aj0eQY2SDsd6d7AklEn1t2os8tO8nlc/Mj433sGo1Go4mNbLDYNRqNRhMDWtg1Go0mx8gaYReR/xSRt0Rkl4jcnu752I2IfF1ElIhUp3sudiEiPxWRN0XkHyKyVkQq0j2nRBCR+d5r8F0R+Wa652MXIjJRRJ4XkTe8f19fTfec7EZEnCKyU0QeT/dcUkFWCLuIXAA0AKcqpWYBP0vzlGxFRCYCnwD2p3suNvMMcIpS6lTgbeC/0zyfuBERJ/Ab4BJgJnCViMxM76xsYwC4QSk1A5gDfDmHzs3kq8Ab6Z5EqsgKYQe+BPxEKdULoJQ6lub52M1K4EYgp1aylVJPK6UGvJtbgAnpnE+CnA28q5Taq5TqAx7CMDayHqXUYaXUDu/PHRgCOD69s7IPEZkAfBK4J91zSRXZIuzTgbkislVENorIWemekF2IyOXAQaXUa+meS5L5AvBkuieRAOOBDyzbB8gh8TMRkcnAGcDW9M7EVn6BYTh50j2RVJExzaxF5FlgTJC3vo0xz0qMx8SzgNUiMlVlSaxmhHP7FnBRamdkH+HOTSm13rvPtzEe9/+UyrnZTLDOnVlx/UWLiJQCjwJfU0q1p3s+diAilwHHlFLbReT8dM8nVWSMsCulLgz1noh8CVjjFfK/i4gHo6BPY6rmlwihzk1EPgJMAV4To+PvBGCHiJytlDqSwinGTbjfG4CIfA64DPiXbLkRh+AAMNGyPQE4lKa52I6I5GOI+p+UUmvSPR8b+RhwuYhcChQBZSLygFLqmjTPK6lkRYKSiCwFximlvisi04G/ArVZLhRDEJF9wGylVLZXoAOMKBJgBTBPKZUVN+FQiEgexgLwvwAHgVeAq5VSu9I6MRsQw6r4A9CilPpauueTLLwW+9eVUpeley7JJlt87P8LTBWR1zEWrT6Xa6Keo9wBjACeEZFXReTOdE8oXryLwF8BnsJYXFydC6Lu5WPAtcDHvb+nV70WriZLyQqLXaPRaDTRky0Wu0aj0WiiRAu7RqPR5Bha2DUajSbH0MKu0Wg0OYYWdo1Go8kxtLBrNBpNjqGFXaPRaHKM/x90788f/hnQHwAAAABJRU5ErkJggg==\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def apply_to_mg(func, *mg):\n", " #apply a function to points on a meshgrid\n", " x = np.vstack([e.flat for e in mg]).T\n", " return np.array([func(i.reshape((1,2))) for i in x]).reshape(mg[0].shape)\n", "\n", "def plot_with_contour(samps, data_idx, cont_func, method_name, delta = 0.025, pl = pl):\n", " x = np.arange(samps.T[0].min()-delta, samps.T[1].max()+delta, delta)\n", " y = np.arange(samps.T[1].min()-delta, samps.T[1].max()+delta, delta)\n", " X, Y = np.meshgrid(x, y)\n", " Z = apply_to_mg(cont_func, X,Y)\n", " Z = Z.reshape(X.shape)\n", "\n", "\n", " # contour labels can be placed manually by providing list of positions\n", " # (in data coordinate). See ginput_manual_clabel.py for interactive\n", " # placement.\n", " fig = pl.figure()\n", " pl.pcolormesh(X, Y, Z > 0, cmap=pl.cm.Pastel2)\n", " pl.contour(X, Y, Z, colors=['k', 'k', 'k'],\n", " linestyles=['--', '-', '--'],\n", " levels=[-.5, 0, .5])\n", " pl.title('Decision for '+method_name)\n", " #plt.clabel(CS, inline=1, fontsize=10)\n", " for (idx, c, marker) in [(0,'r', (0,3,0)), (1, \"b\", \"x\")]:\n", " pl.scatter(*data[distr_idx==idx,:].T, c=c, alpha=0.7, marker=marker)\n", "\n", " pl.show()\n", " \n", "for (kern_name, kern) in [(\"Linear\", LinearKernel()), \n", " (\"Student-t\", StudentKernel(0.1,10)), \n", " (\"Gauss\", GaussianKernel(0.1))\n", " ]:\n", " (sim, dec) = kernel_mean_inner_prod_classification(data[distr_idx==1,:], data[distr_idx==0,:], kern)\n", " plot_with_contour(data, distr_idx, sim, 'Inner Product classif. '+kern_name, pl = plt)" ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "22a5c812-ee34-42d5-b27b-5b3212e71336" }, "slideshow": { "slide_type": "fragment" } }, "source": [ "Obviously, the linear kernel might be enough already for this simple dataset. Another interesting observation however is that the Student-t based kernel is more robust to outliers of the datasets and yields a lower variance classification algorithm as compared to using a Gaussian kernel. This is to be expected, given the fatter tails of the Student-t. Now lets look at a dataset that is not linearly separable." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "nbpresent": { "id": "abdbdc86-9fe5-4658-adcc-b725c3b0eb9e" }, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data, distr_idx = sklearn.datasets.make_circles(n_samples=400, factor=.3, noise=.05)\n", "\n", "for (kern_name, kern) in [(\"Linear\", LinearKernel()), \n", " (\"Stud\", StudentKernel(0.1,10)), \n", " (\"Gauss1\", GaussianKernel(0.1)),\n", " ]:\n", " (sim, dec) = kernel_mean_inner_prod_classification(data[distr_idx==1,:], data[distr_idx==0,:], kern)\n", " plot_with_contour(data, distr_idx, sim, 'Inner Product classif. '+kern_name, pl = plt)" ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "66eecb99-27ad-44ea-a116-7d2736209377" }, "slideshow": { "slide_type": "fragment" } }, "source": [ "In this dataset, the Linear kernel is not a good choice, simply because the classes are not separable linearly in input space. Gaussian and Student-t work, and Student-t shows slightly better robustness properties." ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { "id": "8575ad05-c6ee-4dc0-8a37-9d27d05930d3" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## The kernel mean map\n", "One of the objects we looked at, the kernel mean map is particularly interesting. In fact, for so called *characteristic* kernels, the integral\n", "$$\\mu_\\PDK = \\int \\PDK(x, \\cdot) \\mathrm{d}p(x)$$\n", "preserves all information about the distribution $p(x)$, like e.g. characteristic functions, while not even assuming that $x$ is numerical (remember that the only restriction on the codomain of $\\PDK$ is that it be nonempty).\n", "\n", "When we have an estimator $\\widehat{\\mu}_\\PDK$ and a function $f \\in \\RKHS$, we have\n", "$$\\int f(x) \\mathrm{d}p(x) \\approx \\prodDot{f}{\\widehat{\\mu}_\\PDK}$$\n", "because of the reproducing property. In other words, integration for functions in the RKHS $\\RKHS$ is just a dot product in $\\RKHS$. The unfortunate restriction being that functions in the RKHS are real valued (or complex valued in the more general case).\n", "\n", "**Lemma** If a kernel is *strictly* positive definite, it is characteristic.\n", "\n", "Thus the Gaussian and Student-t kernel and many other kernels induced by densities will be characteristic. The embedding gives us a distance measure between distributions for free.\n", "\n", "**Definition** The *Maximum Mean Discrepancy* of two distributions given their kernel mean embeddings $\\mu_\\PDK, \\nu_\\PDK$ is defined by\n", "$$\\mathrm{MMD}(\\mu_\\PDK, \\nu_\\PDK) = \\|\\mu_\\PDK - \\nu_\\PDK\\|^2_\\PDK$$\n", "\n", "Furthermore, marginalization, the chain rule and Bayes rule can all be represented as operations in an RKHS. Also, independence tests for random variables operating in a RKHS have been proposed." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" }, "nbpresent": { "slides": {}, "themes": { "default": "8bb3c166-b694-42e2-9585-0561e49677aa", "theme": { "8bb3c166-b694-42e2-9585-0561e49677aa": { "id": "8bb3c166-b694-42e2-9585-0561e49677aa", "palette": { "19cc588f-0593-49c9-9f4b-e4d7cc113b1c": { "id": "19cc588f-0593-49c9-9f4b-e4d7cc113b1c", "rgb": [ 252, 252, 252 ] }, "31af15d2-7e15-44c5-ab5e-e04b16a89eff": { "id": "31af15d2-7e15-44c5-ab5e-e04b16a89eff", "rgb": [ 68, 68, 68 ] }, "50f92c45-a630-455b-aec3-788680ec7410": { "id": "50f92c45-a630-455b-aec3-788680ec7410", "rgb": [ 155, 177, 192 ] }, "c5cc3653-2ee1-402a-aba2-7caae1da4f6c": { "id": "c5cc3653-2ee1-402a-aba2-7caae1da4f6c", "rgb": [ 43, 126, 184 ] }, "efa7f048-9acb-414c-8b04-a26811511a21": { "id": "efa7f048-9acb-414c-8b04-a26811511a21", "rgb": [ 25.118061674008803, 73.60176211453744, 107.4819383259912 ] } }, "rules": { "blockquote": { "color": "50f92c45-a630-455b-aec3-788680ec7410" }, "code": { "font-family": "Anonymous Pro" }, "h1": { "color": "c5cc3653-2ee1-402a-aba2-7caae1da4f6c", "font-family": "Lato", "font-size": 8 }, "h2": { "color": "c5cc3653-2ee1-402a-aba2-7caae1da4f6c", "font-family": "Lato", "font-size": 6 }, "h3": { "color": "50f92c45-a630-455b-aec3-788680ec7410", "font-family": "Lato", "font-size": 5.5 }, "h4": { "color": "c5cc3653-2ee1-402a-aba2-7caae1da4f6c", "font-family": "Lato", "font-size": 5 }, "h5": { "font-family": "Lato" }, "h6": { "font-family": "Lato" }, "h7": { "font-family": "Lato" }, "pre": { "font-family": "Anonymous Pro", "font-size": 4 } }, "text-base": { "font-family": "Merriweather", "font-size": 4 } } } } } }, "nbformat": 4, "nbformat_minor": 1 }