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@tanutarou
Created October 15, 2017 11:50
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最小二乗法、ガウスノイズモデル、ベイズ線形回帰モデルによる多項式あてはめ
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.core.pylabtools import figsize\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline\n",
"import numpy as np\n",
"figsize(12.5, 4)\n",
"import seaborn as sns\n",
"sns.set(context='paper', style='darkgrid', rc={'figure.facecolor':'white'}, font_scale=1.2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# データの準備\n",
"3次の多項式に平均$0$, $\\sigma=2.0$のガウシアンノイズをのせて、データを生成。多項式のパラメータはランダムに生成。"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True parameters\n",
"w=[ 7.02419783 1.10560521 -0.72663653]\n",
"b=0.5\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7f51adeff0b8>"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ad542f60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(39)\n",
"def build_toy_dataset(N, w, b, noise_std=2.0):\n",
" D = len(w)\n",
" x = np.sort(np.random.randn(N))\n",
" xx = np.array([[r ** i for i in range(1, D+1)] for r in x])\n",
" y = np.dot(xx, w) + b + np.random.normal(0, noise_std, size=N)\n",
" return x, y\n",
"\n",
"N = 30 # データ数\n",
"D = 3 # データの次元数\n",
"\n",
"# 真のパラメータの設定\n",
"w_true = 5*np.random.randn(D)\n",
"b_true = 0.5\n",
"print(\"True parameters\")\n",
"print(\"w={}\".format(w_true))\n",
"print(\"b={}\".format(b_true))\n",
"X_train, y_train = build_toy_dataset(N, w_true, b_true)\n",
"\n",
"# plot\n",
"plt.scatter(X_train, y_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 最小二乗法\n",
"1次、3次、15次の多項式あてはめを決定的手法である最小二乗法で行ってみる。"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"(-10, 20)"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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mtLSUv/zlL1x33XXk5eVxww03MGvWrECPUfRx/m7lJoTofecTlPf4tW+aKJUVbSvmjhKf\nfuha+x1E6313mTSjo2lMSiVlYDINg+3UJI/DPSQTY9RQnyJRMzERVLXrx3ISZiZH8a3x6dy0KJ2p\nYyp8dk/1l642iDpr60khRL/W4xx50zTZs2cPBQUFDBgwgIkTJ/LHP/6RV199lfXr1wdyjKKPk8vJ\nQoS/83lDXlRcxcDallzz2gqS6ipJqqvAtvdFBlJH0/ETqE4nMVXlqK5mn3ONAQPbWilmZOCaONmn\nvaKnxWIav99azEe7HJ3eXDS2v3oQo5CbpNB67eBsj8Uvu6d2of0GUYF4oyCE6Ht6FMhv2LCB1157\njfz8fL797W8zbdo0779dccUVARuc6B/kcrIQ4a/9G3JNd5NYX0libSX6a4VExRu+7RZbVta/caqM\nNbrucz+nowagZgyiJCqeI2YiFdk5VMYlkjZ6GLMWTPYpED2bvccqvEE8eP7GfLizBFtCNJ9/XcYx\nRw1mF1cPgr24EKg3CkKIvqdHgbzVamXjxo2kpKR0+rff/e53fh+U6F/kcrIQYaKhAfXY0bZCUKcD\nrSUoX3y0iFmHi0isqyS+ocMGRaqKkZLatoPouHyM+ZdjpNl496TO1nKF8phEqmMTuHjSEKbm2Tp3\nb1Eg0T7qnP4udBWQm8DLHxzxOdZxxV0WF4QQ4aJHgfztt9/e7b8NHjzYb4MR/ZNcThYiiNoXiHZY\nMfduVuR0oDocqKerSW5/qsXiDc5j0+wUjZvMx02RlMd4eqBnTRjBomtmYCSngKXr/24uAZKO+eac\nv7W90C8r4l0F5N0xTPjnp0UAjBqSIIsLQoiwIH3kRciQy8lC+FHHAtH2LRXbHdOcTpT6Ot9To6I8\nfc7tnlzz5lG5GDY7UUOHUBuX2FYgmpTkLRAFyABOH6vA7axhfEtQbnB2HV/7/loR73i172wKjlSw\n+2iFN81GFheEEKFOAnnRZ0lvetEnGQbKqVNozpLOq+etX5e27CDa1OR7atyAtmLQQYNwT5jk2/u8\n5WtzYHyXO4hGJsTgqqrvdLy97t6Qn8vr0V/pdh2v9ikm/OWDw2cM6rsqbBVCiFAVkoH85s2befLJ\nJzFNk1tvvZWVK1cGe0gizEhvehF2XC7UstK2NJaOqS2tQXpZKUqHAlEjsWWVPM2OPmw4rhkzO3Rv\naSkQjY0N+MPoKmAHzun16O90u9aA3DRNHJX1Piv0iXERVNZ26IgjXbOEEGEi5AJ5t9vNU089xQsv\nvEBsbCzXXHMN8+fPJzExMdhDE2FEetOLkNHY2GHlvMRbINo+3UUpL0cx25aKTUXBTElFby0QHTMW\nY+48DFt65x1EIyOD+ADbdPcGemqe7bxej/5eEe/qDQLAf3RRWCuFrUKIcBBygXxBQQEjR44kLS0N\ngDlz5rB161YWL14c5JGJcBLs9nGi7/MUiHZIbXF0sYpeXeVznmmxtNtB1I5rytS2oNzetkGRkZLa\nbYFoqOruDbRC54LTYL4e279BME1TCluFEGEr5P6XKC0txWazeb+32+04nc4ub6tpCgkJZ+8lLM6d\npqlhPbdjhqXwygeH0dtV2mmq53goPK5wn99QdkFza5pQWQklJSiOEihxeD47SlCKWz47HJ5/r+tc\nIEp6OqbdDvZ0zHFjMe123OnpYLdjpg+C9HRITvYWiKotH+HibHPrrC7uMmC3RlrQVEL29bh29WTm\nXlTG4ZPVDMuIJ394aq+PQf4mBI7MbeDI3AZfyAXy50LXTarOUnglzk9CQkxYz+3g5BguGee7ynbJ\nuHSGpMSGxOMK9/kNZV3ObUuBqOp0oJV2UyDaspLeXYFoa4qLMWZ85wJRu73bAtFOTjf68dGem54U\nnJ7pNmd73trjo7rsNjNhaBLNTe6QfT0CDEmJZUiKp4YgGGOSvwmBI3MbODK3gZWaevYUv5AL5NPS\n0nxW4B0OB2PGjAniiEQ4kt70/UT7AtHWgLy6nLjCE94Ni1RHNwWiCQkY9nRPgejQHFwXz+jUvUVP\ns0NcXJAenH/1pAD8QovEu+s2M3poMqOHJsvrUQgh/CzkAvn8/HwOHDhAaWkpsbGxbN68mdtuuy3Y\nwxJhStrHhamOBaLtVtG1dseV8lOdCkRJTcWaakO323GPHotx2TxPT/SOBaJRUUF8gL2vJwXgF1ok\nfrY30PJ6FEII/wq5QN5isXD//fezZs0aDMPgO9/5jnSsEaKvqK31pLa0b6/odPp0b1GdDtSqDgWi\nmuZbIDr5ok6r560Fogmp8T6Xen1SRVIHkDu4f+4n0JMCcH8ViUvALoQQvSPkAnmAefPmMW/evGAP\nQwjRE6aJUl3VFpA7SnyD8vaBel2t76mRkd4VcsNmxzViBIY9vS0fvWUl3WxXIHpuQ5P9BFr1ZLdU\nf+2oKoQQoneEZCAvhAgBhoFSXu6T2qI5Ouwm2tJmsVOBaGxcuxVzG+788Z6gvH17RZsNMz7hrAWi\nF7JDr+wn0KYnu6X6a0dVIYQQvUMCeSH6G7e7c4Foa1Fo+1X0slIUt9vnVCMhoW0H0eyhuKZN79S9\nxZ8Fohe6oi77CbTpSQG4FIkLIUR4kUBeiL6iqalz3nn7ItGWvPSuCkTN5JS21fO8MRhz5vmktrQG\n671dIHqhK+qSKtJZT/LXJcddCCHCgwTyQoSIblNIWgtEu+x97kR1lvSsQHTSlK4LRFPTwGoN0qM+\nswtdUZdUESGEEH2ZBPJCBINpolRVtrVRdDr4aksB1YeKyKqtJLGuAou7hoSais4FohERbQWi9nRc\nw4d36n3uLRDVtCA9QP84nxV10zTZd6zC+4bopitzJVVECCFEnySBvBD+ZBgoFRWezi2tBaLdtFlM\nafTd4XOaNYrK2EQqYhOpjE3kaFwOY2eMISV3qG+BaEJiz3YQ7QPOdUXdNE2efWUX735e1CmnXgJ4\nIYQQfY0E8kL0hNuNeqqsrSi0fXDevkC01Nm5QDQ+wZvGog/JwnXRNCKHDqFuYJI3OP9HkYsXtzs6\n/diVlw1j4bSs3nqUIedciy/3FVby3hdF0qVGCCFEvyCBvOjfmpq8LRRVp9NnJb31mOZ0oJwq8ykQ\nBTBSUlqKQW3oo/JwzboM3WbDsKW35aCn2SA6utOPtSbE0NRu06JMrQL1U0dYF2W2prR8tr8UgIty\n08jLTvLL5ks9Lb4sdNagG77H+muXGiGEEH2fBPKib6qr83RqKe3QXrHjKnplpc9ppqZhpKa1dXCZ\nOInmNN/2ioEoEA33okzTNPn9W/v4sKDtqsIHO0uYNb53N1/Ktg1AU/EJ5sPtDZEQQgjRUxLIi/Bh\nmiinq7vp3lLim4NeW+N7avsCUZsd17BLOnVv0W3pQSsQDff+3fsKK32C+FYf9nJaS25WInMnD+mU\nIx9OcymEEEL0lATyIvhaC0Rbg/N2q+haa7pLyyq60qFA1IyJQbe17RbqHjvOm+7iUyCamBQWBaLh\n2r+70FnT5XGzl9NaFEXh9mvymTAsKSzfEAkhhBDnQgJ5ETjtC0Q79T5v2azI4fDsIOpy+ZxqDIz3\nBOP2dG+BqE/v89YAPW5AWATofV13qStKkNJawvUNkRBCCHEughbIP/bYY7z55ptkZmby0ksveY8X\nFRWxdu1aampqmD59Oo888ohfiuWEH3UsEO2wg6j386kyFMO38tBITm4rEB2Zi+vSOS0FonaflfSu\nCkRF6MrNSuTSfHun9JpLJa1FCCGECJigBfJXXXUVy5cvZ926dT7Hn376adauXcusWbO48847ef/9\n97nsssuCNMp+pr6+JZ3FgVJTSfTRQt989NbgvaLC5zRTVX0LRMdP8G5W1GkH0YiIID04EUiKovDt\nq0Zz8Wg7n+5zAjBVWj4KIYQQARW0QH7SpEmcOHHC55hpmuzcuZMNGzYAsHz5cjZv3iyB/IUwTZSa\n020BuaOk+1X0mtM+p8Zare3aKNpxTZveqXuLnmbHTEkJ+x1EhX9ISkt4ufbaJVRWVqCqKlZrBCNG\njGLlyuuZOXN2j+/D4Sjhpz/9MSdOHEdRFCZMmMg99/yElJSUAI5cCCEEhFiOfGVlJQkJCd7v7XY7\nTqcziCMKYabpWyDa7kPrsIquNDT4nhoT4+3eotvsuEeP8enoYtjTGTByKFVqlOSfC9HH/ed/PsvY\nseOorKzkgw/eY926h7njjh+yfPm1PTp/4MB4HnnkcQYNykDXdX7722fZsOE/WLfuiQCPXAghRMAC\n+cWLF3d5/JVXXiHCT+kVVqtGamo/7g+dNhBys8/5NAXQWj7O1Ak99fxGJXqoXz93A0zmtmc0TSUx\nMYbU1AGkpg5g5MhvYbXCb37zG26++ZtoXVxp6zy3A8jKsgHQ3NxMbGwkZWUO+R2cB5mzwJG5DRyZ\n2+AKWCD/+uuvn/M5iYmJVFVVeb93OBykpaX5c1hCCCHOYN68eTzxxBMcPXqUu+66i5KSki5v97Of\n/YwlS5Z4v58yZQp1dXVomsaTTz7ZW8MVQoh+LaRSaxRFYdy4cWzZsoVZs2bxt7/9jeXLlwd7WEII\n0W+0Lp5UV1ezadOmHp/3+eefU1tby8svv8yQIUMCNTwhhBDtqMH6wQ8//DCrVq1i7969zJo1i3ff\nfReAe++9l2eeeYb58+cTHx/PnDlzgjVEIYTod0pLSwGIj48/53Pj4uJYvnw5d9xxB6Zp+ntoQggh\nOgjaivy6des6tZ4EyM7O5pVXXgnCiIQQQrz33nskJCQwdOhQFi1aRHFxcZe3e+SRR1i6dGmn47qu\nU1ZWRkNDAzExMYEerhBC9GshlVojhBAiOCorK3nnnXfYsGEDd999N5qm8cYbb5z1vM8++4zo6Gjy\n8vKora3lF7/4Bfn5+RLECyFELwhaao2/GYbBypUrueuuu4I9lD7llltuYdmyZSxatIhf//rXwR5O\nn1FZWclNN93EVVddxZIlS3jrrbeCPaQ+57HHHmPGjBlcd911wR5KSLvpppuYOHEiCxYs4PXXX+fJ\nJ5/kxhtv9LnN5s2bWbBgAVdccQUvv/yyz7/V19dz3333MWXKFK688koaGxt55plnevMhhLU777yT\niy66SP7vCoAjR46watUqFi9ezIoVK/j000+DPaQ+o6mpiWuvvZZly5axePFiXnrppWAPqc9paGjg\nsssu4+mnnz7j7RSzjyQyvvTSS3z88ccoisL69euDPZw+o7a2lri4ONxuNzfccAOPPvooo0aNCvaw\nwl51dTWFhYXk5+dTXl7OihUrePvtt4mKigr20PqML7/8koiICNatWyf/yVwAt9vN4sWLef7554mN\njeWaa67hxRdfJDExMdhD6xO2b99OXV0dmzZtkv+7/OzkyZM0NTWRk5PD4cOHuf3223n77beDPaw+\nwTRNb/pcfX09S5Ys4dVXX2XgwIHBHlqfsX79egoLC8nMzOTee+/t9nZ9YkW+qqqKN954g+uvvz7Y\nQ+lz4uLiAM9/5m63O8ij6Tvi4+PJz88HIDk5mYSEBKqrq4M8qr5l0qRJPhvMifNTUFDAyJEjSUtL\nIzY2ljlz5rB169ZgD6vPmDZtGrGxscEeRp+UkZFBTk4OADk5OdTW1koRtp8oiuJNn2tubsY0TQzD\nCPKo+o5jx45x5MgRZs2addbbBi2Q7+6S15ku4XZn/fr13HHHHahqn3hfEnLWrFnDjBkzmD59uqzG\nB8DevXsxDAObzRbsoQjRSWlpqc9zU3bcFuHo3XffZfTo0SiyW7nfNDY2snTpUubMmcMtt9wiCyd+\n9NRTT3H33Xf36LZBK3aNjIzk8ccf97nk9eabb/LUU0/xwgsveC/hzp8/nzVr1nR5H6+88gqHDh3i\n9OnTTJs2je3bt/fyowh/PdmB94UXXqCuro61a9fy9ddfM3LkyN4cYtjqydyePn2aH//4x112cBJn\n1hu7Rwshwt/Jkyf55S9/yXPPPRfsofQpUVFR/P3vf6eiooIf/vCHLFiwgJSUlGAPK+y98847ZGdn\nM3ToUL766quz3j5ogXxGRob369ZLXjt37vRewgW8l3DPtEvsjh07+Pzzz5k7dy5NTU3U1dXx85//\nnJ///OeBfgh9Qk934I2NjWXGjBls2bJFAvkeOtvculwufvjDH3LTTTcxadKkXhpV33E+u0eLc5eW\nluazAu8OlAbrAAAgAElEQVRwOBgzZkwQRyREz9XW1nLHHXfw0EMPkZWVFezh9ElJSUnk5eXx2Wef\nsXDhwmAPJ+zt3LmTN998k3/+85/U1dXhdruJi4vje9/7Xpe3D4n2k62XvMrKys75Eu4NN9zADTfc\nAHiKhv785z9LEO8ndXV11NfXk5qaSnNzMx9++CHf+MY3gj2sPuORRx5h7NixXHvttcEeihDdys/P\n58CBA5SWlhIbG8vmzZu57bbbgj0sIc5K13V+9KMfcf311zNz5sxgD6dPqaiowGKxMHDgQGpra9m+\nfbv8X+Yn99xzD/fccw/gucJ85MiRboN4CIGuNSdPnuTmm2/mueeeY9++fXzxxRc8+OCDAPz+979H\n13VuueWWLs91u3XCtm6lvBztnrtR//T/MObORf/N/8DQocEelZemKeh6uE5u6JP5DRyZ28CRuQ0c\nmdvACZW53XmojMf+73b0djWhmgoP3TyN/OGpwRvYBQiVue2rNm16jSNHjpyxa01QV+Q7XvIqLy8/\np0u4pglVVfW9MVT/06Lhmd8QsXg5cfeuxTJxPHUPPEzDLbeBpgV7dCQkxITv3IYBmd/AkbkNHJnb\nwJG5DZxQmdu9h0/5BPEAugF7Dp9iSEp4di4Klbntq66++uqz3iZobV66uuTV/hJuXV0dmzdv7vOX\nw5rnL6Dyw+00rlxN3E//jYQlC9AO7A/2sIQQQgjhR9m2Aagdmuaoiue4EOcraIH8li1b+OSTT9i4\ncSPLli1j2bJl1NfXc//997NmzRqWL1/OzTff3C82HTEHDKT2l+upevUN1FNlJM69hJjH10G9vMsV\nQggh+oLcrERm5qd7g3lVgZn56eRlJwV3YCKsBT1H/kK4XHrfu6TT0EDMfz5NzH89g5GeQe2Tv6R5\n/oJeH4ZcLgssmd/AkbkNHJnbwJG5DZxQm9t9xyo45qwh2zYgsEG8aYLLBS4XiunJ6TFRoLWXvtLF\n11YrnMOePKE2t31NaurZr9ZIIB+itINfE/fju4n4aAtNi5dR+9iTGIMyzn6in8iLM7BkfgNH5jZw\nZG4DR+Y2cEJybk0TGhtRT1ejVFejVFe1+7oapa4Opb4Opb4epaEepb4eGho6HVMaGsHtQnG5wO0C\nlxvF3RK86/r5DU3TIDIS0xoBERGYkZGYVqvnWESk51hMLGZcHNbEeJoiojDjBmDGeo6ZcQMw4uIw\n4xMwExMxEpMwEpMgNrbtjYPokZ4E8iHRflJ0po8YSfVfNxH515eIe/gBEi+5iPofP0DDd74HFvm1\nCSGEECHBNFFqa1BOnUI9VYZaXo5afgrlVBlq67GKcpTqKpTqatTqapTT1SjNzV3fnapixsZhxsRA\ndDRmdAxmTNuHkZaGGR0DMTGYkVGYERGeuMBqxbRYwWrxBN4Wa8sxi6eJRuu6rWn6ft3us+J2Q1OT\nZ2yuZpTWr5ubUZqbPJ+bmjxvNOpqoaIMa/Vpz/e1NSi1td0/rogIjMQkb3BvJiZhpKZh2GwY9nTP\nZ5vd85GSGhKNP8KBRIShTFFouvZ6mudfQey/ryP2Zw8StfFFap54GvfF04M9OiGEEKLvMgyU8nJU\nRwmaoxjV4UB1lLR9OJ2eIP1UWZfBqxGfgJGcjJmSipGUjD4qD3NgPGZCAkZ8vOfr+ATM+HiMgfGY\n8S0fsXFhs3Ld5dWO5mZPUF9VhVpZgVpZgVJZ6flc0fJ9VSVqeQXWo0dQSx2o5eU+d2GqakuQb8cY\nlIE+ZAjG4CHomUMwhgxBHzwEMz4hbOYpkCSQDwNmQiK1v1xP46obiLv/bhKXLqDx6mupe/jRXk23\nEUIIIfoE00Q5dQrtRBHqieNox4+jnjyOVlKCWlKM6nSgOh2elJV2jJRU9PRBGHY77vzxGKmpmMkp\nGMkpGCmpGMkpmCkpGEnJEBERpAcXZBERmEnJmEnJGAzr2TnNzailzpZ5d3rnX3U60E6eIOLdf6Gd\nOI7S1OQ9xRgw0BPcDx6Mnj0UfdgI9GHD0YePwLCn95sgX3Lkw42uE/WnF4h9/BGUhgbq77yb+tt/\nCNHRfv0xIZlT2IfI/AaOzG3gyNwGjsytn+m6JxAsKmJAhZOmrw+hHj/uDdyVoiK0pkbvzc3oaPSM\nTIz0DAy7HSN9ELrdjmH3BO2GPR0jzdZ/g/Nu9Orz1jBQy0pRjxehHS/yfC4qQjteiHb0CGpRIYrR\nUtQbE4t72HD0YcPQc4ajjxiJO28M+vARYfU7lGLXPkypriLm6aeI/t3/YAzKoPZnj9G8eKnf3oHK\nfyqBJfMbODK3gSNzGzgyt+fB5fIEc8eOoB092vK55aPwmE+6izEwHiNzMHrmYPYYcexwxeIckMap\n+FRyLh7LddfN6DcruP4UUs/b5ma0Y0fRDh1EO3wI7fBBLC2f1VOnADAtlpagfrQnsG/5bGQODsnf\nvwTy/YD29QHiHvo3Ija/S/PMWdQ+9hT66O53w+2pkHpx9kEyv4Ejcxs4MreBI3PbDZfLE5wdOewb\nqB89gnq8yNuZxdQ09CFZGENzPGkWQ3PQs4aiZw5mwNhRVOFZhd17rIJfbdyB0S7yURW45/oJ0s/9\nPITL81apKMeyby/avj1Y9u3FsncP2v59qHW1gOeNnntcPu7xE3FPmIhr/ESM7KFBD+6la00/oI8c\nRfWfXyHiX/8g9qGfkDj3EhpXf4P6+x/ASB8U7OEJIYQQZ6VUV6Ed/Brt0EEsB79u+fprtGNHPZ1U\nADMy0hOkZw+lacFVnmC9JXA3Mgd7eqB3JSEGWoLNQmeNTxAPYJhwzFkjgXwfZiYl47rkUlyXXNp2\n0DBQjxe1BPa7sezcQeTf/krMf2/w/HNCAu78tsDePXlKSNYlSiDfFygKzVcspHn2XKJ//1tifvUL\nol55mfrvfZ+GH6zFHDAw2CMUQgjR3xkG6skTaAe/xnLoa7SDBz3B+sGv0Uqd3pvpgzLQh4/ENfsy\nGr7zPfThniJGI33QOW1W1JVs2wBUhU4r8tm2s698ij5GVTGysmnOyqb5yqu8hxWnE2vBV1h2fIVl\n51dEvfhHYjb8CgA9IxPX1Gm4pl6Me+rFuEePDXqbTEmt6YOU6ipiNqwn+rn/xoyLo+6eH9P4zZvP\nqcAjXC6XhSuZ38CRuQ0cmdvA6VNza5qoJcVY9u1B27cPy/69aPv3YTl4AKWhwXOTiAj0nGHoI0bh\nHjECffhI9BEj0YcNx4w7/6DaNE32F1Z6d07NzUokMTHWO7emafKHf+zno4ISDNMTxM/MT+dbC/P8\n8tD7mz71vO1O6/P5i8+xfvoJ1s8+wVKwE8XtxoiNwz35Ik9wP206roumQUyM33605Mj3c+qJ48Q+\n9e9EvvQiRlY2tT/9Oc1Llvco56tfvDiDSOY3cGRuA0fmNnDCdW6VinIs+/e15B63Be3q6WrA0w3G\nPSoXPXc07pG56CNH4h4+EmNIlt83N+wuSF+7enKnud13rMIb7EtKzfkL1+ftBauvx/rVF1g//QTL\np59g/exT1NPVmBERuKZMxXXpbJpnzsY9aXL3KV89IIG8AEDbvYu4Rx8mYvO7uCZMpO7fforrsvln\nDOj77Yuzl8j8Bo7MbeDI3AaOP+a2q9VoxV/FenV1WA7s8wnatf17vSkxpsWCPnwE7tw8T9CeNwZ3\nbp4nYO+l1IPuClkfvmUaQ1Jie2UM/Y38TWhhGGj79hLx0QdYP9qCdetHqLU1mDGxNE+fgWvmbFyz\nZuMeM+6c0sNCOpC/88472bZtGzNnzmT9+vUAFBQU8MADD9DU1MSyZcv4wQ9+cMb7kED+3Fg/2Ezs\nE+uwfvkFrqkXewL6mbO6vK28OANL5jdwZG4DR+Y2cC50bv2WMmKaqE4Hlt0FaHt2Y9m9y/P1kcMo\nLeGCnpXtCdTzWoL23NHow4YHvT/3W9sLeXnz4U7H1yzM5bLx0vwhEORvQjfcbiw7vyLiww+wfrgF\n62efoDQ2YqSk0Dz3cprnX0HznLmYCYlnvJuQ7lpz4403snz5cjZt2uQ9tm7dOtavX09OTg6rV6/m\n8ssvZ9SoUcEaYp/jmn0ZVbPmEPGvfxDz1OMkXL2Y5pmzqPvxT3FPuzjYwxNCiH6ndRXdUV2MPT7q\nvFfR9xVWeoN48BRzflRQwrQ8W/epI263p/B0z66WgH0Xlr27vD23jbgB6GPG4pozl4bv/wj36DG4\nR+VBbGiubndXyDosIz54gxL9k8WCe/JFuCdfBGvvhcZGrJ9tJ+K9d4h4922iXnoRU1VxXzSN5nmX\n0zTvCvSx486r3WXQAvlp06axfft27/dOpxPTNBkxYgQAS5Ys4f3335dA3t9aO9zMX0DEm68T+4t/\nJ3HJFTTPnU/djx/EPXFysEcohBD9Qner6DddmXvOKTJna6uonK729M7eXYCldaV9/17vlvd6Ribu\nseNo+ObNuMfm4x4zFiMr+4K7xPSm3KxEZuand5rP/OGpsmosgisqCtels3FdOpu6nz2KeryIiHf/\nRcS7bxPzzNPEPr4O3Z7uWam/8iqaL50D0dE9uuuQaT9ZWlqKzWbzfm+329m2bVsQR9THqSrNi5fS\nvHARka+9QswvnyBxwWU0zbuc+rX3wYK5wR6hEEL0aV2ton+4s4SqmiZ2H604pxSZ9qvRA+urGe48\nzIjSQ1z5ZTmJRw+gFR4DWnLZR+XhHjOWpmtWeoN2MzH8Cz4VReFbC/OYlmeTQlYR0ozBQ2j81i00\nfusWz2r9tq1EvPNPIt/+B9F//ANmTAzNcy+HTX87632FTCB/PjRNISHBf21++q2bb8L85o24X3yR\niF88ReSSKzBnzybxx/+GOe/MRbHi/GiaKs/dAJG5DRyZW/9yVhd3WkU3gV1HKmg9bJiwdVcJcy8a\nQv7w1M53UlGB8uUXzPjiCwZ9+B4D9+8i7XQZAE3RcVgvmoS5dCnu8eMx88dDXh5ERqIBGhAZwMcX\nLNMnxDC93ffyvA0cmVt/iIEVS2DFEgzTxNizB/Xvr2H9eGuPzg6ZQD4tLQ2ns21DCIfDQVpa2hnP\n0XVTLpf505Jr4KrlRLzxdwb+13osVy3ENWky9T+6l+YFC8PqEmuokwKhwJG5DRyZW/+yx0d1yukG\n6NiBQjdgz+FTZFldWAp2ejeqse74Cq3omOecmFiG5I+ndNFSPhw0gqiLp5J96aTOf7cbdGjoX79D\ned4GjsxtAGTmwB13wR130cVb905CJpBvTas5ePAgOTk5vP7666xbty7Io+qHNI3mpStwr7mB+r/+\njZj1TxN/02rceaOp/9E9NC1d4ffev0IIEW780eqxq5zuMUOT2HO0gsjGeoaVHmG48xAjnIe56OXj\nRB8/5vnZ0dG4x42nacGVuMdPxD1hkqdrjKYRCeT6/+EKIUJU0NpPfve736WgoICGhgbi4+N59tln\naW5u5sEHH/S2n/zhD394xvuQ9pOB432XbZpYP/6ImPVPE7FlM3rmYBpuvZ3Gb3wTc8DAYA8zbMkq\nRuDI3AaOzK2Hv3cHPbD3OM1f7SCraD8ZRQeo+3g7iSVFqJg0WSIozxpJ4uzpuCZMwj1+IvqIkbKg\ncg7keRs4MreBFdJ95P1BAvnA6erFadn5FdG/+TWRr72CGR1D4zduouG7t2NkDg7SKMOX/PELHJnb\nwJG59ehu46F7rp9w9uLK+npPx5gCT2qMZedXaF8fQDFNzIgI3GPG4h4/keMZIzlgG0bClPHkDred\n+T7FGcnzNnBkbgMrpPvIi/DjHj+Rmmd/R91DjxD9f54l6oXfE/1/fkPT0uU03P5D3BMmBXuIQgjR\nJX/temqaJp/tc56x1aNXY6OnR/uOr7AU7PDktB/Yh2IYmBYL7tFjcU2dTsOttxN16XSqMnIwrVaf\ncY7KOvOGMUKI/k1W5EWXevIuW6k5TdSfXiD6ud+gHS/CNW06DTffStOipUHf4S/UySpG4MjcBk64\nzq2/UmFa72fLzpJO/xahu3hwYiQjSg9jKdjhCd7370VxuzE1DT13NK4JEz057eMn4M4bA1FR3vMT\nEmKorKzza8qO8AjX5204kLkNLFmRFwFlDhhIw23fp+GW24h84+9E/e45Bt52M0ZqGg1rbqLxmzdj\nDMoI9jCFEP3cee16eob70XQ3WeVFDHccYnjpYYY7D5FzqhBNd2OqKvqoXNzjJ9J44zc9QfuYcT3a\n3MVf4xRC9B8SyIsLZ7HQtOxqmpZdjbZnN9H/+1tinv1vYv7zVzRfuYiGm2/FNXOW9KMXQgTF2XY9\nPSO3G+3Afqw7v8L+zy384qsvGVp2jAjdhYHCiaQManLH0XDnd3GNn4R7zFiIje39cQoh+qUeBfLf\n+973WLVqFbNnzz6vnELRf+hjxlL79DPUPfwIkS+9SPT//paEa5bgHjGSxjXfonHlaszk5E7n+St/\nVQgRXnrjtd9+19NWquI57kPX0Q5+jWXHl1h3fuVJj9mzC6WxEYDBQ3L4LCGTD0ddykHbMI6m5dAU\nGc09108gzQ+Bdo/HKYQQLXqUI//BBx+wceNGDhw4wIoVK1i5cqW373swSY584Pgt7800sX60hej/\n/S0R/3wTwLNKf+MaXLPngqb5vZVbOJC8wsCRuQ2cs83tuQblvfHaN02Tfccq+OuWIxxz1GC2/pyx\nNm4ZacWy40vv5kqW3QUo9Z7H584eSsWIMRRljsI6dQqD5l+COTA+YOOVHPnAkb8JgSNzG1h+bz9Z\nWlrKX/7yFzZu3EheXh433HADs2bNuqBBXggJ5AMnEC9O5dQpol7+M1F/eh7Lgf3ogzJoXHUDuy9d\nyuMflZ9fK7cwJX/8AkfmNnDONLfnE5SfqY1jblbiBa/Ut45p686T2CpLGOE4xKTa40yqLWLg13tR\n62oB0Idk4x4/Adf4ibgnTMQ1Lp/ff+Ls9rHsO1bhHZe//ka1n9tA3H9/Jn8TAkfmNrD8Gsibpsn7\n77/Pxo0bOXHiBEuWLOGLL74gNjaW9evXX/Bgz4cE8oET0BenaWL54jOi/vQCka/+FbWulp2Dx7F5\n9Bw+Hj6dhsgYAFZeNoyF07ICM4Ygkz9+gSNzGzhnmtvz6a3+1vZCXt58uNPxa+fkUFrZcH4r04aB\ndvQwlp07qN6yjaot2xhWeoSY5gYAygakoEyeTNT0qRxNH8He5KGkjxjs80bhgvrEnyd53gaOzG3g\nyNwGlt+61mzYsIHXXnuN/Px8vv3tbzNt2jTvv11xxRXnP0LRPykK7ilTqZ0yldp1T1Dxv3/E8n9/\nz9p//he3v/M/fDZsCh/kzWHoNaODPVIhRA+dT6FmdznhKkrPure0C9o9H19h2VWAWnMaAC3Fzon4\nLP46ZQWHbMM5bMuhOiaBWfl2jpfVcaywBvNYOeqX5T5vFKToVAgRLnoUyFutVjZu3EhKSkqnf/vd\n737n90GJfiQujsQf3MYfhs9m/Uc7uXTfh8zZ9wEPvvY4xpbf0LRkBY3XXo976jRQ1WCPVgjRjfMp\n1MzNSmRmfnqnlXezw/0AmIZB+Ze7iPyy1BO0F+zAUrDTG7TrGZm48yfQ8P07PWky+RPZW6fxHx1W\n1gG2FDh8vjdM2LKzBAWYmmcjKy1Oik6FEGFBNoQSXQrG5TJvXmhaHGPrion660tEvvIyWkkxekYm\nTYuX0rR4Oe6LpoZ9UC+XIwNH5jZw/J0j36pjTvi+I6f403P/IMdxmBHOQwxzHmZY6RFimz0/Wx+U\n0baxUkvQbqamnnVMPaEqcMk4O4qi9GrRqTxvA0fmNnBkbgPL78WuoUYC+cAJmRenrmPdtpXI114l\n8o2/o54qQ7en07xoCU1LluOaNh00rctTQ7mlZcjMbx8kcxs4PZnbcy7UdLs9LR937cSye5fnc7uV\n9rK4ZA7bhuEaP5H8lZd3G7T3ZEylFfV80MWurB215sMDvVZ0Ks/bwJG5DRyZ28CSQF6ct5B8ceo6\n1u3biNz0NyJe/zua04GRkkrToqU0LbwK1yWzIDIS6J22dhciJOe3j5C5DZwLmVvTNPl6/0lOf/ol\nI8qOkll8CMueXVj27fX2adcHD8E9ZpxnpX3CRPYmZnPQFem3QHrfsYouU2260tvF9vK8DRyZ28CR\nuQ0svxW79rbNmzfz5JNPYpomt956KytXrgz2kEQo0DRcM2bimjET/v0XWD77lMjXXyPy9deI/sPv\nMGNiaZ4zl6YFC9k9aqpsdS5EELReCSv5uoi8ykJyyo5i2VVA3SefM91RhGYa6IpKxaBsBky/iKZl\n1+Ael4977DjMRN/X5vCWD3/pmJMPYEuMorSqEVPy4YUQYSjkVuTdbjeLFy/m+eefJzY2lmuuuYYX\nX3yRxMTETreVFfnACat32aaJtmc3kW+/RcTbb2H98gtMReGAbQSfDbuIT3OmcCwlGxQlZFpahtX8\nhhmZ28Dpcm4NA7WoEMue3Vh27aTkvW0kHNpLSm05AK6ISBpGjmarZuNw6lCOpOVQmDwEd0Rk0PaK\naJ/+k5uVGBJX7+R5Gzgyt4EjcxtYYbkiX1BQwMiRI0lLSwNgzpw5bN26lcWLFwd5ZCJkKQr62HHU\njx1H/d33ozidlG98lao//5VrP/0ra7b+PypiE9k5JJ/0gctQsxdj2OzBHrUQ4aeiAusnn6Pt3Y1l\n314se/d4UmPq6wBwxSdSGz+EnbmXciQthyOpQ3EkDeKSCZmdc9OD2M4xLzvJ5+d+a2Ee0/JssgmT\nECLshFwgX1pais1m835vt9txOp1d3lbTFBISYnpraP2KpqnhO7cJQxn40F38c8x8/mP7IfKK9jCx\naCczS/eQ+vO74ed3Y44dhzF/Hua8+ZiXzoKY3n2sYT2/IU7m1g+ammD/fpTdu1F2FaDs2e35+uRJ\nEgDTYoHcPMyxYzGuXoE5dizmuHxePdTAC/840OnurJEWNBV0o+2YpsKYYSkh87uaPiGG6UH8+fK8\nDRyZ28CRuQ2+kAvkz4Wum3JJJ0D6wuWy1fOGM2FYEseceSTbvg3ZSZxyOonYspmIDzZj/dOLWJ55\nBjMiAtfki3BNn4Hr4ktwTZkKcXEBHVtfmN9QJXPbvU6dnDIHohUVYvn6ANqBfVj27cGyZw/qoYOo\nuhvwtHp0jR6DfvV1REyZxOms4ejDR0BERKf7tydUdNl/fcLQJJqb3D7pK5eMS2dISqz8rlrI8zZw\nZG4DR+Y2sMIytSYtLc1nBd7hcDBmzJggjkiEs46X0E2bjaaVq2haucqTW79/HxEfvIf1461E/+9v\nif3VLzE1zdOb+uJLcE2/BNe0izETOtdoCBE2mptRjxzmo5feo/bLArLKT5BZcZykqmIsrmYAjNg4\n9LzR7B6Uy/aMSzmakkVRahYTp47w5otbE2LQz/CfdncbPI0emszoocmSviKEEH4WksWuixYt4oUX\nXiA2Nparr76aP//5z1Ls2sv65btsw0A7sB/rtq1YP9mKddvHaE4HpqKg5+bhmjQF96QpuCZNQc/N\n67Z/fU/0y/ntJf16bhsa0A4fwvL1frSv92M5cADt4AG0I4dR3J4V9trIWIqSB3M8aTAnUgYzdcVs\nBl06BSMjk72FlfyqQ3vG1p7qedlJPZ7bc+4lL/r38zbAZG4DR+Y2sMJyRd5isXD//fezZs0aDMPg\nO9/5TpdBvBB+p6roeaPR80bTePOtYJqoR49g3b4N66efYP3yc6L+9AKKaWLGxOIaP8Eb2LsnT8FI\nHwQhsuGUaBPKG4OdF7cb9XgRliOH0A4fQjty2PtZPXEcpWVtxkhJxT0qF9eMmTR8+zts0xN54bhG\nVUyCz/PUmjMMe+ZgAAqdNZ16rBvnUZTa8UqYEEKIwAi5QB5g3rx5zJs3L9jDEP2domDkDKMpZxhN\nq7/hOVRbg2XHV1i+/Bzrl18Q+deXiPn//hMAIzkZ95h83GPG4h47DvfYfE8usdUazEfRr4X6xmDd\nMgxUp6NDoN4SuBceQ3G5ADCtVvTsoejDhtO0eBl6zjD0Ubm4R4zCTE72ucuoYxWc3rgDztAvPds2\noMscd+mpLoQQoSkkA3khQpUZNwDXzFm4Zs6ioeWYWnwSy5dfYNldgGXvbiI3/Y2Y3/yX5/aRkbhH\n5eEeOw49bzTuEaPQR46C+JHBexBh5kJW1PcVVobsxmBKdRVaUSFqYSFaUSFa4VHUopavjxd5dzs1\nFQVj8BD0nGG4Zl9GY84w3MOGo+cMx8gcDJae/RnvLn+9/Tz05DZCCCFChwTyQlwgY1AGzYMyaF68\n1HtMqazwbJCzuwDL7l1Yd3xF1F82ojR7CgvN2FgSho9EHzESfeQob4CvD8mCyMhgPZSQc6Er6v5K\nFTlnpolSUYFafBKt+CTqyRNox4vQCo+1BOvHUKuq2m4eHY0+eAh6VjauWXNoHJKNnpWNPmw4elY2\nREVd8JAURTlrv/Se3EYIIUTokEBeiAAwE5O8K/debjda0TG0r78mrugwesFutIMHiHjrDdS6Ws95\nioKRPsiTLpGVjZE91Pu1nj3Us4V9OOd3n6MLXVEPSKqIaaJUVaIWF6MVn0AtLkYtPoF28iRqSbEn\naC8pRmloaDtFVTEyMtGHZOEeO47mqxajD8ny/F6HZGOmpfXa77Un+euS4y6EEOFBAnkheovFgp7T\nkhKREENNa6W/aXoCwINfU/bVXpoPHMRW6SBhzy60Nzahnq723oUZE4OePghjUIYn4M/IwEjPwBg0\nCD09A2NQBmZiIqhqkB6kf13oinqPU0VME+rqUMtKUUtLUUudno8yZ4fvy1BLnd4cdWh585Vmw8jI\nwBiUSfPoMZ7fSUYG+iDP78Sw2XucAiOEEEL0lPzPIkSwKQp6+iD+787TfNRkYmTloWa3pJBcmYtS\nVYl27KgnLePkSdSSk2jFxWiHD2L98ANUpwPFaNsy07RYMJKSMVNSMZJTMFJTMJJT2r5PScVMTMQY\nMBAzPh5z4EDMAQNDMvg/5xX1pibMsjqOfnoQ5/FSBkca3BrhYlnUCWqKnaTq9aT+qwF1YwVKZQVq\nZcA1bSAAACAASURBVAVKZaXnc0vaUytT0zBS0zwfaWm488ZgzrZhpHmO6fZBnuDdni4FzUIIIYJC\nAnkhQsDZUkjciUm4J07u+mSXy7NaXNyS2lFW6lk5Li9HPVWGWlyMpWAnavkp1MrKbsdgDBjoCeoH\ntgT3sbGY0TGYUVGY0dGY0dEQ5flsRkVjRkdBRCRoGqamefrqWywtX1tavtcwVU+/fcXQwTA8D05v\n/Vr3vAkxDNB1TzDd2IjS1ITS1MjkxkYe3F9MaUklVreLCL2ZQXEa2Ts01NpalJoalNpalNrTns8t\nwfjUDo8tAc+GR2ZSEkZikueNjM2Gnpvn+b7luCdot2Gk2TCTkkLyzY0QQgjRSgJ5IULABaWQWK0Y\nGZkYGZln/0EuF2pFOUpVFcrpapSa06jV1SinT6NUV6PWnEaprvJ8X1+HUluDeqoMGhpQGhtQGhtR\n6us9wXZDPYqun/+D7oapqp43DFGRmJFRTI6MpFG10qBasMbGEB0Vh2mJRM8cjBk3AHPAAMy4OMwB\nAzjRqPDajlPUWaOpj4imISKGuug4bllzCbkj0/0+ViGEECKYJJAXIgT0Wv9uq9WTr22z++f+WlbS\nTZeLP/1zH58UFKMaOqppMCZzILdeNcoT7CuKZ3Vb00BVMRW15fuWz63HoqLOmEve3PLRnU+3F/JR\n3eFOx49WNpN74Y9WCCGECCkSyAsRAsK2f3dLEL7vZA3vHajGjIz1/tPHFVD7cTlrr5vQa8PJtg1A\nU0FvKxmQDY2EEEL0WRLICxECwr1/d6GzBrOL4wVHKth3rKLXHktuViJzJw/h3c+LwusNkRBCCHEe\nJJAXIoSEa//uM614B3zzpXYUReH2a/KZMCwpLN8QCSGEEOdCAnkhxAXLzUpkXE4Su45U+BwPVlpL\nuL4hEkIIIc5F0HqrPfbYY8yYMYPrrrvO53hRURFXX301l19+OQ8//DCm2dUFeyFEKFEUhbUrx5Of\n0xY8S1qLEEIIEVhBC+SvuuoqnnvuuU7Hn376adauXcu//vUvqqqqeP/993t/cEKIc6YoCmuvm8B9\nqyaw8rJh3HP9BL61MC/YwxJCCCH6rKCl1kyaNIkTJ074HDNNk507d7JhwwYAli9fzubNm7nsssuC\nMUQhxHmQtJbQde21S6isrEBVVazWCEaMGMXKldczc+bsHt9HRUU5Tz75KHv37qa+vp733vu4258B\ncMUVC7nvvgf8+jiEEEJ4hFSOfGVlJQkJCd7v7XY7Tqez29tbrRqpqdJWLlBkbgNL5jdwZG67pmkq\nzz//PBMmTKCiooK3336bRx99mPvuu4/Vq1f36D5SUwdyxRXzWbPmRn70ox91muv2P0OcG3neBo7M\nbeDI3AZXwAL5xYsXd3n8lVdeISIiIlA/VgghRA8kJSWxatUqGhsbeeaZZ7juuuvQNK1H561evbrT\nFVUhhBC9L2CB/Ouvv37O5yQmJlJVVeX93uFwkJaW5s9hCSGEaGfevHk88cQTHD16lLvuuouSkpIu\nb/ezn/2MJUuW9Og+v//972OaJhMnTuSBBx4gIyPDn0MWQgjRIqRSaxRFYdy4cWzZsoVZs2bxt7/9\njeXLlwd7WEII0We1LpZUV1ezadOmC76/p59+mjFjxuByuXjmmWf4/ve/z6uvvoqiKBd830IIIXwF\nrWvNww8/zKpVq9i7dy+zZs3i3XffBeDee+/lmWeeYf78+cTHxzNnzpxgDVEIIfq80tJSAOLj4/1y\nf5MmTSIyMpK4uDh+8pOfUFhYKGk4QggRIEFbkV+3bh3r1q3rdDw7O5tXXnklCCMSQoj+57333iMh\nIYGhQ4eyaNEiiouLu7zdI488wtKlS8/pvmUVXgghAiukUmsuhGEYXH/99WRmZrJ+/fpgD6fPuOWW\nWzh16hRut5uFCxfygx/8INhD6hMqKytZu3YtZWVlaJrGHXfcwcKFC4M9rD7lscce48033yQzM5OX\nXnop2MMJOZWVlbzzzjts2LCBu+++G03TeOONN7q87ebNm3nyySf59a9/za233srSpUtpbm4GoKmp\nCUVRiIiIoLi4GKfTydixY3G5XGzYsIHMzEwyMzN786GFlTvvvJNt27Yxc+ZM+b/Lz44cOcIDDzxA\nbW0tVquVn/zkJ0ydOjXYw+oTmpqauPHGG3G5XOi6zje/+c1OG3yKC9PQ0MBVV13FokWLuPfee7u9\nnWL2ka1TX3rpJT7++GMURZE/hn5UW1tLXFwcbrebG264gUcffZRRo0YFe1hhr7q6msLCQvLz8ykv\nL2fFihW8/fbbREVFBXtofcaXX35JREQE69atk0C+xdy5cykv///bu/P4KOr78eOv2SPZZHMDCRDO\ncIYjRaykUIrciHIpIIIgWECBihcetf2CiFalammr9aDaH4KKHPVAUVQuQVTqBVFAThMVcpCEZJPN\ntbszvz9CAsGEBNjd2dm8n48Hf2QzO/PeYTL73s++P+9P3uk+8laSk5OZOnUqw4YNq/M5brebUaNG\nsXLlSux2O+PHj+eHH36osU1iYiJbt27l8OHD3H333fz000/YbDZ69+7NAw88QOvWrX390gxr9+7d\nOJ1O3nnnHXnv8rLjx49TXl5OUlISR48eZe7cuXz44Yd6hxUUNE2jtLSU8PBwSkpKGD16NG+++SZR\nUVF6hxY0li1bRkZGBq1atTpvIh8UI/IFBQVs3LiROXPmyBu2l0VERACVb+Zut1vnaIJHdHQ0KSkp\nADRp0oSYmBgKCwslkfei2hada+y2bt16wc9JS0ujc+fO1ZNiBw4cyG233VZri+FOnTp5ZcJsY5Ka\nmsru3bv1DiMond0tKSkpieLiYjRNk5IvL1AUhfDwcAAqKirQNA1VVXWOKnikp6dz7NgxBg0axLFj\nx867rW6TXb1p2bJlzJs3r3olQeFd06ZNo1+/fvTt21dG431g//79qKpKQkKC3qEI8Qs5OTk1rs36\nFuoTIhBt2bKFbt26SRLvRWVlZYwZM4aBAwcyc+bMGgt6ikuzdOlS7r777gZtq9uIfF21a1W1mJqm\nMXv2bCZOnHjexaWOHDmCw+GQUY2L1JCFu1atWoXT6eTOO+/k0KFDdO7c2Z8hGlZDzq3D4eD++++v\ndeK3OD9ZdE4I0RDHjx/niSeeYPny5XqHElRsNhsbNmwgPz+f+fPnM2LECJo2bap3WIa3efNm2rVr\nR/v27fnmm2/q3V63RD40NJRHH320Ru3ae++9x9KlS1m1alV1LebQoUPPu7jUnj17+PLLLxk8eDDl\n5eU4nU4WL17M4sWL/fdiDKyhC3fZ7Xb69evHjh07JJFvoPrOrcvlYv78+UyfPp3evXv7KargcTGL\nzokLFx8fX2MEPisri+7du+sYkRANV1xczLx581i4cCFt27bVO5ygFBcXR3JyMl988YU0bfCCvXv3\n8t577/HBBx/gdDpxu91EREQwZ86cWrfXrRYlMTGRpKQk4Ezt2t69e6trMe12OwMHDmTXrl3n3c+U\nKVPYuXMnW7du5W9/+xuDBg2SJN5LnE4nJ0+eBCpr4Hbu3Fn9fyYu3UMPPUSPHj2YMGGC3qEIUaeU\nlBQOHjxITk4OTqeTbdu20b9/f73DEqJeHo+HO+64g0mTJsk162X5+fk4HA6g8sPS7t27ad++vc5R\nBYcFCxbw8ccfs3XrVu6//34mT55cZxIPAdK1ZvPmzbz++utMmDCBr776ij//+c8ArFixAo/Hw8yZ\nM2t9ntvtQf/og5PZrODx+PfkWnr2QB0+HPWpv3lvn0ntUG+civrwI17bpzfUdn7N14yEcDuedet1\niio46HHtNhZybn3HL+c2Kwtrm1a4V6xEmzLFt8fSw5EjWLt1xb3pA7TBQ6ofru3cKq+9hmXGTbjy\nC+B0Uwdf0zSN59/4ltZPLSH1yG7mzXqOwZe3Ye74FL8c3xfknuBb77zzNseOHQvsrjVn164dOHDg\ngp6raVBQUOKjyBq3mJhwv5/bWFWlotyF04vHjfOolFW4KQmw66S28xulKVBegSPAYjUaPa7dxkLO\nre/449yGbtyEFSi8rA9qEP4/KkooTQHn8Rwqznp9tZ1bW+4pIoGCCsBP52J/ej5bvvyR6afzXo8K\nW778kV4d4khuF+eXGLxN7gm+dd1119W7ja5tXs6tXautFrOq5ZkQF80oXQosFpAWn0IIHwnZ8hHu\n5G6oLVrqHYpPaKd7mJschfVuq5SWoIWFgR+73WVkF6FWDV6fLidQNUjPLvJbDCL46JbI11a7JrWY\nwuuMVHtltqBIIi+E8AVVJWTbZiqGDNc7Et+xWtHC7SiFDUjkS04n8n7ULiES0znjSial8nEhLpZu\npTU7duzg888/Jzc3lzVr1gCVbQ7vu+8+pk2bhqqqzJo1i9jYWL1CFMFA0wBjjMhrFguKx6N3GEKI\nIGTZ8zWmvDwqhtS9im8wUKOjURwF9W9YWooWbvd9QGfp2jaW/ikt4OPKn00K9E9pYdiyGhEYdEvk\nBw0axL59+37x+JAhQxgyZEgtzxDiIhmltMZsltIaIYRPhGz+EDUiElef3+gdik9p0dGYGjQi7/T7\niLyiKMwYmUzZRwlE/mxhwaReksSLS6b7ZFchfMpIpTUWKa0RQvhGyAfv4xo4GKxWvUPxKS06BqWg\n/hF5paTE7yPyVZpE2wgNtUgSL7xC18muQvyCLxJvg4zIaxYLeCSRF0J4l+mHY1i/3Uv56LF6h+Jz\nlaU1gVkjf+bgxnhPEsYgibwIHD64uSmaZpybptkCbqmRF0J4V+g7b6HZbJQPu0rvUHxOi2poaU0J\nhIf7IaI6GOjLYhHYJJEXwc1QpTVmKa0RQnhd6NtvUjF0hN8WPtKT1tAR+dIStDAdE3khvEQSeRH8\nDDIiL6U1QghvMx85XFlWM2ac3qH4hRodXW/7SU3TKD3l4OcSjQPp+fh9gXuDvCcJY5BEXgQ5o5XW\nSCIvhPAe2ysvo8bEUH7VNXqH4hdaVMx5S2s0TePlTd+Tl5nHwTwXT63Zw8ubvvdjhNWR6HBMEYwk\nkRfBzVClNdK1RgjhRRUV2Na+RtmESWCz6R2NX2gxMSglTnC5av39gYxTfJKWSairgnJrCKoGn6Rl\nciA938+RCuEd0n5SBD+DjMhXltbIZNdgoBQXYf1sF+YD+zE5HGjh4XjaJ1Hx2wFo8fF6hycaiZBN\nGzHl5lI2dYbeofiNGhUNgFJYiNa06S9+n5FdhKqBzVVGuaXyw42qQXp2kf/aQRrkPUkYgyTyIrB4\newTdSCPyJpOU1hicKf0Hwpc9ge2t/6KUlqJGRKLFxqIUF2E6dQqAit8NpHTuH6gYMlze0IXvaBrh\nzz2D64pUPN266x2N32jRlYm8yVGAp5ZEvl1CJCYFQt3llFtDK7dVKh/3KyO9N4mAJqU1InD4Kqkx\nSrIkpTXG5XYT/tRS4n77a0I3f0jJ7XeTv+tL8o7+TP5X35F3MIO8bw9RtOwZFEch0VMmEj1hLKYf\njukduQhS1k8/wfrVF5TcfrfeofiVGhUFwGe7DtY6kbVr21j6p7Qg1FVOuSUUkwL9U1rI4kzCsCSR\nF8HNSH3kLRZQpbTGaJS8PKLHjyb8icconXMbebv3ULLgfjydOte49tSE5pTdeBMFH26n8OXVmDN+\nIHZwf0LXr9ExehFMNK2yC8v7uzPQHn8cd9duVAwboXdYfqNpGuv35AHw+acHa53IqigKM4Z0wKq6\n6ZHShgWTejFjZLJ/AzXKe5IwBEnkRXAz0NeXmiwIZTim4z8Tc/UQLAcPUPjGuzgXPlR/r25FoWLk\nNZza+gkVI64iat5s7H+6V+ZHiEtS1Y3lqTV7OPqfdcTu3sl7g2+sLNlrJA5knOLjH5wARJQVV09k\nTTtyssZ2SnERAN1T2uo3Em+g9yYR2HT7C7/99tu54ooruOuuu6ofS0tLY9SoUQwbNoxnnnlGr9BE\nkNGMMvohpTWGomRnEz1+NEpFBafe24KrX/8Ler4WFU3Rcy9R9NgThL20nKjZM6CszDfBioBVNYr+\n5sdHLqmneVU3FsXtZtbH/2FfYjIv2bo1qm4sGdlFFIXa8SgmIssqk3VVg6PHa7ajVIqLAdAawQJZ\nIvjplsjfeOONLF26tMZjS5YsYdmyZWzatIkdO3Zw8OBBnaITQUPDOF9jWsyyIJRBKAWniJk4BsXp\npPC/G1CTOlzkjhTKZt6K46VVhHy0ieibbpBkvhE5exR91fvfX1JP86puLBP/t57E/OP8e+AsVBTS\ns4u8HHXgapcQiWIyUWyLIKrUAVROZO2QGF1ju+pE3u7nCa6nGWZwSRiCbol8amoqdru9+ufs7Gw0\nTaNTp06YzWZGjx7N9u3b9QpPBAsDfX2pyYJQxuDxEHXr7zFlZlK4fgOepI6XvMuKUWMoXLUG62e7\niJo5DSoqvBCoCHRVo+jq6dtUVSnI/h/yqmvdGzpK3y4hkh7H93HD52tZmzqBowkd9OnGoqOqiayO\nsCgiS4uqJ7KmdGxWY7uAGJE30HuTCGwB034yJyeHhISE6p+bN2/OZ599pmNEQg+KT25uBhn9sFhQ\nPB5jTdBthOyPPYz1420UvrYeT5euXtuva+BgHP/vFaKmTyHytlsoev4/jaq+uTGqGkU/m6rBf3cc\nIyOr8ndVyWh9EzK7u3K5/L0nOdSiM6v73tAou7EoisKMkcmE/K0FPaM1FkzqVevrr6qRl9IaEQwC\nJpG/GGazQkxMuN5hBCWz2eT3c2s2m1FCrV49roJGWHgIoQF2ndR2fpWoyp9jIkMrO9iIi+LLa1fZ\nsAHLP/+G59HHsF83xvsHmHAtHlZhm3ID1g5JqI897v1jXAI97gvBrHuHprzx8VE86pnHFCA9q6h6\nwFbVYNe3mQy+os0vRpar7d2LZdI4aJlAxUvruLHUSofE6Lq3D3LmNi2ILC+jda9WlT+fc90qWuWq\nr1GJ8aDD9WyyWTGZgiN/kXuC/gImW4iPjyc7O7v656ysLOLrWQHR49EoKCjxdWiNUkxMuN/Pbayq\n4ip3UezF4zbRoLTURWmAXSe1nd/Qcg9RQEGuo9Esp+4Lvrp2TdlZxN4yi/LhV+GYOQ98dU0NvZqw\nxX8hYvGfKWnWgrLfz/bNcS6CHveFYKHk52HZ9x2m4z9jzsqEsjK6qip3HS8hrVDhVHgMWTEtCOnS\nkaMna86T8Kiw72gubZraa+7U5SJsxYvYH1mMJ6kjha+to2WLlrQ8/evG+n8VERWDZd+31a//3Os2\nNCev8l7rMfvu7/g8wstd2DxqUPz/yD3Bt5o1q780LmAS+aqymsOHD5OUlMS7777LkiVLdI5KGJ6R\nylSqRuGlTj7wqCqRt88Fk5miZf/y+TVVOvc2zD+mE/Gne1Fbt6Zi2FU+PZ64cJqm8X3GKdKzi2iX\nEEnXtrEoZ18XZWWEbNtCyOYPCPl4G+YfM6p/pUbHoIWFgcnE74qKuLLIceZ3FivHoxL4Ka4Vx2MT\n+TkukazYliSXRWLKtKKUlmBK/wHr559hW78G0/GfKbvxJoofWQrhMjIKoMU1wZRfd7ceU3ERmtUK\noaF+jEoI39Atkb/llltIS0ujtLSUAQMG8Pzzz7Nw4ULuvPNOysvLGTt2LF26dNErPBEsDJjIKx43\nMg0qsNheeZmQbVsofHUtWjM/lCsoCsV/+SumHzOInDOLgk1bKxeYEgGhqttM1UTVs+vYzd99i+21\nlZVJdkEBnrbtqBg6HNev++BO6YWndRsIC6u5w/JyYsqLcH7zLeZDB8ndshv7kUMM3r+NJs7TCenr\nNZ+iRkVTPmoMpTNvxdMzxT8v3CDU2DiUvLw6f68UF+tbH2+U9yRhCLol8suXL6/18Y0bN/o5EiEC\ng2auGpGXhYECiZKbi/2RBymbMMm/I+NmM0XPv0TMVYOJuukGCjZtRYuO8d/xRZ1q6zaT9eEOzC/c\nT9yn21GbNqNsyk2UTZqCp2ty/YlbaCgkxOKKaorrykG0mj2HA+n57M0uooMdumkFKIWFKE4nWlgY\namIinvYdZDJ0HdQmTTA5i6G8vNZR98pEXuduPtK1RnhJwJTWCOELigFH5KW0JrDY/7IYPCrFDz7i\n92NrUdE4Vr5OzIhBRM6dhWPVGjCb/R5HMKi3FOYC9vPFgezqJL5D9hGmfPY6fY59iaNlWxz/Wk75\nuPFgtXolzk5tY3ErbS9qX42VFtcEANOpfNTmLX7xe6W4SDrWiKAhibwILF4fpTDQqIelMkGT0prA\nYfliN2GvrqTo0b+indUe1588HTtR9PyLRE2dhP2xh3H+32Jd4jCy85XCXMx+duzNJCnnGJM/e53f\nHP0fJ6Kb8/er7qD3ovkkdzx/kwZ/xNnYqbGVLSeVvDyoNZEvRrPrmcgbZHBJGIIk8iJw+Grk3CAj\n8prp9EirjMgHBo+HiPsX4OqRQtmMWbqGUjHsKpx/fpCIRxbj7tGzcsRXNFhdCy+lJidcUJ/1Axmn\n+GnLZzzw6ev0O/I5WdEJ/H34fLZ3H8hve7W6pCTem3E2dlqTynNlys+jtkJF3WvkQUprhNdIIi+C\nm6YZZ/BDSmsCim3Fi1i/S+PUxo8Coq9/6fy7sHyXRuQd8/B06Ii756/0Dskw6lp4KT27qMEJsvnA\nftr+aSH/3PUR2VHN+OewP7C12yA8ZgtX/qoF070wau6NOAWop0trlFO1d65RHIWoTRtnj30RfBo0\nU2bOnDls3769QctEC3ExNE2jvMJDRnZRg5ckDzpVXWtUtZ4Nha8pOTnYH3uE0inTcF+Rqnc4lRSF\nor8/i7tDJ6KmT0HJydE7Iq/QNI0D6fm8vzvDZ3/77RIiMZ3zgd6kVD5eH8veb4iacSNxV/6G5kf2\n8a9hc5lz87N81HMYHrMFkwJ9kr1TdnUpcYoztOgYNJMJUx2da5TCQn0njiuKjMgLr2lQIj958mTW\nrl3L0KFDeeaZZ2os3CTEpaqqCz1ZWMqRnx08tWYPL2/63ls7N05pjVlG5ANFxJKFYFJw/t9DeodS\nU3g4jpWrUcrLiZ4+GUpL9Y6ohgtNyqv+9p9as4d1245692//rGNomkbb5pHVt4Kq2vM6R7lVFcv2\nrZiuHUvssCtR9+zB8eQ/cHyxh5KpM1At1obt5wJ1bRtL/5QW1cm8t/ffaJhMaLGxmPJrT+RNhQVo\n0dF+DkoI32jQ98VXXnklV155JTk5Oaxfv57rr7+e5ORkpkyZwoABA3wdowhyVXWhE31RF2qgRL5q\nsqsk8vqyfv4ptrWrKfrrMrSmTfUO5xfUVq0pXLmamHFXE3nnPIqe/09AXOMXM1HzfDXhXdvGXnKX\nmXNjAmjfPIIJAzvWem8xZZ4g9K03sL38EpZjR/mxSWtevuoOdiYPoF+zVsyw2ZgxMpnU5ITquLyZ\nZCuK4tP9NyZqXJO6S2sKC1GllasIEg0u/NQ0jX379pGWlkZkZCSXXXYZr7zyCm+++SbLli3zZYwi\nyEld6GlnLQgldOJyEXH/3bh6XUbZtBl6R1Mn9+VXUPT080TdcjOejp0pufcBvUO6qImaVX/70SUF\nJOX8QLwjh3jHSZp/u4qTxU4sJwtpr5got9r4uUUcXXq0RU1IQG3eErVFC9QWLVHjE+psyXluTJXH\nLAYq39MOHsmm6LMv6JrxHa0+30rIF7vRLBZOXjmCf/x6BmmJPao/JJ39Wqr++Yqv998YaLFxtZfW\neDyYHIX6jshLaY3wogYl8v/85z95++23SUlJ4eabbyY19UzN6PDhw30WnGgczq4LVU43XvRaXaiB\nRuSltEZ/YS+9gPn7AxRs2hrw/drLx43HefgQ9icew9OhI+XXTdQ1ngv5QK6cyifkow+4asO7jPh8\nNwmOM/X++fZYiE8guxzCLSGYVBWbKwdb1iEsaZ8Qkn8S5ay/Ec1kQo1PQG3e/EyC37wFalQ01swS\n+h8pwG2yYHOVYXOVEessoOmuZyk58RN9Thwl1F1BhdnKTz360Owfz1IxYiSbDheTtu1og16LCExq\nXBNMebm/eFwpcgCgxciIvAgODUrkrVYra9asoWktXzO/9NJLXg9KNC5VdaFVCbdX60I1Dc0gifyZ\nrjWysqseTFmZhP/1McqmzsB92eV6h9MgJff8EfPRw0TeMQ81oTmu3/5Ot1iqPpCfnczX+EBeVkbo\nu29jW/0q1k93ong8hPVMIS11IKusrTic0IHcqHh+07sNCXHhrDsnkQaYOKgDI69ojXLyJOasE5gy\nMzFlnsCUnYkpMxNz5gmsn+3ClJmJUuSgn6rS76znexQTjrBIsqKb80NMc7b27cP+xGSOxnfAbbFy\nZUwL+jgU2sZHnP+1iICnNovH8s1Xv3hcKSio/H2U1MiL4NCgRH7u3Ll1/q5169ZeC0Y0TlV1oWEP\nh9EhMYoFk3o1zlEvKa3RlX3xnyHEivPPi/QOpeFOd7Ix5eQQNXUShf/dgLv3r3UJpeoD+bk18t3s\nHsIfWojt1ZcxFRTg6vMbiv/yVyquuhq1ZSJtgD7p+cSfVRN+ID2/7kTaZEJLSMCdkAC/uqzugDQN\nraKC1RvT+CLtOCUWGy6z9bzf0H28N5OdaZn8tmfzWl9Lo7wvGZQaH485O+sXj5schYDOI/KKUrnq\nuBBeoH9zZCFOs1nNtE2IpImX3iw1TUNTNfZnnKI8Pf+il2T3F80sk131Yt35MbY31lO07Jnq5d0N\nw2bDsXI10RPHEn3DdRS8vQlPcje/h3HuRM2OoS56bVhJ2NzlaIqJsqnTKZs2A0/nLr947rk14XV9\nKLigRFpRUEJDmXLdFVzWuwPp2UXk5Jfw8d7M8z5N1WDXt1ksmNRLJp0amBqfgJKXC56a33BWjchL\n1xoRLAIykd+2bRuPP/44mqYxe/ZsJk7Ut/ZTGE9Vt4q7NI1vDuXy/po9gb/UuSwIpY+KCiIeuAfX\n5VdQNnmq3tFcFC0iksLX1hMz7hpiJoyhYO1beLr30CWWblEav351BbYXX0DRVEpn3krJvNtRMqyx\nQwAAE+9JREFU4+Iqu9Dszqi3C423u7dUfVA4kJ7PznMmv9amqh5+ZGpbSeANSo1PQFFVlNxcaHKm\nJEoprByRV6Nj9QpNCK8KuETe7XazdOlSVq1ahd1uZ/z48QwdOpTYWPmjEw1X1a3i7tM18oZY6rwx\nlNY4nYS++zaWw4dQmzSl/OpRqG3b6RpS2PP/wnzkMAUfbgdTg5bWCEhabBwF6zcQc/04YsZdTeFr\n6/y6mJVScIqw5/9F2PLn0FwuDlx9A45bb6PDZZ0ALrg1JXi/e8u5I/0ACbE2cgrKajQRkXp441MT\nKhfpMuVkQ5f21Y+bCk4BoEVF6RIXIF1rhFcFXCKflpZG586diY+PB2DgwIHs2rWLUaNG6RyZMBIj\ntrQ807UmOCe7Wj/9hMhbf485OwtPy0RMeblEPPgnysZdR/HDS9ESvLM65oUwZaRjf+pxSn8/G3dK\nL78f39u0Zs0oeGsj0TdeT8yEMRT941nKx4336TEVRyFhLzxL2AvPolSU89WAcTydNIL88FhMH/1M\n/2wPfZITLrg1pU9irWWkv2vb2Fo/ZATqfUI0jBp/OpE/WXMBS1NeLmpsLFiteoQlhNcFXCKfk5ND\nwllv6M2bN5eVZBsTL41SGHKp8yBeEMr6+adET7oW1+VXUPD2+6hJHVCKiwh9Yz32Rx8iblBfCles\nxt3HfyPIaBoRf1yAGh1DyQML/XdcH9OiYyhY+xaRd84j6pabKUnbi/OBhV5PXBRHIWEvvkDYc8+g\nlJZQetPN7L329zy+9ZcJuwIB9cH63JF+WYQp+KjNKgcDTTk5NR5Xck+iNm2mR0hC+ETAJfIXwmxW\niIkJ1zuMoGQ2m/x+bs0WM0qo1SvH/c2vwhhyNB/ldGmN2QSDL29D316tvBDppav1/CouAOyhZsKD\n6bp2OLD8YTba5ZejbNpElM1W+XhMONz+BzyTJmC+fgIx112DZ81atGsu7du3hl67yvr1WLZ8hHvN\nOqJbN7+kYwacmHBYswbPk08QtvD/CNu1A/e/X4SUlHqfqmka3x7N5ejxQjokRtOzQ9PqWnaz2USM\ny4np6X9ieu5ZKClBnTkLz333Y23Vip8+PoKq1ZxMqmpgDbVgNoFHPfO42QTdOzQNmHt4317h9NXx\n+Hrcc4NaTDhaTAz2UydRzjq35sJT0DxB13NtCgtBUQiK/2+5bvUXcIl8fHx8jRH4rKwsunfvXuu2\nHo9GQUGJv0JrVGJiwv1+bmM9Kq5yF8VeOu7kIR0xodG7Szw9rq9saRko10ut57e4nGZAicNJeYDE\n6Q0RCxZgycvj1H/fRS1Toeyc1xYaCWveJmr2dEImXU/hytW4Bg+76OM15NpVHIXE3nUn5cOvwjFw\nOATR+a5h9m1YeqcSecc8LL/pQ+m0GaRNmM0hNbzWCadVk8Rrq2W3fLuXqHWvYVn5MmgapTfdTOnc\n+agtEyufXFBC82hbrW0je7WPo6LcXWO/v+3ZgjZN7QHzN6k3Pe65wS62ZStcR9OxeNTqcxt9IhMt\npgkOHc91eJmLMC048he5bn2rWbP6qwgCLpFPSUnh4MGD5OTkYLfb2bZtG7feeqveYQkD694ujjIj\nfFUehF1rzEcPY3tlBc7Ff0Ft177uDW02HC+uJOrmG4mePoXCV9fhGjDQZ3FF/Ok+lOJiih970jAr\n/14s9+VXcGrzTsKeexrLP/7OZatWUtqpL5u7DeKLq4dy0+gzo/RVk8RVDdA0Wp/MoNmLb2B79Csi\nD+5Di4+n5NZ5lM6eh1bLAoF19pJv34Ru7ZtI+YrwK09iIqbjP9V4zJR7ElfHTjpFJIT3BVwib7FY\nuO+++5g2bRqqqjJr1izpWCMujVEStaquNapaz4bGEfbs02hNmlI6Y2b9G4eG4vjPK0RPnUT0TZMp\neOMdnyxuFPLuBmxrV1O07BnU1m28vv+AZLPx1bUzecHRhZF73mfIvq0MOvAxFW/9hdLuKYR27oga\nF0d8poPbj54goTCHdrnpRJQ7KTeHkPPrfqgrXiN84rWUOF11Hqa+tpHe7kIjxPmoLVth/d9nnD09\nw3QyAGrkpWuN8KKAS+QBhgwZwpAhQ/QOQwQLoyTyVQtCuepOlIzElJ2Fbc1rlCy4H8LCGvYkm43C\nFa8SM3EM0ZPHU7DhAzxdul5SHJqmVfYvzy6ik7mU1HvvoHzESMqmTLuk/RpNRnYRRaERrE2dyNo+\nE+iUdZhuJw4w1HOCxIx0LHu+pq1bxVRuJjeiCW9dPobDCZ3Y37o786emktwujnCrFaj/+pSEXQQC\nT6tWhL55nOo+YB4PSn5e9URYIYJBQCbyQniF0UY8FKVyddcgKa0JXfMaKAqlN8+6sCdGRFD46jpi\nxl1N9MSxFLz7IWqbthcVw9k134rbzV/WL6LUpVL61NPG+YDnJVWdnFQNUBQOt+jM0Zad6TypF/bT\nSbemaWyQVowiSKgtEzE5CvEUFQFmlLw8FFXVf0ReCC+SRF4EFm/m3lWJvJESNqs1aBaEsr2xnorh\nI9FiLrw0TotrQuHat4gZNZzoiWP54tk1HHbb6l0R9Fxn13zP3rGCLpkHWThxCSNLLATwGr8+UVf9\n+tlJurdXVBVCT57WpwcAfvgB2nTE/FMGAGrr1jpGhZTWCK+SRF4EDl8l3AZK5DWzBVzGT+TNB7/H\nsv87nPf88aL3oTZvQcHaN7GNGErCTRP5x8RHKA2LaNCKoFWqFgYb9u1HjPnmXZYPnMV3id1JDuCF\nwXzlQpJ0KY0RwcDToSMAyqFDlYn8j5WJvOciv+ETIhAZdz1yIepjxBEPiwWCYEQ+9M11qJFRVAwd\nfkn7+c4UxwNjFxHvOMmDbz6MvcTBJ2mZHEjPb9Dz2yVE0v/wp/xh83Ns6jmMdy67JvAXBvOx5HZx\njExtK4m6CHpa06aoUdEohw8BYPoxAzUi8qK+JRQiUEkiL4KXwUprNE3DbTJzOD2XA+n5aEb8IHJa\n6PsbqRgxEqoWf7pIGdlF/NC0HYuvXUTiqRM8sfqPJORnkp5d1KDn9/rkHe7d+BSfderLc0PmYDIp\nUvMtRGOhKHg6dqwckQfMP/5YOd9G7/cEKa0RXiSJvBABoGpSZnGFyvdHTvLUmj28vOl7vcO6KKas\nTCwH9lMxeOgl76tqgubBll24Z/JSFDSeWn0vV3yztc43Qk3TOPj9CfJmzCbq7vmUT5mKuuJlxg/p\nzIJJvRpcliOEMD5PUkc4WHkvNf+YLmU1IuhIIi+Cl4FG5KsmZbpNFsyqB1XjgkpIAol1+1YAKgYM\nuuR9VU3QNCmQGduS+6Ys5UTPPiQvuoPosSMJ2fQelJWdeUJuLrvmLqLLNf1J+uAN/j1oFs8MnUty\nx3gpJxGiEXL/qhdKWhqUlWHZ9y2ezl30DkkIr5LJriLoaQZI5KsmZXpMJkxqZddjVYN0A03K1DSN\nA+n5NFv9Nk3adOZ7p5lkTWtwh5na1DZBM27xOAo/eJ/wJx4j+qYb0EJDUVu0BJcLU+YJBqkquzr1\n5ZXf3sjPca0wfZtFarfmhjmPQgjvcaX2RamoIPSt/2LKzcXVJ1XvkCrfk6S0RniJJPIisHjz5mag\nG2VVCYnHZMZyOpE30qRMTdNY8f4BPtl7gpf3fsaWboN5ec1eBvyq4R1mzufcLioVI0ZSMfwqzAf2\nE7JzO6bjxyEkhD1qFC9UtCE/4sy2RvtAJITwHnf3nmh2O/ZHlwDg+nUfnSMSwrskkRcBw+sj5wYq\nrakqIfGcLq0x2kI8BzJOsTMtizZ5PxFbUkhamxQAdqZlkpqc4JvXoSh4unWntFv36ofc6fkUrt0D\n6pnNjPSBSAjhZVYr6vQZmJ/9FxX9B6DFNdE7IiG8SmrkhQgAVSUkTeLsdG5hN9ykzIzTXWS6njiI\nisL3LSrrULXTo+H+0rVtLIMvb4Pp9Gc3o30gEkJ4n/rQEkruWIDj+f/oHUolRfHu4oeiUZMReRG8\nDFRaUyXUbqNNkzDiDJZ4Vo14d808SEbTNpSGhgOV71f+HA1XFIW541Po1SFOViYVQlSKjsb55wf1\njkIIn5BEXgQvA5XWVDNbUNzGWxCqa9tYfpfSnK4rDrIvsVv147/TaTRcViYVQgjRGOhWWvPII4/Q\nr18/rr/++hqP//jjj1x33XUMGzaMRYsWGXpRHBEgjJTIWyzgcukdxQVTFIXf921O6/yf0VJTufJX\nLbj3BmOVBwkhhH9I1xrhPbol8ldffTXLly//xeNPPvkkd955Jx999BEFBQVs377d/8GJ4GDAG6Vm\ntYLHeCPyANavvwQg9eaxTB+ZLCPiQgghhI/plsj37t2bmJiYGo9pmsbevXsZMGAAAOPGjWPbtm16\nhCf04ovk20gj8mYzisuYibzlqy9RY2LwdOiodyhCCBHYDDjQJAJTQNXInzp1qkZy37x5c7Kzs+vc\n3mo106yZtJXzFb+f22/3YgXCvLbDSNA0ory2P++q9fyeXhW1mZ9j8YonHoMnHguI2OW+4Dtybn1H\nzq3vBNS5fXgRPLwoIO6V3hBQ57YR8lkiP2rUqFoff+ONNwgJCfHVYYUQQgghhGgUfJbIv/vuuxf8\nnNjYWAoKCqp/zsrKIj4+3pthCSGEEEIIERQCakEoRVHo2bMnO3bsAOCtt95i0KBBOkclhBBCCCFE\n4NEtkV+0aBE33HAD+/fvZ8CAAWzZsgWAe+65h7///e8MHTqU6OhoBg4cqFeIQgghhBBCBCxFk0bt\nQgghhBBCGE5AldZcClVVmThxInfddZfeoQSVmTNnMnbsWK655hqeeeYZvcMJGqdOnWL69OlcffXV\njB49mvfff1/vkIJOXYvOiQu3bds2RowYwfDhw1m3bp3e4QSV22+/nSuuuELeu3zg2LFj3HDDDYwa\nNYprr72W//3vf3qHFDTKy8uZMGECY8eOZdSoUaxdu1bvkIJOaWkpgwYN4sknnzzvdkEzIr927Vo+\n/fRTFEVh2bJleocTNIqLi4mIiMDtdjNlyhQefvhhunTpondYhldYWEhGRgYpKSnk5eVx7bXX8uGH\nH2Kz2fQOLWh8/fXXhISEsGTJEnmTuQRut5tRo0axcuVK7HY748ePZ/Xq1cTGxuodWlDYvXs3TqeT\nd955R967vOz48eOUl5eTlJTE0aNHmTt3Lh9++KHeYQUFTdMoLS0lPDyckpISRo8ezZtvvklUVKA2\nfDaeZcuWkZGRQatWrbjnnnvq3C4oRuQLCgrYuHEjkyZN0juUoBMREQFUvpm73cZcqCgQRUdHk5KS\nAkCTJk2IiYmhsLBQ56iCS22LzokLl5aWRufOnYmPj8dutzNw4EB27dqld1hBIzU1FbvdrncYQSkx\nMZGkpCQAkpKSKC4uJkjGLnWnKArh4eEAVFRUoGkaqqrqHFXwSE9P59ixY9ULpJ5PUCTyy5YtY968\neZhMQfFyAs60adPo168fffv2ldF4H9i/fz+qqpKQkKB3KEL8Qk5OTo1rs76F+oQIRFu2bKFbt24o\nRlrpO8CVlZUxZswYBg4cyMyZM2XgxIuWLl3K3Xff3aBtA2pl17qcb3GpI0eO4HA4SE1NZffu3X6O\nzPgasnDXqlWrcDqd3HnnnRw6dIjOnTv7M0TDasi5dTgc3H///SxZssSfoQUFWXROCNEQx48f54kn\nnmD58uV6hxJUbDYbGzZsID8/n/nz5zNixAiaNm2qd1iGt3nzZtq1a0f79u355ptv6t3eEIn8+RaX\n2rNnD19++SWDBw+mvLwcp9PJ4sWLWbx4sf8CNLCGLtxlt9vp168fO3bskES+geo7ty6Xi/nz5zN9\n+nR69+7tp6iCx8UsOicuXHx8fI0R+KysLLp3765jREI0XHFxMfPmzWPhwoW0bdtW73CCUlxcHMnJ\nyXzxxReMHDlS73AMb+/evbz33nt88MEHOJ1O3G43ERERzJkzp9btDZHIn8+UKVOYMmUKUDlp6PXX\nX5ck3kucTiclJSU0a9aMiooKdu7cydSpU/UOK2g89NBD9OjRgwkTJugdihB1SklJ4eDBg+Tk5GC3\n29m2bRu33nqr3mEJUS+Px8Mdd9zBpEmT6N+/v97hBJX8/HwsFgtRUVEUFxeze/dueS/zkgULFrBg\nwQKg8hvmY8eO1ZnEQxAk8sJ3SktLmTNnTvVEluHDhzN48GC9wwoKhw4dYt26dXTp0oVPPvkEgKee\neoqOHTvqHFnwWLRoEVu3bqWgoIABAwbw4IMPMmTIEL3DMhyLxcJ9993HtGnTUFWVWbNmSccaL7rl\nlltIS0ujtLSUAQMG8Pzzz9OtWze9wwoKO3bs4PPPPyc3N5c1a9YAlaWi0lnl0uXk5PDHP/4RVVXR\nNI3JkyfTtWtXvcNqlIKm/aQQQgghhBCNibR5EUIIIYQQwoAkkRdCCCGEEMKAJJEXQgghhBDCgCSR\nF0IIIYQQwoAkkRdCCCGEEMKAJJEXQgghhBDCgCSRF0IIIYQQwoAkkRdCCFGngwcPMmzYMAoKCgCY\nM2cOq1ev1jkqIYQQIAtCCSGEqMeKFSv4+uuvSU1N5ZNPPuG5557TOyQhhBBIIi+EEKIemqZx8803\nc/ToUd5++23i4uL0DkkIIQRSWiOEEKIeTqeTzMxMLBYLRUVFeocjhBDiNBmRF0IIcV733nsvSUlJ\ndOnSheeee47Vq1djsVj0DksIIRo9GZEXQghRp40bN3L8+HFuueUWBg8eTLdu3Xj66af1DksIIQQy\nIi+EEEIIIYQhyYi8EEIIIYQQBiSJvBBCCCGEEAYkibwQQgghhBAGJIm8EEIIIYQQBiSJvBBCCCGE\nEAYkibwQQgghhBAGJIm8EEIIIYQQBiSJvBBCCCGEEAb0/wEW6xMnknOsmQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ad620d68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# 最小二乗法\n",
"xs = np.linspace(-4, 4, 1000)\n",
"coef1 = np.polyfit(X_train, y_train, 1)\n",
"y_pred1 = coef1[0] * xs + coef1[1]\n",
"\n",
"coef3 = np.polyfit(X_train, y_train, 3)\n",
"y_pred3 = sum([coef3[i]*xs**(3-i) for i in range(3+1)])\n",
"\n",
"coef15 = np.polyfit(X_train, y_train, 15)\n",
"y_pred15 = sum([coef15[i]*xs**(15-i) for i in range(15+1)])\n",
"\n",
"# plot\n",
"plt.subplot(3, 1, 1)\n",
"plt.scatter(X_train, y_train)\n",
"plt.plot(xs, y_pred1, c='r')\n",
"plt.title('D=1')\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.xlim([-4, 4])\n",
"plt.ylim([-10, 20])\n",
"\n",
"plt.subplot(3, 1, 2)\n",
"plt.scatter(X_train, y_train)\n",
"plt.plot(xs, y_pred3, c='r')\n",
"plt.title('D=3')\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.xlim([-4, 4])\n",
"plt.ylim([-10, 20])\n",
"\n",
"plt.subplot(3, 1, 3)\n",
"plt.scatter(X_train, y_train)\n",
"plt.plot(xs, y_pred15, c='r')\n",
"plt.title('D=15')\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.xlim([-4, 4])\n",
"plt.ylim([-10, 20])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ガウスノイズモデル\n",
"1次、3次、15次の多項式あてはめを確率的手法であるガウスノイズモデルで行う。"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-10, 20)"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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5M56DlZ11qOYLFITcmHslqVODPWkBHBcuusFsCLKHPnHWl9zH9QIlx+98dmNa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\nCCH8kATyQgghhBBC+KH/DzCJ9HR4HS7GAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51a3861cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.cm as cm\n",
"# ガウスノイズモデル\n",
"# 平均と分散は最小二乗法の推定と等しい\n",
"coef1 = np.polyfit(X_train, y_train, 1)\n",
"y_pred1 = coef1[0] * X_train + coef1[1]\n",
"\n",
"coef3 = np.polyfit(X_train, y_train, 3)\n",
"y_pred3 = sum([coef3[i]*X_train**(3-i) for i in range(3+1)])\n",
"\n",
"coef15 = np.polyfit(X_train, y_train, 15)\n",
"y_pred15 = sum([coef15[i]*X_train**(15-i) for i in range(15+1)])\n",
"\n",
"# 標準偏差の推定\n",
"sigma1 = np.sum((y_train - y_pred1) ** 2) / N\n",
"sigma3 = np.sum((y_train - y_pred3) ** 2) / N\n",
"sigma15 = np.sum((y_train - y_pred15) ** 2) / N\n",
"\n",
"# 推定した分布からのサンプリング\n",
"def sample_dist(coef, sigma, sample_size=10000):\n",
" D = len(coef)-1\n",
" sample_y = [np.random.normal(sum([coef[i]*x**(D-i) for i in range(D+1)]), sigma, size=sample_size) for x in np.linspace(-4, 4, 1000)]\n",
" sample_x = [[x for i in range(sample_size)] for x in np.linspace(-4, 4, 1000)]\n",
" sample_y = np.reshape(sample_y, (-1))\n",
" sample_x = np.reshape(sample_x, (-1))\n",
" return sample_x, sample_y\n",
" \n",
"sample_x1, sample_y1 = sample_dist(coef1, sigma1)\n",
"sample_x3, sample_y3 = sample_dist(coef3, sigma3)\n",
"sample_x15, sample_y15 = sample_dist(coef15, sigma15)\n",
"sample_y15 = np.array([np.sign(d)*100 if d > 1e2 or d < -1e2 else d for d in sample_y15 ])\n",
"\n",
"# plot\n",
"plt.subplot(3, 1, 1)\n",
"plt.hist2d(sample_x1, sample_y1, bins=[100, 100], range=np.array([(-4, 4), (-20, 20)]), normed=True, cmap=cm.Reds)\n",
"plt.plot(X_train, y_pred1, c='b')\n",
"plt.scatter(X_train, y_train, c='k')\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.title('D=1')\n",
"plt.xlim([-4, 4])\n",
"plt.ylim([-10, 20])\n",
"\n",
"plt.subplot(3, 1, 2)\n",
"plt.hist2d(sample_x3, sample_y3, bins=[100, 100], range=np.array([(-4, 4), (-20, 20)]), normed=True, cmap=cm.Reds)\n",
"plt.plot(X_train, y_pred3, c='b')\n",
"plt.scatter(X_train, y_train, c='k')\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.title('D=3')\n",
"plt.xlim([-4, 4])\n",
"plt.ylim([-10, 20])\n",
"\n",
"plt.subplot(3, 1, 3)\n",
"plt.hist2d(sample_x15, sample_y15, bins=[100, 100], range=np.array([(-4, 4), (-20, 20)]), normed=True, cmap=cm.Reds)\n",
"plt.plot(X_train, y_pred15, c='b')\n",
"plt.scatter(X_train, y_train, c='k')\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.title('D=15')\n",
"plt.xlim([-4, 4])\n",
"plt.ylim([-10, 20])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ベイズ線形回帰モデル\n",
"ベイズ線形回帰モデルで多項式あてはめを行う。\n",
"\n",
"以下のようにモデル化を行う。\n",
"\n",
"$\\bf{w}$の事前分布:\n",
"$$p(\\bf{w}) = Normal(\\bf{w} | 0, \\sigma_w^2 \\bf{I})$$\n",
"\n",
"$b$の事前分布:\n",
"$$p(b) = Normal(b | 0, \\sigma_b^2)$$\n",
"\n",
"予測分布:\n",
"平均が$\\sum_{j=1}^D w_j x^j+b$の正規分布からサンプルされたと考え、各サンプルが独立に得られたと仮定すれば、サンプルの同時確率は以下のようになる。\n",
"$$ p(\\bf{y}| \\bf{w}, b, \\bf{X}) = \\prod_{n=1}^N Normal(y_n | \\sum_{j=1}^D w_j x^j+b, \\sigma_y^2) $$\n",
"\n",
"ここで、ハイパパラメータ$\\sigma_w^2, \\sigma_b^2, \\sigma_y^2$は既知であるとする。$\\sigma_w^2=1, \\sigma_b^2=1, \\sigma_y^2=2$としてモデルを作ろう。"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import tensorflow as tf\n",
"import edward as ed\n",
"from edward.models import Normal, Gamma, Exponential, Empirical, PointMass\n",
"\n",
"MD = 3 # モデルの次元\n",
"X = tf.placeholder(tf.float32, [N, MD])\n",
"w = Normal(loc=tf.zeros(MD), scale=tf.ones(MD))\n",
"b = Normal(loc=tf.zeros(1), scale=tf.ones(1))\n",
"y = Normal(loc=ed.dot(X, w) + b, scale=tf.ones(N)*2.0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## MAP推定\n",
"MAP推定によって、パラメータの推定値を得る。"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10000/10000 [100%] ██████████████████████████████ Elapsed: 8s | Loss: 83.056\n"
]
}
],
"source": [
"# MAP推定\n",
"qw = PointMass(params=tf.Variable(tf.zeros([MD])))\n",
"qb = PointMass(params=tf.Variable(tf.zeros(1)))\n",
"\n",
"XX_train = np.array([X_train**i for i in range(1, MD+1)])\n",
"XX_train = XX_train.T\n",
"\n",
"inference = ed.MAP({w: qw, b: qb}, data={X: XX_train, y: y_train})\n",
"inference.run(n_iter=10000)"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def visualize(X_data, y_data, w, b, n_samples=10):\n",
" w_samples = w.sample(n_samples)[:].eval()\n",
" D = len(w_samples[0]) #次元数\n",
" b_samples = b.sample(n_samples).eval()\n",
" plt.scatter(X_data, y_data)\n",
" \n",
" inputs = np.linspace(-8, 8, num=1000)\n",
" inputs_list = []\n",
" outputs = []\n",
" # サンプリング\n",
" for ns in range(n_samples):\n",
" # 範囲内のxに対するyの値を計算\n",
" output = np.random.normal(sum([inputs**i * w_samples[ns][i-1] for i in range(1, D+1)]) + b_samples[ns], 2.0)\n",
" # 得られた結果をリストに追加\n",
" for x in inputs:\n",
" inputs_list.append(x)\n",
" for y in output:\n",
" outputs.append(y)\n",
" \n",
" plt.hist2d(inputs_list, outputs, bins=[100, 100], range=np.array([(-8, 8), (-80, 80)]), normed=True, cmap=cm.Reds)\n",
" plt.xlim([-8.0, 8.0])\n",
" plt.ylim([-80.0, 80.0])"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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UEyrGTwhYfhWqVejr09k+v9ZlXKvuW9eEbsIsTm5XuxOKZSmQ2Fpbx8xSTNn+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\nAAB4iIIcAAAA8BAFOQAAAOCh/x8+VmcmUjuv8QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51adeb1978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# 事後分布からのサンプルによる可視化\n",
"visualize(X_train, y_train, qw, qb, 10000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ベイズ推定\n",
"ベイズ推定によって、事後確率分布の情報をすべて使って推定を行う。"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10000/10000 [100%] ██████████████████████████████ Elapsed: 11s | Loss: 87.060\n"
]
}
],
"source": [
"# ベイズ推定\n",
"qw = Normal(loc=tf.Variable(tf.random_normal([MD])), scale=tf.nn.softplus(tf.Variable(tf.random_normal([MD]))))\n",
"qb = Normal(loc=tf.Variable(tf.random_normal([1])), scale=tf.nn.softplus(tf.Variable(tf.random_normal([1]))))\n",
"\n",
"XX_train = np.array([X_train**i for i in range(1, MD+1)])\n",
"XX_train = XX_train.T\n",
"\n",
"inference = ed.KLqp({w: qw, b: qb}, data={X: XX_train, y: y_train})\n",
"inference.run(n_iter=10000)"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def hist_param(w, n_samples=500):\n",
" w_samples = w.sample(n_samples)[:, 0].eval()\n",
" plt.hist(w_samples, bins=300, normed=True, range=(-10, 10))"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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S6NGj5fV6ZbjTMiYYd+FraGiQ2+2Odxi2VlBQoIyMDN92OOPLTr+xSVtwB9Le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\nAMBCFNwAAACAhf4PJS+L7V+nhqIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ae717b00>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# w0の事前分布\n",
"plt.subplot(2, 1, 1)\n",
"hist_param(w)\n",
"plt.subplot(2, 1, 2)\n",
"hist_param(b)"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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T/alrZGREvb29kqTh4WF9+eWX7k+sx7uhoSG5XC5J0sDAgNrb2zVnzhyPMf7OyXi0a9cu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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f515d2a1a20>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# w0の事後分布\n",
"plt.subplot(2, 1, 1)\n",
"hist_param(qw)\n",
"plt.subplot(2, 1, 2)\n",
"hist_param(qb)"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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HUFAeybQKAGDMlaWWyxC1TrkyJk6yXk8aXJualpJe9rBQGOQsUZ3Uyg8pJDpI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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ada027b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# 事前分布からのサンプルによる可視化\n",
"visualize(X_train, y_train, w, b, 10000)"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ToufSwk3dzXGkkogCMTIrXE8swSg9v9DouRH7MpWdutLDr00bN/G56et1g82j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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f51ac5e3198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# 事後分布からのサンプルによる可視化\n",
"visualize(X_train, y_train, qw, qb, 10000)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
},
"toc": {
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"toc_cell": false,
"toc_position": {},
"toc_section_display": "block",
"toc_window_display": false
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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