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@nzw0301
Created November 27, 2016 06:52
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import seaborn as sns\n",
"%matplotlib inline\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def gumbel_pdf(x, location, scale):\n",
" z = (x-location)/scale\n",
" return 1./scale * np.exp(-z - np.exp(-z))\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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K0z3ypjuAVat+SlVVNVdeuRyABx64l+uv/zzz5tUD4PF4WL366ejx5kynZmAf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\nY+pXF61gd8c+nH4XUuch5uVUjbotnVbDbVcs4ge//4iObj+/f3U/uZk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7EZqIlmvmfHJc\nrS4jMW+Gg3tuWcWG3U08v/4Izp4A+2udNP1pG1XRSOvFJyXfD0Brs5Gx+mQyVp+MHIngr6/Du38f\nnn178Rw4gOz3QTiM79BBfIeUctYIAoaSUsyzZmOePQfz7DnocnOT3pdUIzvPymXXLaH2SCcfrjtM\nV7uHrnYPrz2/B0euheVrypk9f+T8GCqpiaokpCnujzfT8vun++Zj7WtOpuDmW9DoJ2fu1eML8crG\nGgCqSjOZXTL6qo3ekJd2n5Lvv8w2uvDJ6YBeo+Pziz7Dz3f8msPOatbXb8QT9HHTvGvRayb+Utdo\nBE5fXMyqeQW8/lEdr2+qocSv5EUIIPO3rfWcqxVYNS8fvS75oYmCRoOpfAam8hk4zr8QORTCV31U\nURj27cV39AhyMAiyTKC+jkB9Ha53lXoZ2swszDNnYayowDRD+Wjt9iT3KPkIgsCMWTmUVTrYv6uZ\nLRtq6On209Xu4a2X9/PR+9UsXFHC3EWFGE3jY51RmViEFE+GIXd19RIKTf0CLzqdBofDykT3J+Lz\n0fbXP+Na/46yQBDIveoaHBdcNG5vPvH05YX3jvDihmoAvn7DMsTy0VsvDnYd5ifbfgnA7cu/yOys\nylG3NRyTNTaTRVD28/iOX3O4U1HS5mTN5D8XfWbSs1Tu29XMO//aD0A1EWLpl2xmPacvLuLMZSXk\nnyB0MpljI4dC+Gqq8R46iO/QIbyHDhJ2j1w6WZeb26cwGGdUYCwvR2cf6GCbbufaifoTDkc4sLuF\nbRtrcXV5B+w3Z0EBC5YVk1eYGspVmo7NmG/6qpIwSUzGCejZt5eW3z9NsF25Hesc2RT9539hnlM1\nrsc5UV/aXV6+/atNBEIRFlQ4uPO6sdWBeLX6LV468hoaQcNDp9+DSWcaU3uDScebg9mu4+H1T7Gz\nbS8AOaZsbllwPZWZ41fV83gEg2H+8qvNuLv92DKMFJ1UylvbGmjp9AzYrqo0k5MXFrJybj7WYd4s\nU2lsZFkm2NaG79BBRXGoPoq/oR7C4RH30dozMJaWYigpxVhaiqW8jIIFVXR7w0nvz3gQ7/hEIjJH\npDZ2fFRHa+PAlM45eVbmLCxgzvwCbPbk5bJIpXNtPFCVhCnGRJ6AYbebtn/8je731vctsy1bQcHN\nt6C12cb1WHDivjz+3E62HWxHIwjcc8tJlOaPTYYfb3mCw65qZmVWcMeK28bU1nCk6c2Bjk43z+59\ngfUNHwCgETRcUnke55WfhVYzseb+TeuPsPWDWgDO/+QCZs3NQ5Zl9tZ08faWerYfah/gVKnTCiya\nmcOyOXksmZ3Tl28h1ccmEgwQqK/HV1ONr7oaf001/saG4yoOCAL6vDwMxSUYiooxFBRiKCzEUFCI\nxjZ1ogFgdOPT1uxm99YGDu5tJTxon+LyLGZW5VIxJxd75vi+DJyIVD/XEkVVEqYYE3ECyqEQzvXv\n0PHCP5QSz4DGZiP/hpuwn7R6wm42x+vLxj3NPPWS8vZ63soyrj939FEUAJ6gl6+//z0icoRLKy/g\nosr4UkcnQpreHPr6s7l5K3+RnscX9gNQbC3kmqrLqXLMmpDjtzZ18/wfthGJyJRVOrjk2sVDzsXO\nbh8f7mnmwz0tNLb3DlgnCDC7JJNlc/JYLuYxf3YeTqdnyoxNJBjAX1dPoLEef309gQbl7/GmKmJo\nLFYMhQXoCwr7lAd9bj763Fw01tTLaDiWa8fnDXJ4fysHdrfQ3DD0f5OTb6Vidi4Vc3LILbCj0Uxs\n39P0PqAqCVOF8TwB5UgE96aNdLz4AsG21r7l9jUnk3ft9egyxi/R0HCM1JfWLg/f+93HeP0hcjNN\nfO/WVZiNY3OY29a6i1/v/gMA/2/ll5mRUTam9oYjTW8OA/rT7u3gd3ue5Wh3bd92S/MWcmHFuZSN\nY8SI3xfiuWe24Or0ojdoueaWlWQ6RvY7kGWZ2pYePtzTzNYDbbS7hlaYzM4wIZZlIZYrn/wsc8o9\nLOMh1N1NuLkRTWcLXQeO4KuvI9Dc3KfgnwjBaEKfm6t8cpS/upxjv5OhRIzXtePq8nJwTwtHDrTR\n0do7ZL3RpJQWLyl3UDIji+y88e9rmt4HVCVhqjAeJ2AkGKD7ww9wvv4ageamvuXG8hnkX38T5jlj\ne2uPl+H64vEFufcPW2jq8CAI8M0bVzC7dPQRDTGe2fsXNjVvwaa3cv9p35mQcL40vTkM6U9EjvBh\n40f888gr9AaPPZgW5c7jrNLTqHLMGtP/NxKJ8O+/7aLuqJKw6OyLReYujj8FsyzLNLT3sv1gO9sP\ntXOkcfg3b4fdyMyiDCqLM6gstDOjMAOLaWoEag0eG1mWCfe4CTa3EGhpJtDcRLBF+R5sbUmoqqVg\nNKLLcqBzONBlZSnfsxzoHFnHlmeMb6Koibh23C4f1QfbqT7UQWOtc9icBSazjvyiDPKL7OQXZZBX\nZMdiHVvkVpreByZfSRBF0Qg8AVwJeIBHJEn68QjbLgN+ASwCdgNflCRpawKHU5UEINDcjOv99XRv\neI+w+5jTj76ggJzLr8C+chXCJMYeD+6Lxxfi0b9u53D0pn7d2tmcv2pseREA3IEevv3BfYQiIU4t\nXs0Nc68ac5vDkaY3hxH70xv08Fr127zX8CGBSLBveZ45hzVFJ7E8fxH5lryEjhmJRHjrpf0c2qdY\ntuYuLuSsi8Qxve05e/wcqHNyuMnNjgNttDpHLoddmG2hNN9GcY6FkjwbxblWChzmuCtUThaJnGty\nJEKos4Nge7vy6WgnFP0bbG9Tskcm+pInCGhtdrQZGegyMtDaM9Bm2I8ts2egjS2329GYTMcdw4m+\ndvy+IA01ThprnTTUOulsG2pliGHPMJKdbyM710p2rgVHrhVHjgWdPj7/mzS9DyRFSXgcOA34LFAB\nPAPcIknSPwZtZwEOAX8Afgt8EfgUMFOSpJGv9oFMWyUh0NJMz/Zt9Gzdgu/woQHrDCWlZF9wEfbV\na5JSCrd/X5rbe/nZP3ZR29oDwFnLSvj0+VXjYgr819E3+PfRNwC4a9UdFNsmpnBRmt4cTtgfd6CH\nt+ve4/2GjXhCAy/JElsR87NFRMdsZmZVYNSO/Jbm9wV586V91B5WclmUzMjikmsXj0vu/v59aenw\nsL+2i4P1Lqqbuqlv6yVynPuXViNQkG2hMNtCXpaJvCwzeVlmcjNN5Gaa0esmX4EY12nHUIhgV6ei\nOESVhpCzK/rXScjZNeClYjQIOp2iLFisaK1WNBYLWqsNrcWCxmpFb7eRkZ+NT9YhmyxorRa0FmW7\nibg3eT0BGmudNNW5aG12097sJhw+/jMsI8uEI8dKRpYJe5aJjCwzGVkmMjLN6A3HZEzT+8DkKgnR\nB387cIEkSe9Fl90FnCNJ0tpB294KfEuSpNn9lh0AfihJ0jNxHnLaKAkhd7cSi33wAL27dxJobBy4\ngUaDdfESss4+B8v8BUmdk9XpNGRmWnjx3YP8+c2D9PoUk+iZS4v59AXigOI+o6XL5+S+zY/iCXmZ\nl13Fl5b+x5jbHIk0vTnE3Z9gOMi2tl180LiZQ86jyAy8J2gFLRUZZZRnlFJmK6HUXkyhJR+tRkvt\nkQ7Wv3YQd9SXoLTCwYVXLUQf59vbWPriD4apa+nhaFM31c1uGtt7aeroJRBHnwUgy24ky2Ygy2Yk\n03bse5bNQKbVSKbNgM2sH1drxGSfa5FgkHC365gC4XQScjoJu92E3d2Kn4S7m7Db3ZeierwQDAY0\nRhMasxmNyXTs0/fbPMxvI4LBiMZgjO5vUP4ajAh6/RCLaTgcobOtl7ZmN61Nbjrbe+lq7yXgP050\nST9MFj02uxGLzYDNbiQnz4ZWp8Fk1mO1G7BYDZjM+ritEanEeCkJiU5OLYnu82G/Ze8D3xpm29XR\ndf3ZAJyMYn2YlsjhMIHWNgKNDQQaG/A3NOCvqR7gY9Af08yZ2JavJOPkU9BlZk2ytEPx+kNs3d3G\nGx/XU9usvKUIwFVnzeKi1eXjorz4Qn6e3vMnPCEvAgIXVox/RIPKMfRaPasKl7OqcDlOv4sdbXvY\n1b6XQ86jBCNBwnKYw65qDruqARAiGjJdBeS3zsLgOuYkmy8amX9mJq6QiwyNDcNxrA/jgVGvZXZp\n5gDfl0hEpt3lpbHdQ0N7D43tvbR2eWlz+ejuPfYQlIEut58utx84/tu2Ua/FZtZhNeuxmvTYzHqs\nZj02sw6LUY/JqMVk0GIy6DDptdHfuugyLQa9dlwU59Gg0evR5CiOjSci4vcT7u4m5O4m3E95CPf0\nEPb0Eu7tJdLbS9jjif7tVUrOj4AcCBAOBOKK6ogXQa8/pjQYDGgMihKRYTSSGV1Oph6/xohbNtEd\nNuIOGugJaekJaPAGBZQ7loLPE8TnCULL8Y+r1QqYzHqMZj0msx6TWYfRpI8u02EwaNEbdOgNWvR6\nLQajVvluUNbp9NoJj86YKBJVEoqAdkmS+nvTtAAmURRzJEnqGLTt7kH7twALEhczNZBlWZkDjESQ\nQyEigQByMIAcCCjfA0Eifh/h3h7lgurpUS6wHjehrk4OdXUR6Og47jyixmTCNLsK27Jl2JYsnbQ6\nCzFkWSYUjuD1h/EGQjjdftqcPho7epFqndQ0uweYeItyLNx84VyqysamwMiyjNPvQuo6xGs1b9Pq\naQfgwoq1455hUWVksoyZnFl6CqcVrcHj9VPdWcehlloaWttxO33onDYsPQ408rE3q6DeT1P5HnZn\nNvP29mNtmbRG7AYbFp0Fk86IWWfCpDNh1pkwa00YdUb0Gn30o0Ov0aHT6JTfWmWZUa/Hq7Xi9viR\nw0quh4EfAQEN2n7L8h0W8h0Wls4Z+GD0B8K0uby0O320Ob10dPtw9vhx9gSif/0EgkPtAYsRAAAM\nPklEQVTf7v3BMP5gmI7ukR+Ix0MADAYtBp0GvU6D2ahDIwjotJq+ZQM/WvRa5btWI6DVCspfjfJb\nM2DZseWxbTWDlgmCgCCg/K/6/R2wXCOgAQSDHSHXjpBXikYAnUbAENueY9trNNHiWUIEmx66GtsI\ndLuJRBUI2ecl4vMR9ip/I9Hfkf6/vT4iPp9SLyNO5GAQORgk0juyb0IMI5AX/cSIoMGnt+HV2/Dq\n7Pj0NvxaC36dGb/OQkBrITSMchsOy/T2BOjtGb21RUsYLRE0gowWGa0gK981DPmu/AWtBgSNEP0b\nPf81yv9foxGi65Qx12gFNJroep2GypMX4nBYRy1vjESVBAsw+EqJ/R6cKmukbRNKqTWRNcldLjfP\nPfoiQUYOGezT/eT+P+JFDziin3KwoXz6NRkRBCIagYgGwhqBiCBACPgoAB9tTvSAE0omsFir3Cxi\nCN3dvP7Xzbw+0k5xzmb13yybpWQDOo2Otl0GnmbD6Bolfr8uQRBIZOotMVeeiWp3ZARhUFsJtBuO\nRIgMmOfVoaWQwWqgYIoQKuugI+8I7lDnkHZ8YT8+rx/oGLJuIlEeZoLyF5R/BrHL99jZK+gEyBIQ\nspRtrIA12u3Y+0Dsu/JX7lve/xMvwejnhAGPMso9IP7AhtREA8o/dbiV+ujHjiDL6EMyhqDyVxeW\n0Ycj6EIy+rDyWxeOrYv0fR+47thybUT56MLR72Gif2U0RLAEu7EER7ZuhAVtn+IQ0JoJao2EtEaC\nGiNBbfSjOfY3pDUixxEVFI6qCX3Xoty3YgKIYNm6nv/56afH3FKiSoKPoQ/52O/B5/5I28YXFKwg\nZGQcP7f7WHA4rNz52H9OWPsqKioqKipTmURf0xuAXFEU++9XCHglSXIOs+1gd/RCYPjJdxUVFRUV\nFZWUIlElYTuKxWxNv2WnAx8Ns+1G4JRBy06NLldRUVFRUVFJcUaTJ+EXKA/7W4FS4HfAzZIk/VMU\nxQLAJUmSTxRFO3AQeBZ4Cvgv4GpgdgJ5ElRUVFRUVFSSxGi8Au8AtgBvA48D35Ek6Z/RdU3AtQCS\nJLmBS4EzgI+BVcBFqoKgoqKioqIyNUj12g0qKioqKioqSSK1EpurqKioqKiopAyqkqCioqKioqIy\nLKqSoKKioqKiojIsqpKgoqKioqKiMiyqkqCioqKioqIyLImmZU4Koih+D/gCirzPAV+WJGl865om\nAVEUfw7MlyTp7GTLMhpEUcwEHkEJddUA/wK+JkmSK6mCJYAoikbgCeBKlJThj0iS9OPkSjU6RFEs\nBn4KnI3Sl78C30yTa+VfQIskSbcmW5bRIoqiAXgUuB6ljs1vJUm6K7lSjQ5RFEuBX6CEuHcAj0mS\n9FhypUqc6PX/MfDfkiStjy6rAH6FUrG4GrhdkqQ3kiVjIozQnzUo9+nFQD3wsCRJv4m3zZS3JIii\n+A2UREyfAi4E1gJ3J1WocUAUxVNQ+jWVY1B/CSxCGZfzgXkoibOmEg8Dy4GzgNuAu0VRvDKpEo2e\n5wATSrKz64DLgB8kVaJxQBTF64CLki3HOPBT4BzgPOAG4POiKH4+uSKNmr+h1NheDnwNuFcUxcuT\nK1JiRB+ozwLzB616AWgEVgB/BJ6PKkUpzXD9iSY4/DdKXqOlwD3A46Ioxn09pbQlIVoj4nbgTkmS\n3o0u+y5wc1IFGyOiKOpRHrAfJFuW0SKKogXl7fsUSZK2R5d9DVgviqJhKry9RvvwOeACSZJ2ADtE\nUXwQ+BLwj6QKlyCiKIooCcsKJElqjy77LvAQ8PVkyjYWRFF0AA8CqVUSNUGi/bgVWCtJ0pbosoeB\n1ShvrVMGURSzUOT+nCRJh4HDoii+iqIA/fO4O6cIoijOA/40zPK1wExgjSRJPuABURTPQRm770+u\nlPEzUn+ATwJNkiR9J/r7sCiKZ6Moqa/E03ZKKwnAAiCHfieeJEnPomhLU5lvAjtQ0lafmWRZRksE\nZZphR79lAqBFKYg9tHZw6rEE5Rr4sN+y94FvJUecMdEMXBhTEKIIKBW+pzIPA88AJckWZIycBjgl\nSXo/tkCSpAeTKM9Y8AK9wC2iKH4TmIVivfpmUqVKjDOBt4BvM7Ay8Wpga1RBiPE+ytRDKjNSf14B\ntg2zfdz3hVRXEmaiPGxOFUXxPiAXxaT69anwpjocoijORZlmWIJi3p6SRC+i1wct/iqwU5KkqaAg\nABQB7ZIkhfotawFMoijmSJLUkSS5EibqB9I3byqKooBiEXkzaUKNkehb3ekoU1pPJlmcsTITqBZF\n8dMoSqgBeBq4V5KkKTXlKEmSXxTFLwE/Q5lq0AJPS5L0u6QKlgCSJPWdT4oRro8ilKmG/rSg1ClK\nWUbqjyRJtUBtv3X5KFOR34237aQrCaIomhj5LSETsAL3o5yMOhQzvQblgZRynKA/TSjyf1eSpLZB\nJ2fKcaK+SJLk6bftl1AKeF0wGbKNExYUB7L+xH4bJ1mW8eYhlDnIlckWZDRE51efBG6LPpSSLdJY\nsQFVwH8Cn0V5GD2F8kb+aPLEGjXzgBdRLD2LUOa534xaeqcyI90Tpvr9IHY/fw5FCYrbdyzpSgKK\neWcdwzvw3QCYUaIZ3gcQRfFOlLmXlFQSOH5/vgloJEn69eSKNGqO15crUG4SiKJ4G/AY8FVJkt6a\nPPHGjI+hF3/st4cpiiiKPwK+AlwrSdK+ZMszSu4BPpIkacpaQgYRAuzA9ZIk1QOIojgD+CJTTEmI\nztF/DiiVJMkPbIs69n2bqT8V7AOyBy0zMoXvBwCiKFpR7tezgVMHTaccl6QrCVGHxGGjLERRPAPl\nASX13wXFHJwnSVLbJIiYECfoz9vASlEU3dFFBkArimI3Sihk/SSJGRfH60sMURT/B8Wx7E5Jkn42\nKYKNHw1AriiKGkmSItFlhYBXkiRnEuUaNaIoPo4SLnyjJEkvJFueMfApoKDftWIEEEXxakmSMpIn\n1qhpAnyDrnEJKEuSPGNhOXAwqiDE2MbU9OUZTANDox0KUcZvSiKKoh14FWXK62xJko4ksn+qh0Bu\nAwIo8/cx5qOE3kyZ+eJ+3IjijLkk+nkS+Cj6ffA8WMojiuLNwI9QLAhT6m0oynYgCKzpt+x0lDGZ\ncoiieDeKOftTkiT9LdnyjJEzUczYsWvlRRQH5iXH2ymF2YjycjO737L5KHH4U41GYLYoiv1fMucB\nR5Mkz3iyEVgene6KcVp0+ZQj6pv0PFABnCFJ0v5E20i6JeF4SJLkFkXx1yjzXZ9FUWoeAH7V781v\nyiBJ0gBtVBTFTpS31il3cUVDuh4Hfg/8NRqPG6NtKoyPJEleURSfAZ4URfFWFOekO5mCIbbREKhv\nA/cBH/QfD0mSWpIm2CiRJKnu/7d3/yxORUEchl9Ba+utLEcsLIStBRELwVXTWojgWllZWfgHIilt\nFDuFLIJfwAU7QSxs1MJuJGAhpBXWTsRYnOCGeNRk2Xhzw/s0ISnChHDD7845ZzL5fNxRGLXxWgHI\nzI/jgVD98fLcGuVo6tIeq/uL55Tu4eOI6AFHKUupbTrd8CevgM+U7+kesAGsU/aRtNFVygyYc8DO\nxO/Ct8z8MssbLHsnAcqchBeUgRDb48dVaGu13RnKptLLlDuLIaUlN2TJdwJPuQG8owwbeQjczsxW\nnPWeskG5nm/x+/eh5XAJGACvgT7wIDMfNVrRHmTmDmUmwhplfsV9oNuivVbTfu25Gt/cnKcsMbyl\n7Iu7sGxLwf8wYvczdShHobfZ/V0YUjYwzuTAaNSq0zeSJOk/aUMnQZIkNcCQIEmSqgwJkiSpypAg\nSZKqDAmSJKnKkCBJkqoMCZIkqcqQIEmSqgwJkiSpypAgSZKqDAmSJKnKkCBJkqoMCZJmFhGdiPgR\nERcnXnsWEZ8i4nCTtUnaf/4LpKS5RMQWcBo4BpwFtoCTmfmm0cIk7buDTRcgqXWuAx+AJ8ApoGtA\nkFaTyw2S5pKZX4ErQAcYAL1mK5K0KIYESXuxDnwHAjjScC2SFsSQIGkuEXEc6ALXgPfA02YrkrQo\nhgRJM4uIQ5RQ8DIz+8AmcCIibjZamKSFMCRImkePsrywCZCZA+AOcHfcYZC0QjwCKUmSquwkSJKk\nKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpKqf\nFg19pce3KyUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11539acf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5, 12, 0.05)\n",
"plt.plot(x, gumbel_pdf(x, 0, 1), label=r\"$\\mu=0, \\beta=1$\")\n",
"plt.plot(x, gumbel_pdf(x, 0, 0.5), label=r\"$\\mu=0, \\beta=0.5$\")\n",
"plt.plot(x, gumbel_pdf(x, 0, 2), label=r\"$\\mu=0, \\beta=2$\")\n",
"plt.plot(x, gumbel_pdf(x, 5, 1), label=r\"$\\mu=0, \\beta=2$\")\n",
"plt.legend()\n",
"plt.title(\"PDF of Gumbel distribution\")\n",
"plt.xlabel(\"x\")\n",
"plt.savefig(\"gumbel_pdf.pdf\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"np.random.seed(3)\n",
"x = np.random.rand(6)\n",
"x[3] *= 4\n",
"pi = x/np.sum(x)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def gumbel(n):\n",
" u = np.random.rand(n)\n",
" return -np.log(-np.log(u))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def gumbel_softmax(n, tau, pi):\n",
" log_pi = np.log(pi)\n",
" numerators = np.exp((log_pi+gumbel(n))/tau)\n",
" return numerators/np.sum(numerators)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x_range = np.arange(len(x))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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MNElIktQB2j7jAcWsB3Bi+VW/r7vm+71GGOcZ4APllyRJ6jCdMuMhSZK2Ay0Fj4gwsEiS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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115f5c160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.barplot(x=x_range, y=pi, color='#0068B7')\n",
"sns.plt.title(r'$\\mathbf{\\pi}$')\n",
"sns.plt.xlabel(\"Categorical value\")\n",
"sns.plt.ylabel(\"Probability\")\n",
"plt.savefig(\"categorical.pdf\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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AeztTTs/YG/gecCITeCruRuzPwAEjwaLWBzy2Q/X0hMz8M/C6ke2IeD7VCsFv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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116154898>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x115dc5518>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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/XN+883iqv2t9HS5vygwXnbcE2CIiGv9bbAUMZuaDHapJG6iIOJfqh+MbMvMr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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1153caef0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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0tP0bsFtmvmwSy5YkSSPohNMiK4BtIqKxlu2A3sZg0dB3u6a27YCVE1ifJElq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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1153c3358>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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IRcDFEXEUxUTRk4EjACJiW+DRzHwCuAb4RER8CrgEeC/FvI+ry+6uBz4eEfcB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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115d19470>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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MDLQPHgsXzuukiRlp4cJ5LFq0oKvjZqtur1nj2NnKsVadY607jrXqJjPWGvoh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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11573e198>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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Ydz3QmDH5WGZeAhARrwdWRsTSzLyuk84sXryAgYH2wWPhwnmdNDEjLVw4j0WL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\nNfgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116147dd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"taus = np.array([2**i for i in np.arange(-6, 7, 2)])\n",
"for tau in taus:\n",
" y = gumbel_softmax(6, tau, pi)\n",
" sns.barplot(x=x_range, y=y, color='#0068B7')\n",
" sns.plt.title(r'$\\tau={}$'.format(tau))\n",
" sns.plt.xlabel(\"Categorical value\")\n",
" sns.plt.ylabel(\"Probability\")\n",
" plt.savefig(\"gumbel_softmax_tag={}.pdf\".format(tau))\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [conda root]",
"language": "python",
"name": "conda-root-py"
},
"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"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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