slides/2_1_cde.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Introduction to Conditional Density Estimation\n",
    "\n",
    "<br/>\n",
    "\n",
    "Please open `2_1_cde_participants.ipynb`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "os.environ['KMP_DUPLICATE_LIB_OK']='True'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "from math import pi, log\n",
    "from torch.utils import data\n",
    "import numpy as np\n",
    "from torch import tensor\n",
    "from torch.distributions import Normal\n",
    "import matplotlib as mpl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "_ = torch.manual_seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A very brief intro to PyTorch\n",
    "\n",
    "Say we are given some data that looks as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KgXCctvbRGuU/ij9/+2cmhE5gcdxi9mTvYdt327gt+LZ2W2CD9fdLgpfo19pr8cyMnNkqmJwuOU12RTZxfnFd3oCvq2NY9gZDGSMb3Cytp+LqYlCg1FRKE00sjltM5JBIFsctJq0wjcvGy20Gr8FMgpfo19pr8aAC83UzX3z/BZNCJ/HFxS84XnQcgBNFJ6xdiB1N3OzOGJY9u9HKGJkAuFR1yfp7YKw3Yqwzsid7j7Xl5apyJcwnzOYceeiR4CX6CHv/GNtr8VTVV3G19irfFH7Dx2c+pqahhqW3LGVR3KJWXYjt7X3U3TGstoKhyWyi2FgMKmwSQWSMTEDbvwcFhgKOXj5KWmEaripXlo1eZtPqkoeeZhK8hNP15I+xrRbPuOBxnCg6wczhM/np2J+yP3c/Kd+ncHvY7dQ01BA1NKrT8Sh7x7BaBsOs8iy2n9nO+YrzAMT4xZCUkES8f7yMkQmg9e9Z1NAoQnWhrBi9ArWbmjCfMLRqLUXGImsXtDz0NJPgJZyqN1ogN7Z4brwh3BV9F3uy97Dp2Cbi/OIoNBaiU+usN4O2Wn09TegwmU0k5yVjrDeyfPRyUMGhi4dIyUshXBfe6wkjom+xZ6zU082Tj89+TGl1KRp3DXNGzuFq3VV2Z++2PtjF+cfJQ8//T4KXcKreaoFY3mtJG24ZGL4r+w4VKjxcPQBQoQJV83nttfrsGcO6sV41DTWE6kKZEtG888H5ivOYGppvaiE+IT26vui77BkrTclL4djlYwT7BLNq4irqGutIyUtBURQSgxJt5iIqKPLQgwQv4WS91QI5WXyS/ef3o6AwxHMII4eOJKcih6zyLKrqqxgfMp6fjv0pKpUKRVHYd34fxcbiDlt9PVmJW++hR+OuIf9aPocLDoOqeQ3FSH2ktW4DcaXvwa67PQkmswmdh45pEdMwNZi4f8z9hOpCuVZ3jWOXjwG0erCL948nszSTY5ePoXXXMnvk7EH5uyPBSzhFy26VnrZADhcc5vlDz3O96Tr+Gn+0ai2VdZU8Mu4RqsxV1Jhr+Cr/Ky5UXrAJkKjotNXXcgyrO0klWrWWOSPn8PHZj9l2ZhsAMb4xrW40XZmnI5ll/Ud3ehJattDMjWbqGuu4UHkBrVpLRmkGWnctitK6leWt9rbufziY11WX4CVuura6VVaMXmHXDfpk8Uk2HtnI5arLTA2fyriQcZy9cpazZWc5VXKKAkNBu2sXBnsH27T60i6nUVVfhZuq9Z+FPUkl8f7xrL59dZvZhj35Xg3GzLL+oqs9CWXVZXya/SmJgYlMCptERmkGhy4e4tvCb21aVECbyUgtuxIlYUOIm6C9bpUVo1d0e/sRk9lESl4Kfl5+xPvFE+UXxbW6a9Q31lPbWMu3Rd8yLXJah2sXWsYb9mTvochYRLx/PLuzd9sEifbK7Ovp2+mSPFq1lmi/6F79Xg3GG1V/0ZWx0qzyLD7N/pTTpadRu6qJHBJJYmAiBy8epLaxFndXd2uLqrNkJEnYEOImMdQbqGusI0ATgLuLe4/++Az1BjzdPInzjyOrPIu8q3nkXM1BURRuDbwVnYeuS2sX1jXW8f217wnXhfPD6B9S11hnEyTaumEcvHiQd0++i7uruzUzrLdbRHKj6p86Gsu0PJAkBiaidlXjonLhwIUDROojyb2ay/1j7re2xNqbiyhZqs1kPy9xU5jMJoqMRXxf+T3HC4/zt1N/468n/8qn2Z/a/cen99Dj6eZJsE8wQd5B5F7Npaquikmhk3jw1gfxdPPscI8uy41kxNARTIuYxtyRc8kozSBqaJTNnkgtu4Ku1V0j7XIaJ4pOUGYqQ+2qJv9aPh+f/RiT2dRr36+2vu5gvlE5g+V31p6fq1atJcQnpNVDRrGxmMq6SkYPG8386PkoKHxT+A1HLx9lmHYYo4eNtj6o3Lgvl2Xsc3zIeHIqcth+Zjs5FTmDNktVWl7C4SzjNnWNdRwvPE5CYAJebl4UGAo4WXySJ25/wq4/vpZdNMHewcweMZvxIeOtf8wad02H3TeWls2k0ElU1FSACqrN1aQVptkEiRu7gspN5SiKwryoeUyJmMLhgsNsO7ONYmNxl7oIu5qAcePXbbjewJjAMd3+Ponuc8RYY1Z5FskXkskszWSjcSNzR84lUh/J5arL6Dx0nLtyjrfS3uLeW+6lrrHO5nfwxvKMDxlPkHfQoE7ikeAlHKrluE2AJoB8Qz5ebl4sT1hORW0FyXnJBHkH2X39jrpownXhzBw+ExQI9mmdLGFp2VyovMAPgn7AjrM7KKkuwd3FvVVWYMuvU15Tzrnyc9a5Yq3+7UB3b4qWr3ui+AQZpRlklWeRXZ4tiRsOZM9YY2cPJNbuwqBEhnkP428n/8bhgsMEeQcRqgtlYexC5oycw46zO/jvb/6bSaGTrL+DbZXnZPFJVoxeMWgDF0jwEg7WctzG3cWdcF04BYYCKmoruFJzBS93rx53g7WVbt6VINGyZdOkNBGpj2Rh7ELGB49v86Zg+Tp6Dz0xfjEcuniI8xXnKTIWEeMbQ7B3cIfl7OimaPletXfzyy7PJjGwexlmkmJvn+6ONXbld81yzaihUWSXZ3N39N2kfJ+CVq0lvSSdFaNXMDF0IqE+oWzJ3ML8qPnWVryMfbZNgpfoNV1ZZslX48vJ4pMk5yXj5e7FuOBx1n793vpD7M6Tsz0ThbVqLUkJSaTkpWBqMBGpj+zSRNH2bkInik+QXZ7d7s3PnptXezfUngS0wRIMuzNxvqu/a5ZrphWmcbX2KoVVhcQHxLMsYRm/SfkN285sI9o3mguVF/D18iXYJ9iu8gwmErxEr+jOMktP3P4EQd5BlFSXcOTSEWoaano1Y6+7N3t7NvTratBrecNv6ybUcL2BjJKMDuftWM47dPEQiqKQV5lnPd7e12zrhlrTUMOJohN2jeMMpvlm3Vka7MaehQBNAKdLTlsfyFrO8bNMy/im8BuMZiO/nvJrTA0mJoRMIK8yjy2ZW/D18mVqxFQA62K8PV2qbKDqE8HrwIED/Pa3v+XMmTMEBgby85//nDVr1qBStT2IkJubS0xMTKvjCQkJfPfdd3ZfV9ins6fP9rYKeef4O1TUVDB8yHBrxt7q21f3+I/yZj2pdhb02rrh33gTGhM4hqzyrE4D7dXaq2w8spGrtVdRoWLk0JHEB8S3uT18W8H7dMlpUvJSmBQ2yfo9SclLwc3FrdPJ04NxvllXH04sv2uf5nzK1ZqrXKq6RJmpjFBdKN+VfddqR4GVt64k2jeaf5z+B/tz9xOhjyA+IJ4QnxDmR80n2CeYS1WX2Jq5tdWDgiwlZqvXg1djYyNubl2/7LFjx1i4cCHLli3jxRdfJDU1lbVr19LY2MhTTz3V5jnp6ekApKSkoNForMdb/t+e6wr7dKWlc+ONPrUgleS8ZG4LuQ1PN0+ihkZx5PKRLmfsdeTGxU6dsf5bR5OxW64mAs3jWe0F2qzyLPZl72P7me3UNdbxw6gf4uvly5FLR/hH+j+4Lfg261w0y02treBdf70eTzdP689IURQOXDhAviGfCF0Ec6Lab/W2tW3HscvHKK4uJtq3Zz+r/qStblOtWsstAbfw5rE3CfUJJco3ini/eHac3UGAJqDVjgIrb13J/Oj5BGgD+OL7L1Chor6xntkjZxPtF93pg4IErf/V7eD1f//v/+V3v/udTaCwSE9PZ+XKldbg0hXr169n7NixfPDBBwD88Ic/pKGhgZdffpknnngCLy+vNr9OWFgYs2bN6tXrCvt0t6VjMpv4tuhbdB46pkdOR+uu5fMLn9NwvaFLGXtdpaDY/HszdRTQb5z/0146vOVGpvfS46fxA6CmsYZor2iuK9cpqS4h9VIqFTUVrZ7Sb2zhzRoxixNFzRmLiqLw25TfUllXiZuLG+U15VTWVbJ6ctutXut4zeU0Gpsa+Xfev7lae9Vhk7P7ghtbzaG6UAqrCqlrrKOusY7ZI2czLngcWeVZHLl0BDcXN/w0fkyNmIqXmxf7c/fj6+Xb5o4CWrWWccHjiPOLaxUMJTmj67o9SXnLli2MHTuW48ePW49dv36d559/nokTJ2IwGDo421Z9fT0HDx5kyZIlNseXLl2K0WgkNTW1zfPS09O59dZbe/26ACaTyeZDdM7S0unqxElDvQGdh47bgm/j26JvrSng4frwTjP2uqLlKgYPj3+YxMBEUgtSe30ScUe6M8E43j+eFaNXEO8fj4JCVnkWWzO3cqK4eXxqRuQMvN29uWK6QomxhCs1V6hrrMNYZySrPIs4/ziSEpKI84+z1tNyzYWxC1kxegXjgscxLXIamaWZbDq2icq6Sn427mc8NPYhvNXenL1yluLq4jbrolVrCdWF8o/T/+DFr17k3JVzLIxd6JTv683QsvWTlJBEhD6Cj777CBUqmpQmSk2lvHXsLQ4XHLb+nk0Om8xQz6GkFqSSU5GDh5sHV2uvcrjgMIcvHabIWITWXWvz829rIrNMTO+6bgevkydPotPpmDJlCi+++CKnTp1iwoQJvPTSS6xatYozZ850+Vp5eXmYzWZiY2NtjkdHN3dFZGdnt3leeno6RqORO+64A09PT4KCgnjqqadoaGjo0XUBvL29rR+BgYFdrstgd+PNsqOnccvKGKOGjbLO/fLX+LN89PJeebps6+n1xtUKHK27AR3+Nx3eEogySzMxXzdTXF3MvOh5oILsq9nsO7+PYdph3BpyK24ubq3qWVxdTJGxCMC6XmSRsYhwXTjzo+YzUj+SyCGRROgjGD1sNE1KEw1NDbTXQDWZTRRWFbIoZhF3Rd/Fw+Mfpqq+qtVKJF3VcuWKnqxi4Sgt09prGmoI0AZgvm6myFjE2OCx/GLiLximHcZnuZ9R11jHpLBJNqtlnL96ngcSH8Bf68+2M9vY9t02fNQ+Xeq6tuf3ZrDqdrdhfHw8x44dY8OGDaxfv57nnnuO+Ph4vvnmG8aOHduta1laaTqdzua4j48PAFVVVa3OKS8vp7CwkMbGRl577TUiIyNJSUlhw4YNXLp0iS1btth1XdF9N44BdLVPvmX2lKebJ9G+0cwaMYtxwePs+ro36iupxd0ZZG+vuyjeP56cihwarjcwKWwSI4eMZHLYZFQqFZerLrfaMqO0upTPcj9D7aq26e6ydH/5afwoMZVgqDfwh+N/INg7mIqaCiaETSDYJ9j6vXVTuVkXHbaUbcbwGZgaTHi6e1Jd1Xolkq5o2R1XUl0CQJB3UJ/KYNR76CmpLuGtY28Rqgvl4rWLXK29SkVtBZH6yOZxQn0E1fXVlJpKSbucxqSwSUTqI7lSc4X/GPUfjBg6ghmRM+zaUUCSM7rGroSNCxcu8MUXX3D9+nVCQkL4/vvv+eyzz0hMTMTV1bXL12lqaurwdReX1g1DrVbLgQMHiImJYfjw4QDMmDEDDw8P1q1bx7p16+y6rkV1dbX1/yaTadC3vtoLFD1Nnbb3D7S7k4+dnVrc1YDeXsAdHzye8cHjMdQbmBIxhZPFJymrKcNF5dJqy4yG6w3WAGjZ4mVL5hbrYq+Wz2ePmM33177n2OVjZJVnMXfkXO4fcz+Xqi7xdf7XFFcXk1uRS4Q+Ar2nnjvC7+jySiQdPVi07I6LGhrFW8feQqVSsSBmARcqL/Qog9GeOWidnWPJSla7qonyjeJKzRXe/uZtIvQR1DbWklWRRYQugi2ZW9h7fi+GOgPRvtHsy9lHYlAi44PH2518JMkZnet28HrhhRd45ZVX8PPzY+/evcydO5f169fz7LPPsm3bNt59910mTJjQpWvp9c1PbEaj0ea4pWVkeb0lLy8v5s6d2+r4ggULWLduHadPn2bMmDHdvq6FViu/MBYdTXTtjeVzuvsH6ujJx87UWcC1jI+0NchvqWeNuYYvLn5hbb1F6CNoUpqI0EfYfD42eCwzh8/krui7OHjxIMvHLCfYO5itmVuJ0EdQ01BDuD6c3MpcArWB/PnEn/lR/I/ILM2ksrYSjbuG+8fcb1M+k9lkXcLK0urraLJ1TUMNobpQoDlI9CQxwZ4HqY5+t7MrshnqOZQVo1dgNBvxUfvw5cUvidRHklmWibnRzJmyM8yNmsui2EUcuniIDzI+4CeJPyHYJ5iPz37MN0XfkBGaMWATWvqCbgev5557jgceeIDf//73DBkyBICXX36ZJUuW8J//+Z/ccccd1rGnzkRFReHq6kpubq7Nccvno0aNanXO+fPn+eKLL1i2bJn16wPU1tYCEBAQYNd1ha2OAoUjls/pipsx+diZ2gu4bXXPtmQ5ZjKbbFpvBYYCXFQuFBgKCPYJpsBQgLHeyAcZHzB8yHAKjYXo1DqCvYOt39sAbQDHC4+jdlETpgsj6ZYktp/dTtrlNFSoyL2ai4vKhWpzNQHaAGvGXfKFZNIK0wjyDuLehHtbbSsDtq3LqKFRFFYVolKprF2fLbsgu9qSsvdBqqNJ3HWNdfw779+cKjlFYmAihVWF6Dx11oCdXZENKrgt+DbcXdyJ9YvF082TMF0YJ4tPMnP4TM5XnCfEJ2TAz4dzpm4nbOzevZvNmzfbBA6ACRMmkJ6ezurVq7t8LU9PT6ZPn86uXbtstrPeuXMner2eiRMntjqnuLiYRx99lI8//tjm+LZt29DpdIwfP96u6wpbHSU9dCcjyrJjbIQ+olVGXHcNhkysGzPQLJmHe3P2sjVzK1nlWR2e23Kw/1LVJZaPXs6lqktsP7Od3Ku5RA6JRO2qBpr3hbJMTbCM82w+vZm0wjT2nt+LoihU1lUSqA3k+8rvqaqvYm7UXIJ8gsgszeT1I69zOL854y5EF8L4kPHMHD6zzW1lbizfvvP70Hnq8FH7sO/8PpvEhPbqXFZd1txtWl1mvaY9yTltnVPbUEtKXgpx/nH8eNSP8df4U2Qsor6xvrn7UPnfOgBklGRYt/U5fOkwLioXsiuyMTWYQAFvtTeTQifd9EShwaTbLa9Fixa1+5parWbDhg3dut66deuYM2cOSUlJPPTQQxw5coSNGzfy6quvotFoqKqq4uzZs0RFRREQEMDUqVOZPXs2a9asoba2lltuuYV9+/bx+9//nk2bNlmDamfXFR3rKOmhq2NK7e0Ya2/3UF8ay7oZ7GlVtLeaiaVb0d3VnQUxC6wtnn3n99lMmFa7qonzjyOvMo9jl48R5B2Eh5sHCgr+Gn/KTGXMjJxJiHcI+YZ8Psv7DL1az7jgcRRVFbW7rUx75QNalbWtOp+5cobd53bTRBMuuLB8zHLujrnbruScziZx1zTUkBiYSJxfHHOj5hKoDbR+nwBOFJ1gbtRcKusqKTAUcMV0hR/F/4gSYwknik5QZCxi6S1LuVB5YcA9XPUlTl8eatasWezcuZP169dzzz33EBoaysaNG1mzZg3QnJp/55138t5777Fy5UpcXFzYtWsXzz//PG+++SbFxcVERUXxl7/8hZ/97Gddvq7oWGeBorMxpfZ2jI3zi+vRH3R/G8vqCXsnrN7YtXhjt+KFygutbvSGegNB3kHWwDZnxBz+euqv1DfWo3HXEKAJ4Kv8r3BRuVBoKKTuep014+5c2TlKTCWoXdWcKjlFQ1NDm8kcHZWvrTpb1gpMzU/ls9zPmBE5g8Vxi9mTvYdt323jtuDbGOY9rFsPNC03dDxZfLLNSdxRQ6MoNBaiQkWgNtAmCFnKtyhuEe4u7hQYCkjOS2Zy2GT0HnrGBI4hszST9JL0Af9w5WxOD14AS5YsaTWh2GLmzJk2XX/QnAL/xhtv8MYbb9h9XdG5zgJFR2NK1o0ewyYROSSSAxcOcOTSEa6YrrBk1JIe/UH3t7Ese/V2yn9nDyQtA5tGreHO4XcyP3o+OrWOitoKTGYT58rPceTyEVDAfN3MxWsXWRC7AJ2HjgJDAXWNdTz4gwet1zWZTRRXF1NjrkGj1nSaMu6mcsNQZ2DHmR2YGkxcqrrEuSvnUFBYHLeYyCGRLI5bTFphGpeNlxnmPYx4/3h8PX25bLxMmE8Yw7yHtTlm1tmGji03L9WpdaCCfef3tfl9svxMWm7ro1VrmR453ZodOtAfrpytTwQv0XfZGygsNyHLHBiNm4brTdfRe+o5UXQCjbtGsrA64Yhu0vYeSNr6WrNHzibaN5oiYxFB3kH8dOxP+bbwW/5y8i/UNdYRpgvD090TnYfOZnPRMYFjrGNX289s59uibykzlTFMO4zbQm4jKSGpzZ+9JbgY6g3sOreL+IB4xgaNZcSQEfxPxv/w8ZmPuTfhXvZk78FV5UqYT5jNeQoKJzjR5lJOcX5xJOcl4+vlS5xfHOU15a02dOysS7OrP5PB8nDlbBK8RJd1NQPMcjOpbaxlS+YWvi74mgJDAYvjF7ModtGgWJW8tziim7S9m2t7X6vljtOx/rFE+0bjr/HngcQH2JO9p83NRU1mE8kXkrlae5Xh+uFMCZ9CobGQq7VXSclLafWzbznWNTViKsZ6Y/OqKwnLUbupyarIIq0wjfTSdFxVriyOX0yj0khZdZnNGJllLtv0iOk2SzlNj5jOgdwDeLl7oXZVE64Px9PNs1UXbEddmo78mYjuk+AluqSr6e4tb0L3JtxL2uU0UgtSSQxMZFHsIlls1A4380m+vVR8S2vjdMlpKusquS30NoZ6DcXXy5e0wjR2nt3JUK+hTA6fjKHeQLmpnBJTCd7u3vhr/VkSv4R/Zv0TQ53BZoFaixvHukYOHcmlqkvWoPiDwB+w+vbVVNZVUttQy9krZ9mb0zwxuLaxlnsT7rXOZTNfN1NUXcTM4TO5J/4eNh3dxO7s3VSbqxkTOIY4vzj25+7HReWCm8q+W6C0rpxPgpfoVHey3m5cF270sNHkVORQ11jn9OWahP1atjYsK31sP7Od0upSRg4didpNTXF1MXtz9gJw7so5quqrqG+sJ9A7kPrGegqNhbioXPDX+Lf62Xe24/bUiKmMGDqCYeZhbM3cav1dPHTxEP+T8T8cuniIGcNnkFORg7HeSEl1iXUpJ3+NP9+Vfcd15TqZZZlklWdR21DLLcNuoVFpdMa3U/QCCV6iU93JertxXTjLBM8FMQtssrskC6v/sbQ2LCt9FFcXsztrNwnDEhgTMIa/nPwL1eZq/DX+3DLsFqrqqiitLiWjLIPcq7kEeQdxW8htbWYhtjWWZNlxu70tQ0qqS7h47SJ1jXV8kPEByXnJGOoNhOvDOVV8iucPPc+tQbfi6+VLmakMdxd3ooZGUVpdSmV9JSHeIfIA1Y9J8BKdujH5oistJ8u6cJYJnnF+cW0ubST6J61aS5GxiPSSdFxdXLlw9QJuLm7UNdZxqvgUt4XcRkl1CffE30Osfyy3h93O8CHDW2UbthxH7cpYUsu9xSxBzjIXa8fZHTyQ+AAzhs9gx5kdfH7hc8zXzZgbzfhr/AnVhVLbWEvd9TpqG2pJGJYgv4f9mAQv0aEbky/SCtMI8Qlpt+V043yhlhNhb9y7SPRfJrOJjJIMgnyCiPGLoa6hjs8vfE5jUyPx/vG4uLgw1GsoXxd8TYxvDJPDJrc5ib2tcdSOFvq1tND25uwlvSSdiaETmRc1D0VR+DTnU2L9YhniOYSlCUupbaxlSsQU3FzcOFd+jntG3cNw/XBOlpzki++/IMo36mZ/20QvkuAlWmm5LcaNyReZZZksjl3MMO9hbZ7bMjNNxrcGLkO9AbWbmntvuZeM0gyqzdW4qFxQu6oZ6jWUs2VnCfEJodBYaE2db6kr46jtBTfLvC5FUYjziyPIO4i0y2k26zhmlGbg5e5FnF8cADF+MaRdTuOS4RJFxiJu8b+lVzY+Fc4jwUvYaHnDuDGTa1LYJPIN+R0Ocg+2JZwGK8tDSl1jHXdF30VaYRo/jPohiqIwwncEY24dQ2ZZJmHGMMYHj291fmfjqJ0Ft2Hew1gUt4jUglTyz+TjonKxruNo+bzl711SQhIpeSmYGkxE6iO7tDGk6NskeA1iN3bJ3HjDsMyZ6c5YF8g8mMGgrYeUu2PvBpr3F/vy4pfWic4djV21l4HalSShjtZxvPH3Tn4nBx4JXoNUW10yOg+dzQ1jUtgk0gqbuwrzDa2fZjsi82AGvvYCQlcCSmct9K4ujdXeOo5tkd/JgUWl3LhwoLAymUx4e3sDzTss9/eNKluOZe3O3m3TJZNTkcPi2MXtHrdsCS9//KI7ssqzSM5LpqahBo27ptXmjB2t2pJVnkVqQSpNSpM1uMmSYsJCglcHBlLwOll8kpS8FDzdPKlrrKO2sZbHJz3OEM8hXKu7xvYz25k1fBZF1UVklmbi7uouNwzRIyaziTeOvoGx3mgz52/17au7/BDU1SXJxODT7c0oRf9zsvgkbx19i1JTKU1KE0M9h5J7NZe0y2nWTR1LTaXszt7NscvHqGusI94/nhWjV0jgEnYrNhZzvuI8M4fPZOWtK607DBcbi7t8DcukaAlc4kYy5jXAmcwmUvJSGOY9jF9M/AX5hnzSS9KJ0EVYx7IarjdQVl2Gp5un9Qn5UP6hNrPEhOgyVSf/CtEDErwGOEO9AU83T8J14eQb8onUR7Inew9B3kE8mPggjUoj5aZyjl0+xvLRy5kSMYXDBYfZdmYbxcZiov2i27yudOeIzgR7BxPjF8Ohi4c4X3GeImMRMb4xMr9K9AoJXgOc3kOPp5snnu6epJeksyd7D1dMV7hvzH3WicY1DTXNb+7iE3JXV5gXg5tWrSUpIYl/5fyL8ppygrRB3B17tzzsiF4hwWuAa5mSrEJFkHcQ9425j3HB46zv6c4TcndWmBcCQO2mRuehQ+2mdnZRxAAiwWuAaas7r7MJmpYn5K6sQNCdFebF4GZ50EkMTJQHHdHrJHgNIB1153U2QbOrKxB0dfKoEPKgIxxJgtcA0VZ3XkpeCm4qN4J9grt0s+jKCgSydqHoKnnQEY4kwWuAuPEp19PNk2OXj2FqMDHUc2ivJlXIOnGiK+RBRzhSn5ikfODAASZMmIBGo2HEiBG8/vrrdLTwR319PS+//DLx8fFotVri4uJ44YUXMJvNNu8LCwtDpVK1+igvL3d0lW66lk+5hVWFfHz2Y4J9grl/zP3E+ceRkpdCbkUuJrOpV76eTB4VXWGZ7L4wdqFMehe9yuktr2PHjrFw4UKWLVvGiy++SGpqKmvXrqWxsZGnnnqqzXOeeOIJPvjgA5555hkmTJjAt99+y/PPP09+fj5/+9vfACgvL6ewsJCNGzcydepUm/OHDBni6GrddC2fco9dPkZpdSmrJq5qnnRsLHRYK0yIzsiCuMIRnL624fz587l27RppaWnWY7/+9a/54x//SGlpKV5eXjbvr6ioICAggA0bNvBf//Vf1uMbNmzgqaeeoqysjICAAJKTk5k7dy65ublERdm3Y2p/XNvQZDZRXF3MZ7mfkRiYSNTQKN5KewsVKp6Y9AQXKi+QU5HDitEr5IYihOi3nNptWF9fz8GDB1myZInN8aVLl2I0GklNTW11TlVVFY8++iiLFy+2OR4f39ySyMvLAyA9PR0fHx9GjhzZrTKZTCabj/7CZDZRZCwCINo3mjkj55BTkcN7p97j+8rvWRCzgFBdKImBiTQpTRjqDU4usRBC2M+p3YZ5eXmYzWZiY2NtjkdHNy9JlJ2dzdy5c21eGzFiBO+8806ra33yySe4u7tbr5Weno6vry9Lly4lOTmZ69evs2DBAt566y2Cg9tfnsbS0uqLTGZT86KmquaJxZ1tl17TUMP+6v24u7izN2cvXu5e1DXWScaXEKLfc2rwMhian/51Op3NcR8fH6C5ldUV//znP3n//fdZtWoVQ4cOBZqDV2FhIQ8//DBPPvkk586d49lnn2XGjBmcOnWqX3QBtpRVnsX2M9s5X3EegBi/GJISkgjXhbe54oWvpy8nik4wLXIac6PmsuPsDv77m/9mUugk2QJdCNHvOTV4NTU1dfi6i0vnvZq7du3ivvvuY+rUqbz22mvW4++++y5ubm5MmDABgGnTppGQkMDUqVPZvHkzjz32WJvXq66utv7fZDIRGBjYlao4lMlsIjkvGWO9keWjl4MKDl08REpeCvOj5lPXWEeAJgB3F3frRNDLxss2qfOhPqFsydzC/Oj5RPu2vdiuEEL0F04NXnp9c9eV0Wi0OW5pcVleb8+bb77Jr371K2bOnMknn3yCp6en9bXJkye3ev+UKVPQ6/WcPn263Wv2xRaZod5ATUMNobpQpkRMAeB8xXlMDSYuVF7geOFx8g35hOvC8dX44qJyIcwnjBOcsE4QvVB5AV8vX1nRWwgxIDg1YSMqKgpXV1dyc3Ntjls+HzVqVJvnKYrC448/zurVq1m2bBn79++3djVCc3fk3//+d7777jub85qamjCbzQQEBPRyTRxL76FH466hsKqQwwWHOXzpMEXGItxUbpy/ep65UXOJ0EdwqeoSyReSGRc8jmHew5gWOY2cihy2n9lOTkWOTBAVQgwYTm15eXp6Mn36dHbt2sWvfvUrVKrmPTh27tyJXq9n4sSJbZ739NNP8/bbb7N69Wpef/1163kWHh4erFq1iiVLlrBlyxbr8T179lBbW8udd97puEo5gFatZc7IOXx89mO2ndkGQIxvDLeF3kZWeRaL4hbh7uJOgaGA5LxkgryDAFkJQwgxcDl9kvK6deuYM2cOSUlJPPTQQxw5coSNGzfy6quvotFoqKqq4uzZs0RFRREQEEB6ejobNmxgwoQJ3HvvvTbzwwBuueUWdDodTz31FOvXrycwMJC7776bzMxMnnvuOX70ox8xa9YsJ9XWPiazCZ2HjkfGPUJVfZU12xAguzzb2jV4peYKXu5eNpmEMkFUCDEQOX2SMjRnC65fv57s7GxCQ0P5+c9/zpo1awA4ePAgd955J++99x4rV67k2Wef5cUXX2z3Wl9++SUzZ86kqamJP//5z/zhD3/gwoUL+Pn5cf/99/Pcc8+1mvjcnr4wSbmzjR+zyrOsW5lo3bXMHjlbVs8QQgx4fSJ49VXODl4ms4mtmVtt0uBvXB0jqzyL5AvJ1DTWoHHTMCdqjgQvIcSA1ycW5hVta2s/pJarY1g3+wtK5OHxD5MYlEhqQWqvLb4rhBB9lQSvPqzlSvHX6q612g+ps+AmhBADldMTNkT7OtsPSTb7E0IMVjLm1QFnj3lZy2E2tZvunlWeRWpBKk1KkzW4yZiXEGKgk+DVAWcHr46Clj3vE0KIgUK6DfuIGwNQZynyLclcLiHEYCPBy8lMZhMnik+QUZKB2k2NChXjQ8ZzouhEq5Xiw3XhEqSEEALJNnSqrPIs3kt/j3dPvEt+VT63Bt3KMO0wNqdv5krNFckiFEKIdkjL6ya5sVvQMkcrxCeE8SHjifGLYUvGFgqrCrlouIiiKLi5uPHw+Icli1AIIW4gwesmyCrPIjkvmZqGGjTuGuaMnIPOQ4eCwqTQSVTUVHCt9hpHLh0hMTCRpaFLuVpzlU/OfYKLyoUhnkNkRXghhGhBgpeDmcwmtp/ZjrHeSKgulPxr+Xx89mMeGfcIKlRcqLxArF8sb3/zNmU1ZUQOieSe+HvwcvOioKqAMcPGSOASQogbSPBysGJjMecrzrN89HKmREzhcMFhtp3ZRlV9FdMip/HxmY/JqcihqakJrbuW6vpqvNy82JO9Bw9XD8YGjZXAJYQQN5Dg5Wiq9v8N9wlnqNdQloxawqTQSWzJ3MIn5z6hoKoAD1cPlo1exjDvYU4otBBC9G0SvBws2DuYGL8YDl08xPmK8xQZi4jxjSHYO7h5bUJFYZT/KIZ4DuHh8Q/jonJhzLAxjA0aK4FLCCHaIcHLwbRqLUkJSdY9tyL1kcweORutWkt2RTbHC4+Tb8gnXBeOr8ZXkjOEEKILZHmoDvTm8lAms4ni6mJQINineRfkrZlb8XTzpLKukgJDAVdMV3ji9icYFzyuV8ovhBADlbS8HMwyv6ukuoQTRSesyz3F+cehoLAobhHuLu4UGApIzksmyDvI2UUWQog+T4KXA1nWJ6xrrON44XHmRs9lUewiMkozyCzNRFEU63YmV2qu4OXuJRORhRCiCyR4OYhlBY04/zgCNAHkG/KprK3E3cWdxMBEssqziPePJ6cip829uoQQQrRPgpeDtNzl2N3FnXBdOAWGguaxrZoruKhcGB88nvHB42U7EyGE6CZZmNdBWu5y3NDUgK+XL1dMV0jOSyanIkdaWUII0QOSbdiBnmYbZpVnWVPkte5aJodPJsg7yK49u4QQQvyvPtHyOnDgABMmTECj0TBixAhef/11OoupH374IQkJCXh5eTFq1Cjef//9Vu/59ttvmTlzJt7e3oSEhPD0009jNpsdVY02WeqhKAoadw0hPiE2q8rH+ceRlJBEnH8cqQWpmMymm1o+IYToj5wevI4dO8bChQuJj49n165d3H///axdu5YNGza0e87OnTu5//77mTdvHp988gkzZ85k5cqVfPTRR9b35OXlMWfOHLy8vNi+fTtr1qxh06ZNPP744zejWtbglBiUyMPjHyYxKNEmOLUcE5M9u4QQopsUJ5s3b54yceJEm2Nr165VfHx8lJqamjbPiY2NVZKSkmyOJSUlKdHR0dbPH374YSUsLEypr6+3HnvnnXcUFxcXJT8/v0tlq66uVgAFUKqrq7taJUVRFKWwqlD587d/ViprKxVFUZTK2krlz9/+WSmsKmy+dn218pdv/6IcunhIqaytVA5dPKS8e+Jdpbq+e19HCCEGI6e2vOrr6zl48CBLliyxOb506VKMRiOpqamtzrl48SI5OTltnpObm8v58+cB+Pzzz1mwYAFqtdrmPU1NTXz++eftlslkMtl82Ktlwsa1umutNpTUqrVMi5xGTkUO289slyQOIYToBqemyufl5WE2m4mNjbU5Hh0dDUB2djZz5861ee3cuXMAHZ4TFhZGfn5+q/cEBASg0+nIzs5ut0yWBI2esgSn1ILUVvO4LKtuhOvCWTF6haTKCyFENzk1eBkMzeM7Op3O5riPjw8AVVVVdp3T3nss72vruo4Q7x9PuC7cJjhJhqEQQvScU4NXU1NTh6+7uLTu1ezKOfZc16K6utr6f5PJRGBgYIfX6oxWrbW2qFpmGCYGJpJRmkFqQSrhunBpdQkhRDc4dcxLr28e/zEajTbHLS0jy+vdPcfS4rrxPZb3tXVdC61Wa/PRUyaziSJjkbWrUDIMhRCi55za8oqKisLV1ZXc3Fyb45bPR40a1eqcuLg463vGjh3b5jne3t6Ehoa2um5ZWRlGo7HN6zpCVnkWyXnJ1DTUoHHXcEf4HdYkDkvLq2UShxBCiK5xasvL09OT6dOns2vXLptJyTt37kSv1zNx4sRW50RHRzNixAh27Nhhc3znzp3ExMQwfPhwAObNm8fevXupr6+3eY+rqyuzZs1yTIVaMJlNbD+znfxr+ahd1eRfy2ff+X2MDxkvGYZCCNFTzs7VT0lJUVQqlbJ06VLlX//6l7Ju3TpFpVIpGzZsUBRFUQwGg3L06FGlrKzMes57772nAMpjjz2m7N+/X3n00UcVQPnoo4+s7zl37pzi6emp3Hnnncqnn36qvPHGG4qHh4fy2GOPdblsPZnndb78vPLAzgeUvdl7lcraSmVv9l7lJ7t+opwvP69U11crhVWFMqdLCCHs5PQVNmbNmsXOnTvJzs7mnnvuYcuWLWzcuJG1a9cCcPLkSSZPnsy+ffus56xcuZI//elP/Pvf/+aee+7h0KFDbN68mWXLllnfEx8fz4EDB6ipqWHp0qVs2rSJX/7yl/zud7+7ORVTtf+vVq21LhMlhBCi+2Rh3g70ZGFek9nEG0ffoNpcTYhPCEXGInzUPqyevFqClhBC9JDTW14DlVatJSkhiUh9JObrZiL1kdybcK8ELiGE6AXS8upAT7dEAawp8rKChhBC9B7ZSdnBWk5SFkII0Tuk21AIIUS/Iy2vDrTsUe3JCvNCCCG6TqPRoFKpOnyPBK8O1NTUWP/f0zUOhRBCdE1Xcgyk21AIIUS/I9mGHWhqaqK8vBzoWjO2pZYr0peWlvbKIr/9yWCu/2CuOwzu+g/mukPv1V+6DXvIxcWFYcOG9fg6vbVCfX81mOs/mOsOg7v+g7nu4Pj6S7ehEEKIfkeClxBCiH5HxryEEEL0O9LyEkII0e9I8BJCCNHvSPASQgjR70jwEkII0e9I8OqhAwcOMGHCBDQaDSNGjOD111+nsxyYDz/8kISEBLy8vBg1ahTvv//+TSpt7+pu3evr63n55ZeJj49Hq9USFxfHCy+8gNlsvoml7j32/OwtGhsbmThxIjNnznRsIR3Enrrv27ePiRMn4uXlRVhYGE888US/XTO0u/VvbGzk1VdfJSYmBq1Wy6233sq2bdtuYol73+XLlxkyZAgHDx7s9L0Ouecpwm5Hjx5V3N3dlQceeEDZv3+/8tvf/lZRqVTKK6+80u45O3bsUFQqlfLkk08qn332mfLoo48qgPLhhx/exJL3nD11f+SRRxSNRqO88sorSnJysvLqq68qXl5eykMPPXQTS9477Kl/Sy+++KICKDNmzHBsQR3Anrrv2bNHcXFxUVauXKmkpKQob7/9tuLj46OsWLHiJpa8d9hT/9/+9reKi4uL8txzzynJycnKz3/+cwVQduzYcRNL3nsKCgqUUaNGKYDy5ZdfdvheR93zJHj1wLx585SJEyfaHFu7dq3i4+Oj1NTUtHlObGyskpSUZHMsKSlJiY6Odlg5HaG7dS8vL1dUKpXy2muv2Rx/9dVXFUApKytzaHl7mz0/e4v09HTFy8tLCQoK6pfBy566R0VFtfq9f+utt5SRI0cqJpPJYWV1BHvqHxwcrDzwwAM2x26//XZl5syZDiunI1y/fl157733FD8/P8XX17dLwctR9zzpNrRTfX09Bw8eZMmSJTbHly5ditFoJDU1tdU5Fy9eJCcnp81zcnNzOX/+vEPL3FvsqXtVVRWPPvooixcvtjkeHx8PQF5enuMK3Mvsqb+F2WzmwQcf5PHHHycuLs7RRe119tT91KlTXLhwgV/84hc2x5944gkuXLiARqNxaJl7k70/+7q6OnQ6nc0xPz8/KioqHFZWR8jIyODRRx/lwQcf5IMPPuj0/Y6850nwslNeXh5ms5nY2Fib49HR0QBkZ2e3OufcuXMA3TqnL7Kn7iNGjOCdd95pdcP+5JNPcHd3b3Wtvsye+lu88MILNDQ08Pzzzzu0jI5iT93T09MB8PT0ZOHChXh5eeHr68uTTz5JfX29w8vcm+z92T/55JNs3ryZzz77jKqqKrZs2cJnn33GT37yE4eXuTdFRESQm5vLpk2buvTQ4ch7nizMayeDwQDQ6mnKx8cHaG5p9MY5fVFv1eOf//wn77//PqtWrWLo0KG9W0gHsrf+x48f5/XXX+err77Cw8PDsYV0EHvqfuXKFQCWLFnCfffdx5o1azh+/Djr16+nrKyMrVu3OrjUvcfen/0vf/lLjh49yl133WU99tBDD/Ff//VfDiqpY/j6+uLr69vl9zvynifBy05NTU0dvu7i0rpRa885fVFv1GPXrl3cd999TJ06lddee623inZT2FP/uro6/vM//5Mnn3ySiRMnOqpoDmdP3S3ZpEuWLGHDhg0A3HnnnTQ1NfGb3/yG5557rt+0vO2pf319PdOmTaO4uJg//elPxMfHc+TIEV566SW8vb353e9+56jiOp0j73n9427ZB+n1egCMRqPNccuThOX1np7TF/W0Hm+++Sb33nsvU6ZMYd++fXh6ejqmoA5iT/3XrVtHU1MTzzzzDI2NjTQ2NqI0J0xZ/98f2FN3y1P2woULbY7/8Ic/BJrHxPoLe+q/c+dOTp8+zZYtW3jkkUeYMWMGv/nNb9i4cSO///3v+e677xxfcCdx5D1PgpedoqKicHV1JTc31+a45fNRo0a1Oscy3tOdc/oie+oOoCgKjz/+OKtXr2bZsmXs37/femPrT+yp/44dO8jOzsbb2xt3d3fc3d356quv+Oqrr3B3d+83c/3sqXtMTAxAq/GthoYGALy8vBxRVIewp/75+fkATJkyxeb49OnTAThz5owjitonOPKeJ8HLTp6enkyfPp1du3bZPDXv3LkTvV7fZtdQdHQ0I0aMYMeOHTbHd+7cSUxMDMOHD3d0sXuFPXUHePrpp3n77bdZvXo1W7ZsQa1W36wi9yp76v/pp59y/Phxm49x48Yxbtw4jh8/zqJFi25mFexmT92nT5+OVqvlww8/tDm+Z88e3NzcmDx5ssPL3Vvsqb8lo/brr7+2OX748GEARo4c6cASO5dD73k9SrQf5FJSUhSVSqUsXbpU+de//qWsW7dOUalUyoYNGxRFURSDwaAcPXrUZg7Te++9pwDKY489puzfv986Ye+jjz5yVjXs0t26nzp1SlGpVMqECROUo0ePtvowGAzOrE632fOzv9GMGTP65Twve+r+xhtvKIDy//7f/1OSk5OVF154QXF3d1fWrFnjrGrYrbv1b2xsVCZNmqQEBAQo77zzjvLFF18or7zyiqLVapXFixc7syo98uWXX7aa53Uz73kSvHpo165dypgxYxS1Wq2MGDFCef31162vWX647733ns05f/rTn5To6GjFw8NDGTVqlLJ58+abXOre0Z26P/PMMwrQ7kdnEx37Int+9i311+ClKPbV/e9//7uSkJCgqNVqZfjw4crLL7+sXL9+/SaXvHd0t/4Gg0FZtWqVEhwcbP27f+WVV5T6+nonlL53tBW8buY9TzajFEII0e/ImJcQQoh+R4KXEEKIfkeClxBCiH5HgpcQQoh+R4KXEEKIfkeClxBCiH5HgpcQQoh+R4KXEEKIfkeClxBCiH5HgpcQA8wnn3zCD37wAzw9PYmMjOTll1/uN1uuCNFVEryEGEAOHjzIf/zHf3DHHXewe/duVq1axUsvvcRLL73k7KIJ0atkbUMhBpDZs2ejVqvZv3+/9dgf//hH1q5dS1lZWb/aO0uIjkjLS4gBora2lq+++oof//jHNscXLFhAdXU1R44ccVLJhOh9EryEGCDy8vJobGwkKCiIxsZG60dAQAAAOTk5Ti6hEL3HzdkFEEL0jmvXrgGwePHiNl+vrKy8iaURwrEkeAkxwLzzzjtMmDDB+vn169e5/fbbnVgiIXqfBC8hBoghQ4YAEBwczG233WY9bmlxDR061BnFEsIhZMxLiAFi5MiRuLm5kZWVZXM8OzsbgNjYWGcUSwiHkOAlxADh5eXF9OnT2bFjh82k5O3bt+Pt7c0dd9zhxNIJ0buk21CIAeSZZ55h9uzZ/PSnP+XBBx/k+PHjvP322zz77LMyx0sMKDJJWYgB5pNPPmH9+vVkZWURGBjII488wm9+8xtcXKSjRQwcEryEEEL0O/IoJoQQot+R4CWEEKLfkeAlhBCi35HgJYQQot+R4CWEEKLfkeAlhBCi35HgJYQQot+R4CWEEKLfkeAlhBCi35HgJYQQot+R4CWEEKLf+f8AhVD1KHkFfd8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 200  # number of datapoints\n",
    "d = 1  # dimensionality of parameter space theta\n",
    "\n",
    "theta = torch.rand((n, d))  # uniform\n",
    "\n",
    "noise = torch.randn((n, d)) * 0.05\n",
    "x = theta + 0.3*torch.sin(2*pi*theta) + noise\n",
    "\n",
    "# Data t_train and x_train\n",
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(theta[:400], x[:400], 'go', alpha=0.4, markerfacecolor='none')\n",
    "    plt.xlabel(r'$\\theta$')\n",
    "    plt.ylabel('x')\n",
    "    plt.savefig(\"figures/2_1_cde/cde_samples_few.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_samples_few.png\" alt=\"drawing\" width=\"900\"/>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We want to train a neural network to predict $x$ from $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/neural_net_illustration.png\" alt=\"drawing\" width=\"1200\"/> \n",
    "\n",
    "Taken from https://texample.net/tikz/examples/neural-network/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First, let's define our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "dataset = data.TensorDataset(theta, x)\n",
    "train_loader = data.DataLoader(dataset, batch_size=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then, we build a neural network. The weights of this network will be optimized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "net = nn.Sequential(\n",
    "    nn.Linear(1, 20), nn.ReLU(),\n",
    "    nn.Linear(20, 20), nn.ReLU(),\n",
    "    nn.Linear(20, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We define an optimizer which optimizes the weights (e.g. with gradient descent):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "opt = optim.Adam(net.parameters(), lr=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Finally, we build a training loop where we optimize the weights with a Mean-Squared error loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for e in range(1000):\n",
    "    for theta_batch, x_batch in train_loader:\n",
    "        opt.zero_grad()\n",
    "        nn_output = net(theta_batch)\n",
    "        mse = (nn_output - x_batch)**2\n",
    "        loss = mse.sum()\n",
    "        loss.backward()\n",
    "        opt.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's see if the neural network learned something..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Evaluation of the neural network\n",
    "\n",
    "Ask the neural network to predict $x$ for $100$ different values of $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "predictions = []\n",
    "for t in torch.linspace(0, 1, 100):\n",
    "    predictions.append(net(torch.as_tensor([t])))\n",
    "predictions = torch.stack(predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(theta[:400], x[:400], 'go', alpha=0.4, markerfacecolor='none')\n",
    "    plt.xlabel(r'$\\theta$')\n",
    "    plt.ylabel('x')\n",
    "    plt.plot(np.linspace(0, 1, 100), predictions.detach().numpy())\n",
    "    plt.savefig(\"figures/2_1_cde/nn_few.png\", dpi=200, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/nn_few.png\" alt=\"drawing\" width=\"900\"/>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# But now, on to the main part..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Density estimation\n",
    "\n",
    "Density estimation means to estimate the probability distribution $p(\\theta)$ from samples $\\theta_1, \\theta_2, ...$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/species.png\" alt=\"drawing\" width=\"870\"/>\n",
    "Plot from https://scikit-learn.org/stable/auto_examples/neighbors/plot_species_kde.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are many ways to do this:\n",
    "\n",
    "- kernel density estimation\n",
    "- non-parametric approaches with order statistics\n",
    "- many neural network methods (GANs, VAEs, Normalizing flows,...)\n",
    "- ...\n",
    "\n",
    "Here, we will discuss (conditional) density estimation with Mixtures of Gaussians."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Let's move to a simple example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "mean = 1.0\n",
    "std = 0.4\n",
    "\n",
    "normal_dist = Normal(mean, std)  # We do not usually know this...\n",
    "samples = normal_dist.sample((50,))  # ...but all we have are these samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(6, 2))\n",
    "    plt.plot(samples, np.zeros_like(samples), 'bx', alpha=0.5, markerfacecolor='none', markersize=6)\n",
    "    _ = plt.xlim([-4, 4]); _ = plt.ylim([-0.12, 1.2])\n",
    "    plt.savefig(\"figures/2_1_cde/samples.png\", dpi=400, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/samples.png\" alt=\"drawing\" width=\"800\"/>\n",
    "\n",
    "Our goal is to estimate the underlying distribution of these samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Fitting a Gaussian to data with maximum likelihood\n",
    "\n",
    "### Learning mean and standard deviation\n",
    "\n",
    "- Maximum likelihood: We maximize the likelihood of the samples {$\\theta_1, \\theta_2, ...$} under the model (i.e. the Gaussian)\n",
    "- Assume that the data comes from a Normal (=Gaussian) distribution.\n",
    "- All we want is to figure out the mean and the standard deviation.\n",
    "\n",
    "$\\mu', \\sigma' = \\text{argmax} p(\\theta; \\mu, \\sigma) = \\text{argmax}_{\\mu, \\sigma}\\prod_i \\mathcal{N}(\\theta_i; \\mu, \\sigma)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can also find the minimum of the negative logarithm (becaus log is monotonic):\n",
    "\n",
    "$\\mu', \\sigma' =  \\text{argmin}_{\\mu, \\sigma} - \\log \\prod_i \\mathcal{N}(\\theta_i; \\mu, \\sigma) = \\text{argmin}_{\\mu, \\sigma} - \\sum_i \\log \\mathcal{N}(\\theta_i; \\mu, \\sigma)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercise 1: Fitting a Gaussian to data with maximum likelihood\n",
    "\n",
    "Your job: implement the probability of samples under a Gaussian model:\n",
    "$p(\\theta; \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{(-\\frac{(\\mu-\\theta)^2}{2\\sigma^2})}$\n",
    "\n",
    "Then train the model and check if the learned mean and std are around $(1.0, 0.4)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "dataset = data.TensorDataset(samples)\n",
    "train_loader = data.DataLoader(samples, batch_size=10)\n",
    "\n",
    "learned_mean = torch.nn.Parameter(torch.zeros(1))\n",
    "learned_log_std = torch.nn.Parameter(torch.zeros(1))\n",
    "\n",
    "opt = optim.Adam([learned_mean, learned_log_std], lr=0.005)\n",
    "\n",
    "for e in range(500):\n",
    "    for sample_batch in samples:\n",
    "        opt.zero_grad()\n",
    "        learned_std = torch.exp(learned_log_std)\n",
    "        ###################################################\n",
    "        # Implement probability of sample_batch under a \n",
    "        # Gaussian with (mu, sigma) = (learned_mean, learned_std) \n",
    "        # prob_Gauss = ...\n",
    "        loss = -torch.log(prob_Gauss).sum()\n",
    "        loss.backward() \n",
    "        opt.step()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned mean:  1.0079320669174194 , learned standard deviation:  0.4179263412952423\n"
     ]
    }
   ],
   "source": [
    "print(\"Learned mean: \", learned_mean.item(), \", learned standard deviation: \", torch.exp(learned_log_std).item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "true_dist = Normal(mean, std)\n",
    "learned_dist = Normal(learned_mean, torch.exp(learned_log_std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "x = torch.linspace(-4, 4, 100)\n",
    "true_probs = torch.exp(normal_dist.log_prob(x))\n",
    "learned_probs = torch.exp(learned_dist.log_prob(x)).detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(6, 2))\n",
    "    plt.plot(samples, np.zeros_like(samples), 'bx', alpha=0.5, markerfacecolor='none', markersize=6)\n",
    "    plt.plot(x, true_probs)\n",
    "    plt.plot(x, learned_probs)\n",
    "    plt.legend([\"Samples\", \"Ground truth\", \"Learned\"], loc=\"upper left\")\n",
    "    _ = plt.xlim([-4, 4]); _ = plt.ylim([-0.12, 1.2])\n",
    "    plt.savefig(\"figures/2_1_cde/fitted_samples.png\", dpi=200, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/fitted_samples.png\" alt=\"drawing\" width=\"800\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercise 2: Theory question\n",
    "\n",
    "Why do we parameterize the logarithm of the standard deviation instead of the standard deviation itself?  \n",
    "\n",
    "```python\n",
    "learned_log_std = torch.nn.Parameter(torch.zeros(1))\n",
    "# ...\n",
    "for e in range(500):\n",
    "    for batch in samples:\n",
    "        learned_std = torch.exp(learned_log_std)\n",
    "        prob_Gauss = 1/torch.sqrt(2*pi*learned_std**2) * exp(-.5/learned_std**2*(batch-learned_mean)**2)\n",
    "        loss = -torch.log(prob_Gauss).sum()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Summary of part 1: Density estimation\n",
    "\n",
    "- goal is to identiy a probability distribution $p(\\theta)$ from samples {$\\theta_1, \\theta_2,...$}.\n",
    "- this is done by:\n",
    "    - assuming a model, e.g. a Gaussian\n",
    "    - learning its parameters with maximum likelihood $\\text{argmax}_{\\mu, \\sigma} \\prod_i p(\\theta_i; \\mu, \\sigma)$\n",
    "    - in practice, we minimize the negative log-likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Conditional density estimation\n",
    "\n",
    "What is the probability of a taxi's drop-off location given the pick-up location?\n",
    "<img src=\"figures/2_1_cde/taxi.png\" alt=\"drawing\" width=\"1500\"/>  \n",
    "We can model this with a conditional probability $p(\\text{drop-off | pick-up = position}) = p(x | \\theta)$\n",
    "\n",
    "Image from Dutordoir et al. 2018"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Let's look at a simple model\n",
    "Generate data from $x = \\theta + 0.3 \\sin(2 \\pi t) + \\epsilon$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# generate data\n",
    "n = 4000  # number of datapoints\n",
    "d = 1  # dimensionality of parameters theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "theta = torch.rand((n, d))\n",
    "\n",
    "noise = torch.randn((n, d)) * 0.05\n",
    "x = theta + 0.3*torch.sin(2*pi*theta) + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "val_to_eval = torch.tensor(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data t_train and x_train\n",
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(theta[:400], x[:400], 'go', alpha=0.4, markerfacecolor='none')\n",
    "    plt.axvline(val_to_eval.numpy())\n",
    "    plt.xlabel(r'$\\theta$')\n",
    "    plt.ylabel('x')\n",
    "    plt.savefig(\"figures/2_1_cde/cde_samples.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n",
      "findfont: Generic family 'serif' not found because none of the following families were found: Arial, sans-serif\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data t_train and x_train\n",
    "\n",
    "mean = val_to_eval + 0.3*torch.sin(2*pi*val_to_eval)\n",
    "\n",
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(4.5, 2.2))\n",
    "    x_vals = torch.linspace(-0.2, 1.0, 1000)\n",
    "    n = Normal(mean, 0.05)\n",
    "    y_vals = n.log_prob(x_vals).exp().numpy()\n",
    "    x_vals = x_vals.numpy()\n",
    "    plt.plot(x_vals, np.flip(y_vals), linewidth=2)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    ax.spines[\"left\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.set_ylabel(r\"$p(x|\\theta=0.1)$\", rotation=90, fontsize=18)\n",
    "    plt.savefig(\"figures/2_1_cde/conditional.png\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_samples_raw.png\" alt=\"drawing\" width=\"900\"/>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The goal is to estimate parameters of a conditional distribution:\n",
    "<img src=\"figures/2_1_cde/cond_assembled.png\" alt=\"drawing\" width=\"1500\"/>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# How to do this?\n",
    "\n",
    "We will assume that, **for a given $\\theta$**, the probability density of $x$ is Gaussian, i.e.:\n",
    "\n",
    "$p(x|\\theta) = \\mathcal{N}(x; \\mu(\\theta), \\sigma(\\theta))$\n",
    "\n",
    "Importantly, the conditional mean $\\mu(\\theta)$ and the conditional st.dev. $\\sigma(\\theta)$ can be **non-linear functions** of $\\theta$, i.e. \n",
    "\n",
    "$\\mu = f(\\theta)$  \n",
    "$\\sigma = g(\\theta)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cond_assembled.png\" alt=\"drawing\" width=\"800\"/>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/nn.png\" alt=\"drawing\" width=\"2000\"/>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Learning mean and standard deviation conditional on inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "dataset = data.TensorDataset(theta, x)\n",
    "train_loader = data.DataLoader(\n",
    "    dataset, batch_size=20)\n",
    "\n",
    "net = nn.Sequential(\n",
    "    nn.Linear(1, 20), nn.ReLU(),\n",
    "    nn.Linear(20, 20), nn.ReLU(),\n",
    "    nn.Linear(20, 2))\n",
    "\n",
    "opt = optim.Adam(net.parameters(), lr=0.01)\n",
    "for e in range(100):\n",
    "    for theta_batch, x_batch in train_loader:\n",
    "        opt.zero_grad()\n",
    "        nn_output = net(theta_batch)\n",
    "        mean = nn_output[:, 0].unsqueeze(1)\n",
    "        std = torch.exp(nn_output[:,1]).unsqueeze(1)\n",
    "        prob_Gauss = 1/torch.sqrt(2*pi*std**2) * torch.exp(-.5/std**2*(mean-x_batch)**2)\n",
    "        loss = -torch.log(prob_Gauss).sum()\n",
    "        loss.backward()\n",
    "        opt.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We now have a neural network which outputs the parameters of a probability density distribution given inputs.\n",
    "In this case, it was a Gaussian distribution of which we learned the mean and standard deviation. To evaluate the result, we can look at samples from the returned distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Inspect the distribution for $\\theta$ = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "theta_test = tensor([0.1])  # the theta at which we evaluate the neural network.\n",
    "nn_output = net(theta_test)\n",
    "conditional_mean = nn_output[0].detach().numpy()\n",
    "conditional_std = torch.exp(nn_output[1]).detach().numpy()\n",
    "print(\"Conditional mean: \", conditional_mean, \", conditional std: \", conditional_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/anaconda3/envs/workshop/lib/python3.8/site-packages/numpy/core/shape_base.py:65: FutureWarning: The input object of type 'Tensor' is an array-like implementing one of the corresponding protocols (`__array__`, `__array_interface__` or `__array_struct__`); but not a sequence (or 0-D). In the future, this object will be coerced as if it was first converted using `np.array(obj)`. To retain the old behaviour, you have to either modify the type 'Tensor', or assign to an empty array created with `np.empty(correct_shape, dtype=object)`.\n",
      "  ary = asanyarray(ary)\n",
      "/home/michael/anaconda3/envs/workshop/lib/python3.8/site-packages/numpy/core/shape_base.py:65: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
      "  ary = asanyarray(ary)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data t_train and x_train\n",
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(theta[:400], x[:400], 'go', alpha=0.4, markerfacecolor='none', zorder=-100)\n",
    "    plt.plot([theta_test, theta_test], [conditional_mean-conditional_std, conditional_mean+conditional_std], c=\"r\", linewidth=2)\n",
    "    plt.scatter(theta_test, conditional_mean, c=\"r\", s=30, alpha=1.0)\n",
    "    plt.xlabel(r'$\\theta$')\n",
    "    plt.ylabel('x')\n",
    "    plt.savefig(\"figures/2_1_cde/cde_fitted.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_fitted.png\" alt=\"drawing\" width=\"600\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercise 3: Evaluate the NN for different values of $\\theta$\n",
    "\n",
    "Use the two cells above to evaluate the NN for other values of $\\theta$, e.g. $\\theta = 0.4$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Alternative evaluation: for every $\\theta$, sample from the Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "samples = []\n",
    "theta_test = torch.linspace(0.0, 1.0, 500).unsqueeze(1)\n",
    "\n",
    "for single_theta in theta_test:\n",
    "    network_outs = net(single_theta.unsqueeze(1))\n",
    "    m = network_outs[:,0]\n",
    "    s = torch.exp(network_outs[:,1])\n",
    "    conditional_distribution = Normal(m, s)\n",
    "    sample = conditional_distribution.sample((1,))\n",
    "    \n",
    "    samples.append(sample)\n",
    "samples = torch.cat(samples).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(theta[:400], x[:400], 'go', alpha=0.5, markerfacecolor='none')\n",
    "    plt.plot(theta_test, samples.squeeze().detach(), 'ro', linewidth=3.0)\n",
    "    plt.xlabel(r'$\\theta$')\n",
    "    plt.ylabel('x')\n",
    "    # plt.savefig(\"data_prob_std_fit.png\", dpi=200)\n",
    "    plt.savefig(\"figures/2_1_cde/cde_fitted_samples.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_fitted_samples.png\" alt=\"drawing\" width=\"500\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Small detour\n",
    "How does this relate to e.g. Bayesian linear regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<img src=\"figures/2_1_cde/bayes_lin_reg_assembled.png\" alt=\"drawing\" width=\"1500\"/>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# But what if the conditional distribution is not Gaussian?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Again, generate data from $x = \\theta + 0.3 \\sin(2 \\pi \\theta) + \\epsilon$. But now, predict $\\theta$ from $x$, i.e. learn $p(\\theta | x)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(x[:400], theta[:400], 'go', alpha=0.5, markerfacecolor='none')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel(r'$\\theta$')\n",
    "    plt.savefig(\"figures/2_1_cde/cde_samples_inv.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_samples_inv.png\" alt=\"drawing\" width=\"600\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "# Exercise 4: Your guesses.\n",
    "\n",
    "What will the neural network predict for $x = 0.35$ ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "_ = torch.manual_seed(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Let's train this just like before, but now predicting $\\theta$ from $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "dataset = data.TensorDataset(x, theta)\n",
    "train_loader = data.DataLoader(dataset, batch_size=20)\n",
    "\n",
    "net = nn.Sequential(\n",
    "    nn.Linear(1, 20), nn.ReLU(), nn.Linear(20, 20), nn.ReLU(), nn.Linear(20, 2))\n",
    "\n",
    "opt = optim.Adam(net.parameters(), lr=0.01)\n",
    "for e in range(100):\n",
    "    for x_batch, theta_batch in train_loader:\n",
    "        opt.zero_grad()\n",
    "        nn_output = net(x_batch)\n",
    "        mean = nn_output[:, 0].unsqueeze(1)\n",
    "        std = torch.exp(nn_output[:,1]).unsqueeze(1)\n",
    "        prob_Gauss = 1/torch.sqrt(2*pi*std**2) * torch.exp(-.5/std**2*(mean-theta_batch)**2)\n",
    "        loss = -torch.log(prob_Gauss).sum()\n",
    "        loss.backward()\n",
    "        opt.step()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "samples = []\n",
    "x_test = torch.linspace(-0.1, 1.1, 500).unsqueeze(1)\n",
    "\n",
    "for single_x in x_test:\n",
    "    network_outs = net(single_x.unsqueeze(1))\n",
    "    mean = network_outs[:,0]\n",
    "    std = torch.exp(network_outs[:,1])\n",
    "    conditional_distribution = Normal(mean, std)\n",
    "    sample = conditional_distribution.sample((1,))\n",
    "    \n",
    "    samples.append(sample)\n",
    "samples = torch.cat(samples).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(x[:400], theta[:400], 'go', alpha=0.5, markerfacecolor='none')\n",
    "    plt.plot(x_test, samples.squeeze().detach(), 'ro', linewidth=3.0)\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel(r'$\\theta$')\n",
    "    plt.savefig(\"figures/2_1_cde/cde_fitted_inv_samples.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_fitted_inv_samples.png\" alt=\"drawing\" width=\"900\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Okey, but how can we fix this?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Mixture Density Networks\n",
    "$$\n",
    "$$\n",
    "<img src=\"figures/2_1_cde/architecture.png\" alt=\"drawing\" width=\"1200\"/>\n",
    "\n",
    "The loss is now the probability under this mixture of Gaussians  <br/>\n",
    "\n",
    "$\\mathcal{L} = -\\sum_i \\log q(\\theta_i | x_i) = -\\sum_i \\log \\sum_j \\alpha_{j,i} \\mathcal{N}(\\theta_i; \\mu_{j,i}(x_i), \\sigma_{j,i}(x_i)$  <br/>\n",
    "\n",
    "We learn the mixture components $\\alpha_j$, the means $\\mu_j$, and the variances $\\sigma_j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Let's look at this in code!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "class MultivariateGaussianMDN(nn.Module):\n",
    "    def __init__(\n",
    "        self,\n",
    "        number_of_parameters, hidden_net,\n",
    "        number_of_gaussians, hidden_features,\n",
    "    ):\n",
    "        # ...\n",
    "        self._hidden_net = hidden_net\n",
    "        self._weights_layer = nn.Linear(hidden_features, number_of_gaussians)\n",
    "        self._means_layer = nn.Linear(hidden_features, number_of_gaussians * number_of_parameters)\n",
    "        self._log_variances_layer = nn.Linear(\n",
    "            hidden_features, number_of_gaussians * features\n",
    "        )\n",
    "\n",
    "    def get_mixture_components(\n",
    "        self, context\n",
    "    ):\n",
    "        h = self._hidden_net(context)\n",
    "\n",
    "        logits = self._logits_layer(h)\n",
    "        logits = logits - torch.logsumexp(logits, dim=1).unsqueeze(1)\n",
    "        means = self._means_layer(h).view(-1, self._num_components, self._features)\n",
    "\n",
    "        log_variances = self._log_variances_layer(h).view(\n",
    "            -1, self._num_components, self._features\n",
    "        )\n",
    "        variances = torch.exp(log_variances)\n",
    "        return logits, means, variances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "class MultivariateGaussianMDN(nn.Module):\n",
    "    def __init__(\n",
    "        self,\n",
    "        number_of_parameters, hidden_net,\n",
    "        number_of_gaussians, hidden_features,\n",
    "    ):\n",
    "        super().__init__()\n",
    "        self._features = number_of_parameters\n",
    "        self._number_of_gaussians = number_of_gaussians\n",
    "        \n",
    "        self._hidden_net = hidden_net\n",
    "        self._weights_layer = nn.Linear(hidden_features, number_of_gaussians)\n",
    "        self._means_layer = nn.Linear(hidden_features, number_of_gaussians * number_of_parameters)\n",
    "        self._log_variances_layer = nn.Linear(\n",
    "            hidden_features, number_of_gaussians * number_of_parameters\n",
    "        )\n",
    "\n",
    "    def get_mixture_components(\n",
    "        self, context\n",
    "    ):\n",
    "        h = self._hidden_net(context)\n",
    "\n",
    "        weights_of_each_gaussian = self._weights_layer(h)\n",
    "        weights_of_each_gaussian = weights_of_each_gaussian - torch.logsumexp(logits, dim=1).unsqueeze(1)\n",
    "        means = self._means_layer(h).view(-1, self._num_components, self._features)\n",
    "\n",
    "        log_variances = self._log_variances_layer(h).view(\n",
    "            -1, self._num_components, self._features\n",
    "        )\n",
    "        variances = torch.exp(log_variances)\n",
    "\n",
    "        return weights_of_each_gaussian, means, variances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def mog_log_prob(theta, logits, means, variances):\n",
    "\n",
    "    _, _, theta_dim = means.size()\n",
    "    theta = theta.view(-1, 1, theta_dim)\n",
    "\n",
    "    log_cov_det = -0.5*torch.log(torch.prod(variances, dim=2))\n",
    "\n",
    "    a = logits\n",
    "    b = -(theta_dim / 2.0) * log(2 * pi)\n",
    "    c = log_cov_det\n",
    "    d1 = theta.expand_as(means) - means\n",
    "    precisions = 1.0 / variances\n",
    "    exponent = torch.sum(d1 * precisions * d1, dim=2)\n",
    "    exponent = tensor(-0.5) * exponent\n",
    "\n",
    "    return torch.logsumexp(a + b + c + exponent, dim=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercise 5: Training the network\n",
    "\n",
    "Your task is to train the neural network. You will have to use the above defined `mog_log_prob()` method to compute the log-probability of the parameters $\\theta$ under a mixture of Gaussians with $(\\alpha, \\mu, \\sigma^2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def mog_log_prob(theta, logits, means, variances):\n",
    "    # Evaluate the log probability of a mixture of Gaussians.\n",
    "    return log_probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "_= torch.manual_seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "dataset = data.TensorDataset(x, theta)\n",
    "train_loader = data.DataLoader(\n",
    "    dataset, batch_size=50,\n",
    ")\n",
    "mdn = MultivariateGaussianMDN(\n",
    "    number_of_parameters=1,\n",
    "    hidden_net=nn.Sequential(\n",
    "        nn.Linear(1, 30), nn.ReLU(),\n",
    "        nn.Linear(30, 30), nn.ReLU(),\n",
    "        nn.Linear(30, 30), nn.ReLU(),\n",
    "    ),\n",
    "    number_of_gaussians=5,\n",
    "    hidden_features=30,\n",
    ")\n",
    "opt = optim.Adam(mdn.parameters(), lr=0.001)\n",
    "for e in range(200):\n",
    "    for x_batch, theta_batch in train_loader:\n",
    "        opt.zero_grad()\n",
    "        weights_of_each_gaussian, means, variances = mdn.get_mixture_components(x_batch)\n",
    "        ###################################################\n",
    "        # Implement probability of `theta_batch` under a Mixture of Gaussians with (weights, means, variances).\n",
    "        # Hint: use the `mog_log_prob` method defined in the cell above.\n",
    "        # log_probs = ...\n",
    "        loss = -log_probs.sum()\n",
    "        loss.backward()\n",
    "        opt.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Let's evaluate this!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def mog_samples(logits, means, variances):\n",
    "    # Draw a sample from a mixture of Gaussians."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def mog_sample(logits, means, variances):\n",
    "\n",
    "    coefficients = F.softmax(logits, dim=-1)\n",
    "    choices = torch.multinomial(\n",
    "        coefficients, num_samples=1, replacement=True\n",
    "    ).view(-1)\n",
    "\n",
    "    chosen_means = means[0, choices, :] # 0 for first batch position\n",
    "    chosen_variances = variances[0, choices, :]\n",
    "\n",
    "    _, _, output_dim = means.shape\n",
    "    standard_normal_samples = torch.randn(output_dim)\n",
    "    zero_mean_samples = standard_normal_samples * torch.sqrt(chosen_variances)\n",
    "    samples = chosen_means + zero_mean_samples\n",
    "\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "samples = []\n",
    "x_test = torch.linspace(-0.1, 1.1, 500).unsqueeze(1)\n",
    "\n",
    "for single_x in x_test:\n",
    "    weights, means, variances = mdn.get_mixture_components(single_x.unsqueeze(1))\n",
    "    sample = mog_sample(weights, means, variances)\n",
    "    \n",
    "    samples.append(sample)\n",
    "samples = torch.cat(samples).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "x_demo = torch.as_tensor([[0.6]])\n",
    "logits, means, variances = mdn.get_mixture_components(x_demo)\n",
    "demo_probs = []\n",
    "for t_demo in torch.linspace(-0.1, 1., 100):\n",
    "    prob = mog_log_prob(torch.as_tensor([t_demo]), logits, means, variances)\n",
    "    demo_probs.append(prob)\n",
    "demo_probs = torch.stack(demo_probs).detach().exp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 450x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with mpl.rc_context(fname=\".matplotlibrc\"):\n",
    "    fig = plt.figure(figsize=(4.5, 2.2))\n",
    "    plt.plot(x[:400], theta[:400], 'go', alpha=0.5, markerfacecolor='none')\n",
    "    plt.plot(x_test, samples.squeeze().detach(), 'ro', linewidth=3.0)\n",
    "    plt.plot(demo_probs.numpy()*0.1+x_demo.item(), np.linspace(-0.1, 1, 100))\n",
    "    plt.plot([0.6]*100, np.linspace(-0.1, 1, 100), linestyle=\"--\", color=\"k\")\n",
    "    plt.ylim([-0.05, 1.1])\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel(r'$\\theta$')\n",
    "    plt.savefig(\"figures/2_1_cde/cde_fitted_inv_samples_mdn.png\", dpi=200, bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/cde_fitted_inv_samples_mdn.png\" alt=\"drawing\" width=\"1000\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercise 6: Evaluate the MoG for different values of $x$\n",
    "\n",
    "Use the two cells above to inspect the distribution for different values of $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Example: estimating parameters of a neural circuit\n",
    "\n",
    "We want to estimate the distribution of sodium and potassium conductances given an observed trace:\n",
    "\n",
    "<img src=\"figures/2_1_cde/full_HH_fig.png\" alt=\"drawing\" width=\"1500\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# What are the limitations?\n",
    "<br/>\n",
    "- One has to decide on hyperparameters: e.g. how many components (i.e. Gaussians) will I need? <br/>\n",
    "<br/>\n",
    "- Training often does not converge perfectly. <br/>\n",
    "<br/>\n",
    "- In practice, high-dimensional distributions might not be captured perfectly even with a high number of components. <br/>\n",
    "<br/>\n",
    "- Normalizing flows, VAEs, and GANs are more flexible. However, Mixtures of Gaussians often allow for useful computations in closed form and are still sometimes used in practice.<br/>\n",
    "<br/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"figures/2_1_cde/full_HH_fig.png\" alt=\"drawing\" width=\"1200\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary: Conditional density estimation\n",
    "\n",
    "- Density estimation means to estimate a probability distribution (=density) from samples. <br/>\n",
    "<br/>\n",
    "- Here, we assume a `model` (e.g. a Gaussian) and fit its parameters with maximum likelihood (i.e. maximizing the probability of the data under the model) <br/>\n",
    "<br/>\n",
    "- In conditional density estimation, we fit the parameters of a distribution given another quantity. <br/>\n",
    "<br/>\n",
    "- We can do this by regressing onto the parameters of the distribution with a neural network. <br/>\n",
    "<br/>\n",
    "- Mixture density networks predict parameters of a mixture of Gaussians <br/>\n",
    "<br/>\n",
    "- Because of this, this can capture variability and multi-modality <br/>\n",
    "<br/>\n",
    "- To look at their predictions, one can either draw samples from the predicted mixture of Gaussians or evaluate the probability of the prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Acknowledgments\n",
    "<br/>\n",
    "<br/>\n",
    "\n",
    "Parts of the code from: https://mikedusenberry.com/mixture-density-networks  <br/>\n",
    "Code of MDNs based on Conor Durkan's `lfi` package.  <br/>\n",
    "Bishop, 1994  <br/>\n",
    "[MDN graphic](https://towardsdatascience.com/a-hitchhikers-guide-to-mixture-density-networks-76b435826cca)  \n",
    "Pedro Gonçalves et al. for figure."
   ]
  }
 ],
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