18_TFP_Regression_vs_MC.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "bT5mgJvq5XCg",
        "pycharm": {}
      },
      "source": "## Linear Regression with TF Probability\n### Variational vs MCMC\n\n* Aim: comparing MCMC Simulation with Variational Bayes\n* Many Ideas and the Edward code taken from https://brendanhasz.github.io/2018/12/03/tfp-regression\n\n**This is work in progress. It (probably) requires TensorFlow 2.0 and Tensorflow Probability version 0.7**\n\nYou can use the following docker container\n```\n    docker pull oduerr/tf_docker:cpu_r_tfp\n```\nAlternatively it should also run in colab after the installation of the required version."
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "source": "# Checking if running in colab and if installing the requited versions\n# Trick from: https://stackoverflow.com/questions/53581278/test-if-notebook-is-running-on-google-colab \ntry:\n  import google.colab\n  IN_COLAB \u003d True\n  !pip install tensorflow\u003d\u003d2.0.0-alpha0\n  !pip install tfp-nightly\nexcept:\n  IN_COLAB \u003d False",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%%\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "TFB Version 0.7.0-dev\n",
            "TF  Version 2.0.0-alpha0\n"
          ]
        }
      ],
      "source": "import matplotlib.pyplot as plt\nimport numpy as np\nimport seaborn as sns\n\nimport tensorflow as tf\nimport tensorflow_probability as tfp\n\nsns.reset_defaults()\n#sns.set_style(\u0027whitegrid\u0027)\nsns.set_context(context\u003d\u0027talk\u0027,font_scale\u003d0.7)\n\n%matplotlib inline\n\ntfd \u003d tfp.distributions\nprint(\"TFB Version\", tfp.__version__)\nprint(\"TF  Version\",tf.__version__)"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "### Creation of some random data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "((40, 1), (40,), dtype(\u0027float32\u0027))"
            ]
          },
          "execution_count": 58,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@title Synthesize dataset.\n",
        "num \u003d 20\n",
        "#x \u003d np.concatenate((np.linspace(-10,-1,num), np.linspace(1,10,num))).reshape(2*num,1)\n",
        "x \u003d np.linspace(1,10,2*num, dtype\u003dnp.float32).reshape(2*num,1)\n",
        "y \u003d np.asarray(np.random.normal(1*x[:,0]+5,np.abs(x[:,0])/3.5), dtype\u003dnp.float32)\n",
        "#y \u003d np.asarray(np.random.normal(5*x[:,0],1.0), dtype\u003dnp.float32)\n",
        "x.shape, y.shape, y.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "\u003cmatplotlib.collections.PathCollection at 0x7f6a52954400\u003e"
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\u003d\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(x,y, marker\u003d\u0027.\u0027)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "x_test \u003d np.linspace(-3,15, num\u003d100).astype(np.float32) #Some x values, where we want to test\n",
        "x_test \u003d x_test[..., np.newaxis]  #Make a (100,1) Tensor\n",
        "x_test_1p \u003d x_test[0, np.newaxis] #Just take a single row"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "#### Training\n",
        "\n",
        "We train using the usual max-likelihood method. I.e., we maximize the likelihood (w.r.t. the weights) that, given the data, the $y_tue$ is observed. Practically, we minimize the negative log-likelihood.\n",
        "\n",
        "##### Definition of the likelihood\n",
        "\n",
        "$$\n",
        "  l\u003d-\\log(p_{\\tt model}(y_{\\tt true} | X, w))\n",
        "$$\n",
        "\n",
        "For more than one data point, we would need to sum. \n",
        "\n",
        "**Comment** This is a function, which compares the true label y with the output of the last layer\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# The likelihood is simply \n",
        "#Short Version: \n",
        "#  negloglik \u003d lambda y, rv_y: -rv_y.log_prob(y)\n",
        "\n",
        "# y_true the true class label \n",
        "# y_hat the output probability distribution\n",
        "def negloglik(y_true, y_hat):\n",
        "  return -y_hat.log_prob(y_true)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "xEvTd7ZJYvDx",
        "pycharm": {}
      },
      "source": [
        "### Case 3: Epistemic Uncertainty (Specifying the uncertainties by hand)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "4O5m3qUU8C-n",
        "pycharm": {}
      },
      "source": [
        "To model the uncertainty which arises, due to the lack of data, we start a Bayesian treatment."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "bxzK6h97N1AM",
        "pycharm": {}
      },
      "source": [
        "#### Definition of the posterior\n",
        "For the posterior $𝑄(𝑤;\\theta)$, we use a Gaussian approximation. For each weights and biases (n in total) a Gaussian Distribution is learned. We assume independence between the distributions for the weights and thus have 2*n parameters for $\\theta$. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "cellView": "both",
        "colab": {},
        "colab_type": "code",
        "id": "VwzbWw3_CQ2z",
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# In more easy code\n",
        "def posterior_mean_field(kernel_size, bias_size\u003d0, dtype\u003dNone):\n",
        "  n \u003d kernel_size + bias_size #Number of weights\n",
        "  c \u003d np.log(np.expm1(1.)) #Magic number for offsetting in softpuls\n",
        "  \n",
        "  model \u003d tf.keras.Sequential()\n",
        "  # Creating 2n variables as a starting point\n",
        "  variables \u003d tfp.layers.VariableLayer(2 * n, dtype\u003ddtype, name\u003d\u0027post_weights\u0027)\n",
        "  model.add(variables)\n",
        "  model.add(tfp.layers.DistributionLambda(\n",
        "      lambda t: tfd.Independent(tfd.Normal(\n",
        "          loc\u003dt[..., :n],scale\u003d1e-5 + tf.nn.softplus(c + t[..., n:])),\n",
        "                                reinterpreted_batch_ndims\u003d1))\n",
        "      )\n",
        "  return (model)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "LKNy1kNSA2ns",
        "pycharm": {}
      },
      "source": [
        "#### Definition of the prior\n",
        "We also make the prior $P(W;\\theta)$ trainable. We assume that it has a Gaussian-Form with fixed stddev\u003d1 but with a trainable mu. This is called empirical Bayes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "cellView": "both",
        "colab": {},
        "colab_type": "code",
        "id": "aAQhyK9Y_lm1",
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "def prior_trainable(kernel_size, bias_size\u003d0, dtype\u003dNone):\n",
        "  n \u003d kernel_size + bias_size\n",
        "\n",
        "  model \u003d tf.keras.Sequential()\n",
        "  # Creating n variables as a starting point (we only learn mu)\n",
        "  variables \u003d tfp.layers.VariableLayer(n, dtype\u003ddtype)\n",
        "  model.add(variables)\n",
        "  model.add(tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
        "           tfd.Normal(loc\u003dt, scale\u003d1),\n",
        "           reinterpreted_batch_ndims\u003d1)))\n",
        "  return (model)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 17109,
          "status": "ok",
          "timestamp": 1554370742411,
          "user": {
            "displayName": "Oliver Duerr",
            "photoUrl": "",
            "userId": "00002413253758210405"
          },
          "user_tz": -120
        },
        "id": "XI7ZCFzSnrWN",
        "outputId": "c3cccf82-47a5-40c6-945b-4f82ae42d5f3",
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# Build model.\n",
        "## Definition of the custom parametrized distribution\n",
        "def my_gauss(mu):\n",
        "  return tfd.Normal(loc\u003dmu, scale\u003d1)\n",
        "\n",
        "inputs \u003d tf.keras.layers.Input(shape\u003d(1,))\n",
        "\n",
        "prior \u003d prior_trainable#tfd.Independent(tfd.Normal(loc\u003d1, scale\u003d1),reinterpreted_batch_ndims\u003d1)\n",
        "\n",
        "# Simple linear regression\n",
        "tt \u003d tfp.layers.DenseVariational(1, posterior_mean_field, prior)(inputs)\n",
        "\n",
        "\n",
        "p_y \u003d tfp.layers.DistributionLambda(my_gauss)(tt)\n",
        "model \u003d tf.keras.models.Model(inputs\u003dinputs, outputs\u003dp_y)\n",
        "\n",
        "# Do inference.\n",
        "model.compile(optimizer\u003dtf.optimizers.Adam(learning_rate\u003d0.01), loss\u003dnegloglik)\n",
        "hist \u003d model.fit(x, y, epochs\u003d1000, verbose\u003dFalse);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 150,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, \u0027ELBO Loss\u0027)"
            ]
          },
          "execution_count": 150,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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JgdqGOI554EsAwMfXj8eATq0Rjdgfn40ZJmxYKpLkXCFmFPssS+hQva8qiyRTlBZJXA62e5tqN9uNtKww5OOrFGQ+kolS31hRg9YtCtCmuFCxv6bPsYRAuVSE8+j7v0SPspb48LpDlb/lTC0mzNi5trYB2Gry92N2RQseq6KKulU277hZI6AeR6LK2rIniIbGzIXlxiIJc/Po9pKu274bY/76GUbd9am6aoFuHIlIu04bymvw2jfrlftuLu5Cpnli59rqlxMpwopFQ++0saxtiOPEh79C7/YlePr8kTorQ9XYxF0E22sb4vjHxz9gdP8OOWuQV2+rxtKNlTh2v66mDa1VA7y5shbvfrsBp47ogc5tikPd03Zrkbzz7QYAQE1DHLGEQGHUWDFar0hUysEsRhbm68QwlopECLE2V4KEEdWrm3qfnb7X78zfgBVbqrBiSxV2VNejQ+sWjevsGhK7Qzz2xUo8OW01npy2Goft3cmZQB454r7PAQB/O32ohaWlLf9m9Q48P32Nbt15T83C8i1VeGveBnx43fg0N1h9LIHaWBxtFe6dXOPWCpDVRjwhUBg13188IZR11cy8mUFYJP+csgyf/7AFz184Cu1aFeVeACZv8Jq11axRZ20J3X87GqSBZwLArtoGfLhoE3bXx2znI1E1NDKLNlTo9p1L3luw0fSYqVM46/EZeH/hRt265VuqAADfJwP1xsmejnvwS+w/8WNs2WVeMj9nuLyoESlQrrIs0lxbiv2bWaH6Ol254aFPl2PBjxUYcecU3PvR9/Y/YPZYWJFYoG7otf8uQiRN2wng6lfn47KX5uL3byywDba76YUGEyOxtkjc7iOWEFi5tRoJAfzHJFaQbWSLwEv6bzye/ltj+q+qTEpQ0yPb8ejUlfYbMXssrEgsUGdtpQfb3TTin/+wFQDw/sKN9haJKrAvy2d32Cw3SqZyudiHrrS6J2n8x4siiSlS14wWSUxRJsUs/Tihf+DS1r8zfwNOevgrLNsDil/KcOwIeH32eny1PNjyQqxILLAuqujwAbboYqrSZHUxErtsMHlfAVskeheVi6wtmwYySNxKI99q1RQBxqKNKveX2eNid2mu+8+3WLihAr99YY4TUZsFT3y5EqPu/lTn4t3TmLZ8K2767wKc9/QsZcckV9gqEiJqTUS3EdFXRPRD8v/tRNQ2FwIGidU4kkyCn8ZML7sSKarMsFg8gXfmb8DqbdWGCsTu5fHC1l11mCb1guTr4ebaZPq7XOBWOcvWRINdjCQulMrGiSxWv0oVFd0TuHvy99i6qw6Xvjg3aFECY8GPTUrUS0Vpr9gNSOwI4CsAHQBMTn7uBuBqAL8konFCiHCVbPURq7EATu+Z3ME0/ka1j7iul5++/rnpa/CX95cCAA4f1JSp5SZw6wffG0a1J1xYUjJyYxq6+lNug+2yRaKIkeiytkwtEvVdcx6HC9k1zAG7ahvsN9oDCPLW240juQvAegAHCSEaWw4iagPgjeT6S7MnXrBY19pydtes3B32wXaRPE7TskkLNqb9BlBbL7l8rjJVCAkbxRkkrtN/pXttFyOJxROuXBHC4aYhu4RMDgmyI2bn2joRwKWyEgGA5PcrAZyULcHCgOq+pBRIJo2e8UarTFF5m3lrd2LEnVOwrappzo7v1pcr5VPJuqs2hjfn5qYAgd6SchMjkT83fVF1zHPd2/aUtaWMkeiVptIi8ShLNi9RWK2dbFe5zhfcuEr9xk6RtIM2I6KKNQDK/BQmbChjJMmbZVZnyojsNze+h3YDEj9ZukVXj8lKPjMZfvfGd7qxLNkikWH6ldPS6n/632KM+9tUbKrI3fgS18F22I0jafocF+oYiWmw3aUsXrGrusCEjyBvj50iWQ9gjMm60QA2+CtOuLAaRyK/2U57i8YXURmDcfE06DOenB83GzToXFvOf+fUtfXc9DXYUF6Dv3+Y3YFxcjvu5l4ABteWMkYinWvCJEZism/jwM1so3pmGhTnxHijLhbH5IUbsa2qzvO+3D6vfmKnSF4A8AIRHSwvJKJRAJ4H8FyW5AoFViPb5VVW1W6tBripGpuM5yOx0CS5UCRycNlN0Ua3kz3VxuLuBPNASpx4QqB8d731xtC7WFQxEvn0EsJkHIlZsD3HbYTqkWloLmWdQ8R9H/2AK16eh1Me+drzvoLM2rJTJPcAmA1gBhGtIaLpRLQGwAwA85PrmzEqP7f2X9XozVy1Hbe/s0g3D7lMQggUFzZd8le/WZe+TYaNvtXP/HrArHzksYwtEnn/6s8y2ZwvxEhKIf76mVnY/89TTOdfSWGstZW2P92ARJMYiek4kuDjQ6nZQRn/eHLaagBa5WevhDbYLoSICyHOAXAEgFcALEr+P1IIcaYQInfdwwCwtEgUrq1znpiJF2euxQF3TsGDnywHYHCVCKClVMkvVXdKxk2j73R0vV8mr5Vocam36iprS1ZADuSUG1ohBD5YuBHLMxjN/dfJS3Hr2wutr1ty1dcrtgMAHvhkmeP928VIEmYxEhtZAHcWX6YoFQm7tkJNkAajoxkShRBfAPgiy7KEDmWwXaSvU71093+yDNceNdDwW4HeHVph5+7ytO1TZOqGsvqVX64tKwUR07d0Lvap/mxGhAg19XHcNXkJync34L1kOvSae05wfMxVW6vw+JerAACn7N8Do/qp529Ly7KzEdBYAsVqfcJkHIkZuVAeMuoYSTgtEk7a0gjSIrFVJEQ0GMBgAN8IIdYR0aUAjgewAMCdQgh753GeoroxqRc6YXBTmGEcR2L3zLtp9HWZYzlwbVntxzj+xSk6d4+D3xEBD3+2HC/NTHcLOqWyNtb4uarOIivOII7drZHPW9XoGsvIK8eRmLSKZi7AbKGMkYRUkTAaQWbV2Y1sPx/A4wDWAehKRPcBuBzANAAXA2gN4PpsCxkU6nEkqQ9Ny+ImNmUiIdLSf+0aWVe9VIeuLb8eMGvXVmZZRQmH1zFFhAiLf6p0fgAFcgNeEDH37hqvqV2cQm5n7ceRuMvaynmMhLO2XJFICN00ArkiyDJJMnbB9j8AOE4IsTeAMwDcAWCCEOIsAEcCOD3L8gXK1a/OT1umGkdi1vgbl8cT9vWV3KX/Sr9z2Mh7wUoJyhk9t72zyNH+LnpuNs57elbjdyfX0Y9XVd5fgcXLb5TGrhNgLIlvtT6RUN+XTIs2+o06RhJOiyRoz9ZT01Zh+MSPMWPl9kDlCHPWVk8hxNTk5ykA6oUQiwBACLEE2oDFZsnu+phyeVOJlKZlZg11PCF0T3lCqKdXlcnUb26lLPwKwlkdQ163qdLZoMFPv9+i+65Khwb0jRoReY4WyLJGDYpETr9NCP0shna3Rt6vOkYibWuS/mtGrtsIVaMUVkUStJ30l/eXYlddDOc/803Ojy0/r2Ee2d6I0GwoYwvhi+SkcRsR/UREu4hohh/79cK2XeYpvNr/pmVmN9A4liAh7C0OVxVhpd1b9Zad9lTu+eB7XPHy3LQGLpEQmL5yG3ZWm8cTjEogk0wx8+sou7a8D+SUG8SCqHl/NpHQW1pu3JL2FonatWV2GrkOpKoOx64ta+oDULR611ZIYyQAiojoBul7C8N3vybWvhrAYQAOArARwAif9psxW6vUverUzdKPCbCwSCQ0i8S/GImsqJxaC2bsqm3AY19os+AdPXgjTh3Ro3Hdy7PW4vZ3F6O0pfntNh4jEzNbNYgP0A92NHP9xBICRQ591E7jOQJ6V6Sta0vatqKmAfWxBIoKmvpqOivWJP3XqBC3V9XhT5OWYN9ubRzJ7Bd5lbWV4+MlEgLPTV+Dfbq1wdgBHXN8dHNCW0YewEzoCzN+Y/g+06sARBQFcDOAsUKIVMmVtAkGiMg8Z1aj1KssMlt3qUsWqNJ/Ywmh7A3EDFlaiYR6etVMmbeu6ZLsrjcf0uNEkcgWhXEU9yNTVwDQGkfT3xuUQCZmttlvPl6yqfGz2YDEeEJgd30MSzdWYkSvdpaBT7lnbSWnEO4mGpPv7e3vLMIzX63Gpzcc1iiLk6KNRmX15/eWYNJ3P2HSd9bH9pt8ipFkm9qGOB75bAXGDOiAQ/bqiHe+3YA/v7cEgLu082wT2nEkQojDcyBDLwDFAH5BRNcC2A7gT0KI13Nw7EaMs6xtrbJ2bRkVh6o9UvXSs9VpsGrknTTqVr1tKyVldoxMFIlZjOT3by5o/ByJqBv0WCKB857+Bt+tL8ctx++DS8YPMD+OQ0suIYTOGnKbKLF6WzXKaxrQvlVRcn/6bVUxEnmbipoGTF6YPm1ANvudSzdW4rKX5mLCvl3S1u2prq1/f74Sj0xdgUemrsCae07A/HV2fdpgCO3IdiuIqIiItthvaUt3aFWE+yT/LgTwBBENkjcSQpRZ/QHwNN/mBc/O1n3fYapIUvLol6vcMrGEfhiZENkLiFXVqZMDAGcPmJVLrbbBXpEYG5lMaobpXE4m22jB9vS18YRoLLF/30fWI9DrpVIfVhaiEPoYia1F4iDlV95WdY3k7Q+/d6pp411VF8O368tt/eJbdtXixRlrHNUKA4ArX5mHtdt346mvVqetC6tFku0y8t+s3qH7LidohKm0fl4qEmiuST8chKkiM3cJIWqFELMAfAxggg/7doyx+mZ9XN14NsZIDMtVjUg8LtIakiButhPlZdVIOOmJ+mKROCmRAjOLxD6OkkKnSOwsEhcxEpVSkpfoR/GbxEgki3enyRQC8UQCh/7tM5z66Nd4w2a+mV8+OQu3v7sYV74yz3K7FNtNOlBAuBRJLhtw432Sn68gAuxm5EXWlgl+SL4MQKBzZc5clZ7/bZeKmm6RqGIkCV3jMXv1jkDm1HbSQJudr1OMKb9mgXMrnLwIESL1FMUuFEldzFkmloC7Eft2wXNjp0LVCKU2r7ZwJy7bXNWoZB78ZLllo5qq55aqF+YFr8+Inzh5Vh78ZDmemrbK87GMz3JUesDC5O7LV4vEF4QQ1QDeAvB/SXfZgdCskU9yJcN7C35KW1ZnUuk09fym1WFSPFDxhN4CeeizFR6kzBxnri1/e1aZWSRNMvxzyjJ8sHBjWiNplbWVImKhSYQQqJNK0RvbcjJsq7dItP8rt1bh9dnr02IcqnNOyWXc17LNVXj8i/RGLnWvrGJeMnWxuOVMnn4SZFaQEaMsVXUxncU0a9V23P/JMvzl/aXY4nBck+mxDPdVdm3JFZEDGNiuI0CDxLZEyg0Wqx0VfHTIlQCeBbADWvrvpUKI7M5gJBFVNDxmJqtqPhJAPVdDLGE/ADEXOHNt+StoJr1Xo5yXvzwPy+86TrcsYhYjkVOETWVK4NR/fY1FG5pKrFi7tvTKLXXvT3zoK9Q0xLFlVy2u+tnAtPXGc2qIJ3Dqo187Ku2SsmAqLGbGlKmLJdIa1dqGOE58+Ct0L2vpaB8yVtZctlwnIjlQ1zg41Ar5ddtRXY/Rd3+Kvh1LMOmqcSAiXWVtrwrQ+G7IGYFyO5HtWE1DPIEHPlmGEb3a4ajB6ckQoa21Bfs52b/0QwghxHYAJ/uxr0xQPQD1JhZJ6pk09vhU28dN0oJzjZPBen4/hH7FSFT+aeVguYT9Cz1n7U6dEgFsXFvCOM+K9rkmmXzw5LTVOkViNvZi7tqdjuuDpXbh3CJJpB130nc/YcWWKqxQTFMAaNMWV9Y24B9nDnfV+GU66Zod5z87G8s27cJH149PG6sUTwh8uGgThvYoRe8OJY3Ljfetqi6GRRsqURdLoLgwqksu8DqHjX7ckdBZHmbtRDZ4YcZaPDpVG+uVSjs2xt2Cwi7994hcCRIkKleI2QNiFiNRbR9LCN/mAvGCkx6Z34FUr1lbKYxyEdQlUnQxElmOeALnPT0L7VsV4Rejepv+7h8f/4DV26p116qypgElRU3zxxiNTmNjr7qE8YTQDUq0w61rqz6WSGtArKzL1duq8dz0NQCAMw7smTagzqrJ9eNZfmPOetQ2xPGrMX0BaK65L5dtBQC8MmsdLj9cn7b90sy1+OP/FgPQj9kwe6brGjRFIicqeG1g5WPFE0LnwZAtknhC4Mh/fI57zxyOA3r7Xz1q8Yb0xFRj/bagsHzCyaa7QkQ9/RUnGFQWta0iMTRn9338Q9q28UQXqW+AAAAgAElEQVQi8DpAgMNgu7TNZz9s9XzMTCwSlTIzusgiBGWKh2470uIY909Zhjfn/oiZq3Zg8sJNWLdjt1LO3fUxPPzZCry3YKNuzMyNb3znLmvLxL1pVRjSSOpwlQ4ViXZcxTUyQVZQu+vSA/pWr7zdc/TN6h249rX5WK+4zjur6/HDpl34/ZsLcPu7i7HwR61RlN8z1biat+ZvSFsGmCu11FTMchamV0UiyxVL6Kv81hiSIlZurcY5T3gep63GMKkbAEMtuJBaJNDGZrRNfSGir4QQ46T1S+T1+YpqFLR5jET7b7xnkxduSts2Fg9HjMRJT1JuxL9cthVz1uzAyL7qCZ+c4FfWlrFnTqSe5En+bYQIxz7wZVrP/Na306sSazEM9fWpqGnQnYf9yHbFMov9q0g1EJW1zhWJ8VJbJRvI97lQYSlZqbynp63C5IUb8ei5B6BraXHa+rMe10rkLdtchQ+uPbRxeVVdDCPunKLbdtW2KgztWapTJEqxTS66WUelpj6O3fUxvPttUwKN1566sYaafH1rFGOsnLi7tlXV4fmkZeiUiCFbrKiA9NZSiLO2jLd2sM36vET14pm5eoSJa0tFWGIkbkukAMCUpZs9HTOTl1fV491erR/fY5b+Kzf4EXKePGBW86pxvy7Sf9VzeCRcuQ1TxzDLGlRhbECs/AhyllGhRcFKFT9V1GLu2p14+LPlltst3aiPB81buzNtm7oGTQ678zS74maN5uw1O3DmY/qar0566omEwLx1O5VVv3VVneNClxRgNRDYiute+xYPG7I47doKub+byjw0VksICjtFYidZ8K2kD6hcAabpv8nFTrR/LBHMAEQjmaT/fv695t7KVBGqstjsUDXo2wwD5EwbFt04EucN5Jw1O/Czf3yuXFdSFNXtd3d93PUEYqmsLaekdlHnoJpA02+MisT8/MslC8/NfCgyql54mkwJgVVbq5Lp1unnn2oI7XrvZpfb7PH6/ZsL0hIbnDz/z89Yg5//azrOe2pW2jq5g9OQSOiukco96ISvVmxLW2bX4ZM7vKnr5maag2ziZwpv3qKySJZv3qXc1k2PUQuEepPND1IvQm1DHMWFWvD42a9XI54QuPjQ/gDSe/A/bN6Ff05Zhpdnrs3omJlM8qN6kYwjrRMmyjnTya9en2M+MrxdSZFuv1t21Vred1XnIuZWkSSPV5fBb1KYnf9/5/6IG99oqv6YaYJFr3Ylttv0v2UyAODm4/ZBT8X2qetoNzLcbK56N24cJ+/gPR9oow3mKepo6WIkcX0Cjdm8RZkQF8KyQSaDS00Igce/bBqLFOb0X2MZ+eIslZEPFJVFYlae4vNlWyGEQI2DB+jiF+bgpmMH2W6XbeIJgSe/XIV7Pvwe954xDP/+fGVjnn3Pdi1x7JBuynEfD31q7cKw4t6P0pMPnMhppNrgOkgItQusSpqH3a90/oZ4QmepNcQFNpSnVyaoi8Vx05sLMGVJujvQbYyksaPS4L9rS1YigJk1YH/xWhQ6z0L76wff474zh6ctTykSu/M0szzcuHE+WrwJv3xqDSaePATHDumq3MYqkUAfI0novjspaCqzels1HvhEXQvOzoiX7+vZj8/E74/Rty1hno/EWEZ+FnwuIx8G3LhCtu6qw5tzf8Tdk52NlwxDWYmEELhr8lIAwA2v6xuTy16ah9m3HqUb7R0Uqh6y0Y2SEELZAF78wpzGz34NDKuPJ9Lu39rt1WnbvTRznS64K+M+RqL9/36T83npM61zVp/hs9kQa/rd1l11mLt2J362T2fT7VUZaCnXnVlNuxRmErpxGac6NZe9NNe07LvT+XyMFkm1S4vkvKdmKTsjgLmVVdsQR4uCiK7Du6G8Bt+u11tPoZ2PJEdl5APHzYhaQF/W3I4wNNBWMxsCwIOfLsNLM9flSBpzVC+zUZEIoa6aK+NXBkiDYrDf2u361FYhhDLdNYXbGEl9LIH/ffcTZq7aYb9xEqO7zekYngaFQnaig+XzOfOx6VizfTeuOXKg6faqDDSVRaISW1efTEq99erG+Wb1Dlz/n29x7ZEDcdZBvSy31aUoJ/TPn9FitsNMiQDqc1qxpQonP/IVjhvSTTemCUjPaAzSjR54ra0wkM0aObUuXBTZQjV+QiYMSgRQN4DGPP24sG+Y/XJt1ccTaTKpXl6r3nHMpWvrxZlrcc2r813JuatW35g5nQteFZ9wcumq62P4y3tL8OGijViTVKz/mmpeR041uDLVk5djQar7Kl9aVZWBTLn2tfnYUF6Dm/5r3Sk0dlxiCX1JmuoMg+0qVIpk4qTF2F0fx3/n/ZjWThkn3wsya4uD7chujRwnGS7ZZvrK9AyRMKK0SOqNri17d6HXkhgpGuJNc5ykMPZAjYU5jbi1SDKhyqBInLqsMpXr2a/XAIBuzhIrK6iyJr3XnpJZ7u2rEhnkYHsskUBRsu/r9ZI6fS+NSjAWF1iwvmmEufH59ILq+ZctNuPaLbv0xSjzuYx8s8BqAJdXan180DJl2WZ1zaWwobRIFK4tu0wfPy1M4wRPT07Tf9cUifnvG+IJpQvJT4wl/J26UxdvqMRcwxiPbLwKNQ3piiQVpJaVhyr2Jetop1MkO0HOPNtZbT4Hi7HXP2PldsyQpp1wGyOxQp2NqE/2kNlitEhCPCBxjyCbri2zEg9MOqrGwZgV0xBXT1Erk+0qrDK/fmYWXpll7hp0m7WVCb8zZGN94bDEzX/mrMfp/56OlVuz29FQuXdrU+m/kvJ4bvqaNCVonFVStdwNqWenh1QZ2cz1W7G7AV8s01/LVNJKCrcxEiuMz//2qjrMlyxiowVZvtvoZmVFEijZtEgY56hcLcZpft+c+6NpanaKXN7O2WvSR23LxBIio8GZXpi12nmgHtCPPPfLLSijmqo5tcyoON4xdLzkpvGNOdocMM9PX4MTH/4qI1kqky41uZCmmZtrwv1f4C/vL1WuS2H3LLrBaP0c88CXOovMbsprDrYHjKrWFpN7nGRtOSGIWSjNiCeELl02jBRGs9sMqO5hXUMcFz77TVr9s7RxGdKl++sH3+OFGU3VgDMhFfOQn7XHv1iZtp0QIs11pMJs0qwbX//O9biOn/97euPn1duq06o6vLdgo+XvOUYSMHuaHvn76cOCFkGJk2B7vhFzOY4kCGRFkg1rTuXa2rKrDlMVLjjjfCTGJ0I1m6kbdtU2YNGGCp1yM8ohhMAuhy6rzSbK5r/zfsTSjfrqGHbPgfz8z1JM/21HkAMSWZEgv1xbndq08PT7z248zDZvHgCKXYxe9guVIrEz53NF3w72ZUFUuC2REgQFUvHGbLwJqntoNt+KMSPP2DiqSpi44V9TV+LEh7/CZ99vMd0mlhBpbiYzrKyA4x+ahnOfnNkYBzJm11nhxBpyI0u2YUWC/LJIDu5nXtp9eM9Sy9+WFEXRv1NrR8dpWRi138hnVFlbq7aljyQPgjbFmVUDmjhpiatKvkEgN9bZaIpU9ajMSovIlsIrs9Y1jlNxQqsi+2f2sx/MFUiKWFxgWwYNuYrpK7fjqxWaxeOmUvAOi0wyM+auKw+s08KKBJln+ZwwrJty+bi9OiqXu6FNiwIM7pY+1YuVrNceZT66GNCP4H/svANNt3vg7P0dSLhn0cLFLIdGjGXVw4Y87iQb0+lurnTeKMuK5Ja3F7o6Tpe26XOkGHEyV0hDIpEWn/DCp0s15WUcOKpCJEsAuSmRk2LSdz8FNm6NFQncl0hJMbRHKd67elza8pcuPhjdFRP/uOHeM4fh8V+lN/ZWkvbp0Mpyn/JMfccO6YrDB3VK2+bXY/rg1BE9HPVMf3lwb0y6apyuPEZRlgO3QVHgcu4Omfnrvbljso3cuAbpHgGaYmKZ+Pt7Z+h+NPK3D77H5w4sF6esSdZn2+VgsrK6WAJnPzHDVYkcmTYtghlj3jzfepfIeuTnI3o4/l3LwiiG9FC7k1p4cA1dNK4fjtmvqzLwSQTTAnltbdwvRoVZXJAuY6pX5+Q9vvCQfhjas1T30rdqkXuXWC6QA9JPnz/S1W+d9IJVvHbJaCz58zGW1qMfrNtejZve/A5vzv0xI5eKn6TiKW6r6gLa8+gHL89ahzfmmk8v4Jb1O7QsQieurV21Mcz3EAfK5RgqGVYk0F/8Ygd+1hTGAUEyXnrmt584GESkTAIgAE/+eiTm3nZU2ro2xda9EeNDpioHfvoBPQE4G9yUcvfIA+5a28iQr8hKuFtpS9PtBnSytgqdMqpfe4zu3wElRQU4Zr8ujn5z/FB1iXQ7HvpsBV6f82PawMZMcTvzokzKNeNmquEUXdq2wKPnHpDxsf3i3IN7677/VF6DWDzhSJGYJSGEHVYk0GdtufGFD+tlHdz2ilKRECEaIXRonZ69VWxjBRkDcUaL5C+nDmmai9uBRZK6VnFpwJ2dVZQvHLVvk9VXFI3oBnuZKewHzt4flx42wJfjy42xk17m/WcPx/0hiW09df5BuMzldWiddMmkXFtO4glG2hQXZuym9oMhPdri/rOHY+yADrrlsYTA8i1VuPa1b233sdlkXErYYUUCvWvL2Bjvqwh4A8AvRvXC+IHpMYYUZjO7uZJLcXe8WDpG/3dhgf6la9+qqPGzE+lTo4PlAG3v9u791EcPdtbjziUH92tqDFoURHTKspWJH7ogSro4lFP+eNJg3bUHgKjq5ltQ2rIQhS5/ky16lLXEhYf0dbx9NEIY0bsMgDYQ75IX5uDNDFxLbYsLAovxjOrXHu9dfShOG9FTmfH4ksOZRl+cYb9dN4/x12wQjicvYORejNxLv/pne8Gs3T7noN6WvR8/0meNFkmHVkW4fsLeGe/P6K2KGvYvKwQnwc5GRSK5tk5zEWNK8cSvRzp236g4qG8703UP/2JERvssLWmyrFoURnQNlNkYm8JoJKMecTRCaQ2gUSEV2VjKbYsL0yo03H7iYNeyqLCaa0RFoQuFSgS8fcVY7N2lDQBgztqd+HjJZjwhTSHrlFZFBboih7lEtiDH790JI3qX4bC9OzW6io3zyJvx4eJNttvIdcLCAisS6F0H8uQxB/RpZxp0tgsql5YUpS27+7ShuGR8f9zgUBnIiuSskT3xza1HNbmeMsAY9zA2PPJ8Bo4skqSWPaBPWeOyCYO74O7ThmJUX/PxLio6t7E+L6sBkn88aT8cOlCdcj2gU2vTdTLGEdXy9xYFUd00qGYDWLUG1P0rFSFKK0RpVEjGSY2MGOUHtKSNu04b4kqWGybsjY+uG49e7VtiaI9STLvpCNfJAtEIocDQAzugdxmeu/CgtPPYt2tbDOtZ5rnj9eyFByESocAKF8rJGIXRCN6+4hA8/5tRaJ1sJ8p3+5fE0F1SJB1apbczQcCKBHrXVlFBBE/+eiT+fMp+OGJQZ1NFUlLU5N546aKD09aXGV7sMf074NyDe+OW4/d13MOT5SKQo97uI+ea98CNvV6jRTJS6tk7eR9TjcUpw3vgjycNxmuXjAYR4dyDe+MwRWqxFd0telmPnXcAjtzH3GLp3KYFnvjVSOVgzYKos+v27R0TdFlychplUUFE19M1621napFEiNLGbxiPUWLT0LZVKBIAGNi5jWM53r3yEFxz5EAM6toG0276GSZdPQ692pfoRqYfslcHiz1oFEQiafK/8tvROHxQZyyeeAyG92rqeKSmLm6XYYN4xoE9seaeE3DEIC2mFdTU1mYdiJSr3M9suB7tmt6V/XqU4sTkeLabj9vHt2O4hRUJ9D3MSIQwYXAX/HpMXwDm2UutJEUyTurxpkzcshL9i238bobcgGWSynfisO64/ii1xZPm2pLM8cP27oSe0hwN8sNqRyRCuPCQfhjdv6mRcdug9utonu107JBulj3N9q2K0LIoilP2T3erRSP2VsKzFx4EItJdHzn7LJ4QGDPA/twKIhGdi8POimjaX7qSN1qLcjbhwj8djV+M6o120jOlskhS+zYyzKQCglnxRrlCbzuFpW2kIEpp425SDSoR4Z0rxjYur04G163ck1YYz9sqo84Kp/fKjKIC9TORGgZQaZE8sHeX1q6y/eS5VEoKo7j/7P3x/jXjcMn4/o734TesSKDv+Ttt/0pMXFupRss4ONCpe2DytYc2fpYbLJVOefGiUcp9HG0SbzA2xrJFYkwqeOTcERjUxXlv1ohZw2ZGf5sXySqImrKMVAkOBRFSpqN2Ky3G6r8er+vNyrSWFHpJURRXHTEQ1x45EG9cNgZEpLwfRQV668dM+Z02oofupXdkkUgNXZviQvz150Pxq9F9GpeZZRuqgvbnSb8zyq9CLrpoTApQURAhy8A/EeGwvTWLNTUmar/upejY2plVIl8L43N2yF4dcNURe2Hiyfs52leKD68d73jbVIxin65N74eZEja6ZEuKovjouvH49y+b0pTLSopcdbz27dZ03MraBhRGI9ive2lgY0gAViQADBaJ4WaYdYTNHpxUo/XLg3vretlO6y31krKedK4txTNyqEnW2L7d2mLyNYfijAN76panKZKIfN76fezTtS0+un58xllipx/QE2P627tBUphle92RDBirGuW7ThuCd688pPG7StdEI6S7VxNP3g9XHD4Ar186xvLFkxVJ6xYFaFkUxfUT9sZBydiPyr2luXSajiVbeDLj9+6oqyoQIUprRI0Ny7H7pY8RuejQ/hjesxSXju9vei5G9yWguVlV2Yhmz7RcgdlurBKgKXa7qRkeOXcEJp68H+4+bagmZ4RwtoNiooA+xbydwdInIvzumEE4f2xf099foFjnZlT8e1ePw8sXH6xLZjA7W2Psp2VhFIO6ttFZ7+1KCl1lm+3TteneOS0umW1YkcCoSPTr3KbxprJriguj+M8loxuXO53+1Ewut72Nwd3bpsUdjM+qvH+zHlGmnZyigghelc7fDtUYmJuP2we/GaeNVla9aL88uI/O355QbFMQiegynnq1b4mbjt1Hp7BVyK4t1SBLVcDdGCM5qG87nKNoHCNEugaeCHj6/IMMcuv3f8n4AbjjxMGYdFVTSZ7SloV496pxuPn4fU3PQ5bnuCFd8cJvRqFX+xJlaR8nri0ntbicZGy1KS7E+WP76pJH+tqU+EnRtmXT/ehkk6SRQhbJLED90kUHK++XkXatinDIXh3RWarEbTbY0Phct0xaU7JbuV1JkatJqVpKFpkxqSEowiFFwMhWuLHBdpuWLvdIZb92JhVgZVHsXk3Vu2v3QustEneK5B3JEsgWskxOGjCVsolGSKdInE4ZIPckVZV/VbspjOrdaPGEwD2nD8N/Lx+La6UEi4JIelB+eK8yXaKE0SVVVBDBb8ZpJWncIA9CPXVED4xPupRUHQczRSK7tuoUc4sYyXRQoBNrB9DL2bmts2kVPrvx8MZ7drrBUj9rpPZ93MCOpnGGVBqvjOzmM4uBGF1bqedKdv2VlRTpnt2uDopP3jhhb7QtLsBfTnWXlZctQlXPgojGAPgawC1CiHtyeNzGz+muraYbfNlhA/CYYjY1QHvR62MJ/GJUU3kEuTFy8gIaUbklzFA1kHYvtCNFolBhw3uVYX/JEsgWsnvESRaZyv1VECGde85pI0dEKCspRPnuBl0sworCaERXcWB7soLsgX3aYaeUtRONkNLClBV/JgMbVcjna0xoOPfg3rr55s3cmMcN7YoZyYmW7DpEhw/qlPGMi61bOIuryY1uZ4fz8/Tt2Arf3HIU4gmBrqXFmHTVOJTX1KNvh1a6cRmq8Tr/PGs4frZPZ/xUXoMjpYoHZVLiQaVJaZM011aycyl3OMYM6IBJ3zVN2GUWfwWaMkSvPnIgrjxir9DM7hoaRUJEEQD3A5id62Nbu7aauPbIgShtWagcl/DZjYdh7tqdOG5IU2l5+YWqN4wTePW3o3H35KW4+bh9cO5Ts2zlstMpKkVg1/uWGxmzd1+1C6/P7mPnHYjLXppru518HOOAQFXMQKVsolG9ReJGOU+5/jBsrKjBsJ7pSlN1rIIooaOkSDZJ5S5kV0ZBRJ2SLFuzfpX62K97W1w6vj9KigoaB/2luO2EfXWKxFjpIMW5o3qjtGUhhvYoxSNTV6Stn3jyfvhh8y5cd+RATxOvOa3TJncYOipKBZkhy2Zm2RkVyXd3HN04ONXoqpXvkVlJF2Px1pSrqyAawYsXjcLG8loctncn3fNt1ono0raFLkM0LEoECJEiAXAJgFkAslvASkHU0iJp+tyyKIrLD1fXEOrZrsQ0uApoc1TLjBnQAZMUfmoZvWvL+qFRtY92HUPdeZvFSBTLvM4ouVdnZ75w+UWNSzdi/u1HKwcomlkkcu/PzcvXqU0LVw1jUTSi84nLdZPkax2NklKhycrGL0VCRKYxFHksFGBukRREI42p1ap7f8heHSyD205p7bBy9Cn798C9H/0AwL6+nFvka3D04C66CgdWmFkkxnp2csaZnCwTd2Byh3km11AoEiLqAOA6AKMBPGCyjV1t5YwVkFV2lF8jZTOLkWTXIok4ipGo9mstix1OJ3GTjy0H0lua5PyrXsYIkS7e4FcDrXoqjIFPOdspanBbqS63n64ts7EiVji5NtceORAfL96kiwkURf1pzJ26to4d0hWDu7d1HJx3g9t4WruSQuzc3YBzRqmD9MZnVTV1A6B/vu85fRjOemxGWlwwzIokLMH2uwA8IIQIZAYgfYPtLP3XLZnOSZEik2D7ft2tGxN5eIWZy0ft2vL2QDtNdZRlcqLQ5ZdxVN/2uHR8fxQXRnWNsm8vo0KclOXz+2MGoTBKeEiq82VMMVc12rqYVYaK5O0rxuLskb3w7wzmMHGSGdirfQnm3j5Bl0JrVwfMKU5dW22KC3DEoM6Wg1gzxW087f1rDsW9ZwzDDRMGKdcbLed+JuOl5Pt9QO92mHfHBF0FaiDzDMpcELgiIaIRAA4C8KTVdkKIMqs/ABWZyqAvRWI4rk+zWHudt9vuJVc1kGMGdMBffz7U9DdR6aXJpWvLab0wXYzEUbC96fMzFx7U6NLRx4Ky9zamYmJXHrEXFv7pGBy5b9PAUONh7WIkmYo5onc7/O2MYVkt7FcYjegUu1+KRFUGZkTvMsy7fYJuWTanKihw8E7IdC9riTNH9jK1ko0WSGogppGHzhmBggjhomS6e9vi9LElYbZIwuDaOgzAIAAbko1lKYAYEfUVQlyWCwF02UGGdb5ZJE79OQZKiqLYXR/HmSPT0w9lzJ6xX4zqjZvfUs99rY8Nme1X4drKsN148aJRKIpGHI2O1mRSu7bMkBs3MzeRm2C7W+TkCqPvXpaeoL7eQc6l4ZZsKJJIhNClbQvdHO99O7RC+1ZFOGFoN7y/cCMAd3MGecHD/FyNGEuvmFlRYwZ0wHd/PFo3RYGx8xTmxyMMiuQJAK9J3x8EsBzAvbkSwOoGBVRMtJGZtxyJndX1tvOxZ1IeQXbpuxmQmGnPyGwkvhmygu/bsRUWbrA2OmVdU2jiorBSgkcM6oSpP2x1JaOMlSIQBk2iuoZ+pfzmAvl8/GzYP73xcCzaUIFznpipWy4fI1elQI5WZAa6xTgGqbXFnOrGeW7ihpL4bJFYIITYDWB36jsR1QCoEkJk7Kpyiy7N1rDOybwcTjiwT2ZF6doWFzoy5TNpg6xKw6TIhmvLKfI5/fGkwaipj+OEYeYv99GDu+ChT5cDMHdnWTX2/zhrfzw1bRVOHNbdXjiXl0B2kRLU0yjLsgXdgbFDVtp+KsDWLQrQX9Frv/GYQZi1egeOG+K9cbfjkxvGY/nmKhzrw7FUtbacYpxaJcR6JHhFYkQIcUGuj2nVMHp9n9+7ehzemLMel5mkDftFJo27s5Ht/mdtmXHe6N54aWbTuAZZvo6tW+Cp80da/n5Ij1K8d/U4dDDUrXLq2mrfqgg3HeusFHdRNKJLoOjucp4YZdaWH76UnCEpRp9bOJWrrEdZS3z1hyNyYo3s1bkN9nJRft8Ko7xu5DdmIbJFEnIsFYlHTTKkRymG9Mj+0JjMXFtyT91kv4pl2XqgbzthMLZU1uHjJZu1Y2dwHNW1ltN//RrEVVQQAZKu/PeuHmdbvdiK1DOWT66tKw7fC2/N26Cbw8YvZLek7BEIsrptENx2wr44+ZGvG7+HOYYWeNZWGJCfT6PeCGrGNbdk8oxlWmsrWy90cWFUV7HYr8B4NoLtcppor/YlaYP70pAeIzMR3M7THiS92pdgzm1H4YXfpE/q5hW/gvf5zrCeZZgvZayFWZHyHUN2XVu5IiPXlpMYibS8V3stpfTiQ/u5PpZT5DRKvzpgdvO6ZIJcTsSJJWHM2pJJyZRPFgmgBZKz0UvOt+uQTeSZI8N8Wdi1BRfZNiHGyUPWxzDnQsRBEHpg59aNcx58eO14bKqsxYBOrR3LlUrnTE1gZIdc5M5J2QgnyLEHJ1WEneB24JqcMGHM5EmdZphdF7kkzD3vIOEYScixfn/zQ5NYvXzvXnkInp+xBtf8TD9XvJNaW/edORy3vL0QZx7YC61aFLhSIoBWbv7DRZvw8xHW42BSyBZJJhWTVehqdvmkSGQ/vpMe9JAebXHB2L6IEGFw97aNc5XLBNETj0bIt2vCZJfuZe4SOnIJu7Zg7e7Il3fMyr0+vFcZ/nnW/uhrSKuUiwSatWHdy1riuQtH4YRh3dQb2NCttCUuPKRfWvG7/14+FiP7tMMrF+t97LJFkukgTiPyPOOZzvhoRB7X4MSSICL86eT9cMdJ2qx68tziqjlCcvXYvXzxwejYukXjTIV+8vczhqF1iwI8/iv35VoOH9QJLQoiuO6ovX2XK9e8cvHB2KdrGzx34UH2Gyu489QhGNWvPf58SjjmHlHBFgkAq0EBfo0jyTZeYyTZHPGt4sA+7fDm5WPTlustEvezSqoYO6ADzjiwJ1q3KEhTpplS5HGAXFFBBN/dcTTq4vHGCsMFAQTbR/fvgNm3How2poMAAAtrSURBVJkVd9JZI3vhjAN6ZpQp98z5B6G6PqacVCzfGLtXR3x4nfM54Y38anQfx3PiBAUrEgNGxZE3FonXcSQh8c+XFDY9kl7rk6UgItx35nBf9pXCj8wizUpraiijAY0jyWZMItPnKhKhZqFE9hTYtWVDvlgkmbQFViP6g6K4qOmR9EuRZINMZwG0grOVmHyFFYkNeaJHMrJIwjiSWo5h5GI630zJhiLhrC0mX2FFYsBo5qdKm/Rsl72y3H7gtdZWWPQlEeG/l4/FA2fvr5zSOCyo6kF5JddxKobxC46R2HDp+P4Y2qM0oxnncsHYAR0wfeV20+lUrQhrD/jAPu0yLnKZK645ciBWb6vWzaHtFTme0NnD3OcMk2tYkRgwxkQKopHG9Mww8sJvRmHzrrqMJjLiHnDmtGpRgCd+bV1EMhP+cOw+WLShAr88ONxZOgwjw4oE4S7PbEdBNJLxbHhytmm+xIKaO5dnuUo0w2QDjpFAH+BtZVd8rxlBulwt1iQMw2TGntNqWtCrfQnOHtkL26vrcYTDmlDNgXy2xBiGCQ+sSJL87YxhQYsQKOzaYpobr/z2YDzwyXLcfJyzycqYzGFFsgfDFgnTnBk7oCPGDghvCnlzgmMkDMMwjCdYkezByMF29mwxDJMprEj2YHRTDLMmYRgmQ1iR7MGUtWyqrhr2EjAMw4QXDrbvwXRuW4x7zxiG6roYhoe4QCLDMOGGFckezpkjewUtAsMweQ67thiGYRhPsCJhGIZhPMGKhGEYhvEEKxKGYRjGE6xIGIZhGE+wImEYhmE8wYqEYRiG8QQrkhAwdkAHAEC30uKAJWEYhnFP4AMSiagFgMcATADQBsA8AFcJIRYHKlgOefTcA/DW/A04fmjXoEVhGIZxTRgskgIAqwCMBtAewCQA7wQqUY5p16oIF43rh26lXO+KYZj8g0TIyr4SURGAWgCdhBDbXfyuvLS0tLS8vDx7wjEMwzQzysrKUFFRUSGEyLjgXuCuLQVjAGwxKhEistMQpdkTiWEYhjEjDK6tRoioDMATAG4JWhaGYRjGGaGxSIioGMC7AN4TQjxjXG9ndiUtFrZKGIZhckwoLBIiigJ4DcB6AL8LWByGYRjGBWGxSJ4EUAzgTBG26D/DMAxjSeBZW0TUB8AaaJlacWnVcUKIaS72kwBApaXs3WIYhnFKRUUFAAghRMYeqsAViV8QUQyaq64yw12kNFCFPxIFRnM5D4DPJazwuYQPL+fRFkBCCJGxh6rZKBKvpNKLveRSh4Hmch4An0tY4XMJH0GfRyiC7QzDMEz+woqEYRiG8QQrEoZhGMYTrEgYhmEYT7AiYRiGYTzBioRhGIbxBCsShmEYxhM8joRhGIbxBFskDMMwjCdYkTAMwzCeYEXCMAzDeIIVCcMwDOMJViQAiKgzEX1IRLuJaBERjQ5aJjOIaCIRLSGiBBGdIy2PEtHDRFRBRD8R0cWG312UXF5BRI8QUaD3nohaENGzRPRjUqapRLSftP42ItqW/Lvd8NsTiWgVEVUR0WtEVJL7M9BDRP8moo1EVElEC4noRGldXp0LABDRmOQz9n/J73n1fKUgos+JqDZ5fauI6ANpXd7cF9K4LXmNdxHRjOTycNwXIcQe/wfgLQD/AtASwPkANgBoEbRcJrKeB2ACgJkAzpGWXwNgNoAOAPYHsAPA8OS6/QFsBzA8uX4ugKsDPo9WAG4H0BNAFMANAJYn150MYDWA3gD6AFgL4KTkuq4AygEcBaANgPcA/CME92UfAMXJzyOTMrbL03OJJJ+vWQD+Lx+fL+lcPpffE2l5Xt2X5PWfAqBH8v4cGKb7EviNDvov+aDUA+giLfsewDFBy2Yjt+4FSb74Z0nfHwPw1+TnewD8S1p3DoAZQZ+D4XyKACSSD/xrAG6S1v0fgFeTny8DMFlaNxrAxqDlN5zLSAA1AAbn47kk5XoQwHOSIsnL58tCkeTNfYHW0doIoJ9iXSjuSyjMz4AZCKBcCLFZWrYQWiOQTwwGsEj6Lp+D1bqwMAbAFiHEdrg/l65E1C4nUlpARP8iohpoPcRPACxFnp0LEXUAcB2APxpW5fPz9TARbSWiKUQ0LLksn+5LL2hTkf+CiDYnXdtnJdeF4r6wItFcLMZZFSsBtA5AFi8Yz0M+B6t1gUNEZQCeAHBLcpHjcxFCVEObojnw8xFCXJGUYwKAT4TWDcy3c7kLwANCiHLD8nx9vm4C0A+aC2sKgMlE1Br5dV+6AyiD5oLrA+BCAE8Q0SCE5L6wIgGqobm3ZNoCqApAFi8Yz0M+B6t1gUJExQDeBfCeEOKZ5GLH50JEraCZ/qE4HyFEXAjxCYCjiOgY5NG5ENEIAAcBeFKxOi+fLyHEN0KIKiFEjRDi79DkGoU8ui/Q3KQAcJcQolYIMQvAx9A6LKG4L6xIgOUA2hFRF2nZEABLApInU5ZAkzuFfA5W6wKDiKLQfNXrAfxOWuX2XDYJIXZmUdRMKAAwAPl1LocBGARgAxFtAnA2gFuJ6DHk4fNlQiL5P5/uyzIADSbrwnFfgg6GheEPWtbWI9D8kL9CuLO2CpNyfpmUtRhah+AaaFk27aFlaWyHPntjG4Bh0ILZsxGCrBoAzwD4EEChYfnJAFZBc0f0hpZdI2fU7ATwM2hm+v8QfEZNa2jZdK2hKZDTAdQCGJpP5wKgJClT6u8/AP4CoDRPn68yaL32FtCSOa6HFrRuk0/3JSnTa9AyS4sAHJiUb5+w3JdAb3RY/gB0AfARgN0AFgMYHbRMFrI+B0AY/g6HZno/AqAi+bJcbPjdxcnlFQAeBRAN+Dz6JGWvgWZup/4OTa6/PflSbAdwu+G3JyVf/OpkY1cS8Lm0AvAZtJTRCmhplqdJ6/PmXBTPWiprK6+er6RMnQDMST5XOwB8CmD/fLwvSUXwv+S5LEcyUyss94Wr/zIMwzCe4BgJwzAM4wlWJAzDMIwnWJEwDMMwnmBFwjAMw3iCFQnDMAzjCVYkDMMwjCdYkTBMCCCivkQkiKhj0LIwjFtYkTCMgeRkSHXSZEipv2jQsjFMGGFFwjBqbhVCtDb8xYMWimHCCCsShnEBEa1JTnk6Oznl6edENEBa35mI/kNEW5LTCD+QrHCcWj+QiP6XnB9jBxG9ZTjECUS0PDk16uvJyrOpqYmfTv6uMjknxeG5OWuGsYYVCcO457cALgDQGdrkVW8RESXXvZr8PwBaufJDANwNNJYj/wTaZEN9oRUHfNiw75OgzbA4EFoRvsuTy88HMALA3tCKKJ4EYJ2vZ8UwGcKKhGHU3ElE5dLfdGnd40KIxUKIGgC/hzbr3HAi6gGtYuwNQohdQoifoM00eEHydydCK2N+qxCiWghRL4SYajjuRCFEhRBiC7QifQcml9dDq0S7L4CIEGKlEGJVFs6bYVzDioRh1NwuhCiT/sZK69amPgghqqBVj+0BoCeAmBBig7TtKmjz3ZRAq3i8UlhXSt0ofZYnJnoJWtn9RwFsI6KXiKhrpifHMH7CioRh3NMn9SE5bWsHaHPY/AigIGmZpOgLYKcQYjc0BdRfcoM5RggRE0LcI4QYAc3t1RbA3zM/BYbxD1YkDOOeS4hocDKIfg+0OMmCpCUyFcB9RNSGiLoBmAjg+eTv3oc2MdmfiagVERUR0RFODkhEPyOi/YmoANq8ObXQ5hFnmMBhRcIwau5SjCPpnVz3NDTlsBXaLIinCyFSU7ieC22WxFXQJlWaBeBWoNENdhSAA6AFyjcBuNKhPF2gBfLLoU1NXADg/7ydIsP4A09sxTAuIKI1AH4nhHgzaFkYJiywRcIwDMN4ghUJwzAM4wl2bTEMwzCeYIuEYRiG8QQrEoZhGMYTrEgYhmEYT7AiYRiGYTzBioRhGIbxBCsShmEYxhP/D7IuBN3K/z2sAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(hist.history[\u0027loss\u0027][400:])\n",
        "plt.xlabel(\u0027Epochs\u0027)\n",
        "plt.ylabel(\u0027ELBO Loss\u0027)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "([\u0027dense_variational_2/constant:0\u0027, \u0027dense_variational_2/constant:0\u0027],\n",
              " [array([ 1.3229319 ,  3.2696323 , -2.1848109 , -0.40408733], dtype\u003dfloat32),\n",
              "  array([1.3986531, 3.1327233], dtype\u003dfloat32)])"
            ]
          },
          "execution_count": 71,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "names \u003d [weight.name for layer in model.layers for weight in layer.weights]\n",
        "names, model.get_weights()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "#### Sampling from the posterior\n",
        "\n",
        "The weights of the network, follow a distribution. We can sample from the posterior by calling\n",
        "```\n",
        "    p \u003d model(x_test)\n",
        "    # Note that p is a distribution, with mean and std,...\n",
        "    p.mean() #Sample the mean from it\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 157,
      "metadata": {
        "scrolled": true,
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(x,y, marker\u003d\u0027.\u0027)\n",
        "plt.plot(x_test,model(x_test).mean())\n",
        "for _ in range(25):\n",
        "    plt.plot(x_test,model(x_test).mean(),ls\u003d\u0027-\u0027)\n",
        "plt.xlabel(\u0027x\u0027)\n",
        "plt.ylabel(\u0027y\u0027)\n",
        "plt.title(\u002725 random draws of weights from the posterior\u0027)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "#### Averagring\n",
        "\n",
        "Now, we average over many runs of the network. This is the same as taking the mean of the predictive distribution. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 1514,
          "status": "ok",
          "timestamp": 1554370745244,
          "user": {
            "displayName": "Oliver Duerr",
            "photoUrl": "",
            "userId": "00002413253758210405"
          },
          "user_tz": -120
        },
        "id": "CJmnH-CD_p8T",
        "outputId": "cd4e629d-8ff6-4440-9172-9502631b135f",
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "mus \u003d np.zeros(shape\u003d(50,100))\n",
        "for i in range(0,50):\n",
        "    y_hat \u003d model(x_test)\n",
        "    mu \u003d y_hat.mean()\n",
        "    mus[i] \u003d mu[:,0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 156,
      "metadata": {
        "scrolled": true,
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(x,y, marker\u003d\u0027.\u0027)\n",
        "m_var \u003d np.mean(mus,axis\u003d0)\n",
        "s_var \u003d np.std(mus, axis\u003d0)\n",
        "plt.plot(x_test,m_var, c\u003d\u0027r\u0027)\n",
        "plt.plot(x_test,m_var + 2*s_var, c\u003d\u0027g\u0027)\n",
        "plt.plot(x_test,m_var - 2*s_var, c\u003d\u0027g\u0027)\n",
        "plt.xlabel(\u0027x\u0027)\n",
        "plt.ylabel(\u0027y\u0027)\n",
        "plt.title(\u0027100 random draws averaged mean +- 2 sd\u0027)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "### MCMC (with Edward)\n",
        "\n",
        "The models can be defined using either Edward or by programming. We start with Edward.\n",
        "\n",
        "#### Defining the model using Edward\n",
        "\n",
        "Here we define the models generative process. Using the Distributions provided in Edward2. The Syntax seems to be:\n",
        "\n",
        "* input the data value x\n",
        "* variables with names. These names are later used to feed in the variables from the MCMC runs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "def linear_regression(x):\n",
        "  \"\"\"\n",
        "      features is a list containing []\n",
        "  \"\"\"\n",
        "  D \u003d x.shape[1]      # number of dimensions\n",
        "  betas \u003d ed.Normal(         # normal prior on weights\n",
        "      loc\u003dtf.zeros([D,1]),\n",
        "      scale\u003dtf.ones([D,1]),\n",
        "      name\u003d\"coeffs\")   #\u003c--- The name of these variables is important\n",
        "  alphas \u003d ed.Normal(          # normal prior on bias\n",
        "      loc\u003dtf.zeros([1]), \n",
        "      scale\u003dtf.ones([1]),\n",
        "      name\u003d\"bias\") \n",
        "  noise_std \u003d ed.HalfNormal( # half-normal prior on noise std\n",
        "      scale\u003dtf.ones([1]),\n",
        "      name\u003d\"noise_std\")\n",
        "  predictions \u003d ed.Normal(   # normally-distributed noise\n",
        "      loc\u003dtf.matmul(x, betas)+alphas,\n",
        "      scale\u003dnoise_std,\n",
        "      name\u003d\"predictions\")\n",
        "  return predictions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "from tensorflow_probability import edward2 as ed\n",
        "# Joint posterior distribution\n",
        "log_joint \u003d ed.make_log_joint_fn(linear_regression)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "\u003cfunction tensorflow_probability.python.edward2.program_transformations.make_log_joint_fn.\u003clocals\u003e.log_joint_fn(*args, **kwargs)\u003e"
            ]
          },
          "execution_count": 77,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "log_joint"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "def target_log_prob_fn(coeffs, bias, noise_std):\n",
        "  return log_joint(\n",
        "      x\u003dx,\n",
        "      coeffs\u003dcoeffs, #\u003c-- This has to have the same name as above \n",
        "      bias\u003dbias,\n",
        "      noise_std\u003dnoise_std,\n",
        "      predictions\u003dy.reshape([len(y),1]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# Defining the program\n",
        "metropolis\u003dtfp.mcmc.RandomWalkMetropolis(\n",
        "    target_log_prob_fn\u003dtarget_log_prob_fn,\n",
        "    seed\u003d54)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "#Parameter sizes\n",
        "D \u003d 1\n",
        "coeffs_size \u003d [D,1]\n",
        "bias_size \u003d [1]\n",
        "noise_std_size \u003d [1]\n",
        "current_state\u003d[\n",
        "        tf.zeros(coeffs_size, name\u003d\u0027init_coeffs\u0027),\n",
        "        tf.zeros(bias_size, name\u003d\u0027init_bias\u0027),\n",
        "        tf.ones(noise_std_size, name\u003d\u0027init_noise_std\u0027),\n",
        "    ]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.5/dist-packages/tensorflow_probability/python/mcmc/sample.py:335: UserWarning: Tracing all kernel results by default is deprecated. Set the `trace_fn` argument to None (the future default value) or an explicit callback that traces the values you are interested in.\n",
            "  warnings.warn(\"Tracing all kernel results by default is deprecated. Set \"\n"
          ]
        }
      ],
      "source": [
        "states, kernel_results \u003d tfp.mcmc.sample_chain(\n",
        "        num_results\u003d2000,\n",
        "        num_burnin_steps\u003d100,\n",
        "        kernel\u003dmetropolis,\n",
        "        current_state\u003dcurrent_state\n",
        ")\n",
        "        \n",
        "coeffs, bias, noise_std \u003d states"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(TensorShape([2000, 1, 1]), TensorShape([2000, 1]))"
            ]
          },
          "execution_count": 82,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "coeffs.shape, bias.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[\u003cmatplotlib.lines.Line2D at 0x7f6a475e8358\u003e]"
            ]
          },
          "execution_count": 85,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\u003d\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(coeffs[:,0,0])\n",
        "plt.plot(bias[:,0])\n",
        "plt.plot(noise_std[:,0])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "### MCMC\n",
        "\n",
        "The programming is a bit tricky. Also for the data the  shapes need to be followed.\n",
        "\n",
        "The random posterior variables which are optimized need to be lists. We create a small data set to show the shapes. To that also the shape of the y\u0027s need to be nxp."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Shape of the weights  (2, 1)\n",
            "Shape of the x-data  nxp (3, 1)\n",
            "Shape of the y-data  nx1 (3, 1)\n"
          ]
        }
      ],
      "source": [
        "w \u003d  tf.ones([2,1], name\u003d\u0027weights_init_state\u0027)\n",
        "xs \u003d np.array([1.,2.,3.],dtype\u003dnp.float32).reshape((3,1)) #We want the data to be with dimension Nxp\n",
        "ytrues \u003d np.array([3.,4.,5.],dtype\u003dnp.float32).reshape((3,1))\n",
        "\n",
        "print(\"Shape of the weights \", w.shape)\n",
        "print(\"Shape of the x-data  nxp\", xs.shape)\n",
        "print(\"Shape of the y-data  nx1\", ytrues.shape)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "**Attention this is a bit tricky!**\n",
        "Let\u0027s keep it easy and say that we want to evaluate at three data points. In that case we draw 3 values **from the same distribution**. Let\u0027s try it the obvious but wrong way first:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 87,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(\u003ctfp.distributions.Normal \u0027Normal/\u0027 batch_shape\u003d(3, 1) event_shape\u003d() dtype\u003dfloat32\u003e,\n",
              " \u003ctf.Tensor: id\u003d1380092, shape\u003d(3, 1), dtype\u003dfloat32, numpy\u003d\n",
              " array([[2.],\n",
              "        [3.],\n",
              "        [4.]], dtype\u003dfloat32)\u003e,\n",
              " array([[-1.4189385],\n",
              "        [-1.4189385],\n",
              "        [-1.4189385]], dtype\u003dfloat32))"
            ]
          },
          "execution_count": 87,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "d \u003d tfd.Normal(loc\u003dxs*w[0]+w[1], scale\u003d1)\n",
        "d, d.mean(), d.log_prob(ytrues).numpy()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "### Batch-Shape vs Event Shape\n",
        "\n",
        "\n",
        "TensorFlow Probability Distribution have two dimensions\n",
        "\n",
        "(batch shape, event shape)\n",
        "\n",
        "* Batch shape denotes a collection of Distributions with **distinct parameters**\n",
        "* Event shape denotes the shape of **samples from the same** Distribution.\n",
        "\n",
        "This result has a batch_shape of 3 and a event shape of 1. This is the absolute oposite of what we want. The batch shape of 3 corresponds to 3 independent distributions. But we want three samples of the same distribution. In that case we want 3 independent draws from the same distribution (i.i.d). We can assure that be the function `tfd.Independent` with the argument `reinterpreted_batch_ndims\u003d1`. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(\u003ctfp.distributions.Independent \u0027IndependentNormal/\u0027 batch_shape\u003d(3,) event_shape\u003d(1,) dtype\u003dfloat32\u003e,\n",
              " \u003ctf.Tensor: id\u003d1380125, shape\u003d(3, 1), dtype\u003dfloat32, numpy\u003d\n",
              " array([[2.],\n",
              "        [3.],\n",
              "        [4.]], dtype\u003dfloat32)\u003e,\n",
              " array([-1.4189385, -1.4189385, -1.4189385], dtype\u003dfloat32),\n",
              " \u003ctf.Tensor: id\u003d1380152, shape\u003d(), dtype\u003dfloat32, numpy\u003d-1.4189385\u003e,\n",
              " \u003ctf.Tensor: id\u003d1380165, shape\u003d(1,), dtype\u003dfloat32, numpy\u003darray([-3.2265239], dtype\u003dfloat32)\u003e)"
            ]
          },
          "execution_count": 88,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rv_a \u003d tfd.Normal(loc\u003d0., scale\u003d10.)\n",
        "d \u003d tfd.Independent(\n",
        "        tfd.Normal(loc\u003dxs*w[0]+w[1], scale\u003d1.0),\n",
        "    reinterpreted_batch_ndims\u003d1)\n",
        "d,d.mean(), d.log_prob(ytrues).numpy(), tf.reduce_mean(d.log_prob(ytrues), axis\u003d-1),rv_a.log_prob(w[0])\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "Now the event_shape is 3 corresponding to 3 draws from the same distribution. \n",
        "\n",
        "A usual pattern is to write a function which takes the weights, the data (here x and y) and computes the probabiliy \n",
        "\n",
        "$$\n",
        "    p(y|x,w) \n",
        "$$\n",
        "\n",
        "this probability is conditioned on but not on the weight. Hence it is called joined log prob."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 89,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "def joint_log_prob(x, y_true, w):\n",
        "    \n",
        "    rv_a \u003d tfd.Normal(loc\u003d0., scale\u003d1.) #This is the prior for the slope and\n",
        "    rv_b \u003d tfd.Normal(loc\u003d0., scale\u003d1.) #intercept.\n",
        "    \n",
        "    #y_prob \u003d tfd.Independent(tfd.MultivariateNormalDiag(loc\u003d[x*w[0],w[1]], scale_diag\u003d1.0 * tf.ones([len(w)])), reinterpreted_batch_ndims\u003d1)\n",
        "    y_prob \u003d tfd.Independent(tfd.Normal(loc\u003dx*w[0]+w[1], scale\u003d1.0), reinterpreted_batch_ndims\u003d1)\n",
        "    return (\n",
        "         tf.reduce_mean(\n",
        "             rv_a.log_prob(w[0])+\n",
        "             rv_b.log_prob(w[1])+\n",
        "             y_prob.log_prob(y_true), axis\u003d-1) \n",
        "    )"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(\u003ctf.Tensor: id\u003d1380187, shape\u003d(3, 1), dtype\u003dfloat32, numpy\u003d\n",
              " array([[2.],\n",
              "        [3.],\n",
              "        [4.]], dtype\u003dfloat32)\u003e,\n",
              " array([-1.4189385, -1.4189385, -1.4189385], dtype\u003dfloat32))"
            ]
          },
          "execution_count": 90,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y_prob \u003d tfd.Independent(tfd.Normal(loc\u003dxs*w[0] + w[1], scale\u003d1.0), reinterpreted_batch_ndims\u003d1)\n",
        "#y_prob \u003d tfd.Normal(loc\u003dxs*w[0] + w[1], scale\u003d1.0)\n",
        "y_prob.mean(), y_prob.log_prob(ytrues).numpy()#, tf.reduce_mean(y_prob.log_prob(ytrues), axis\u003d-1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "We wrap this in a function of a single variable."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# Create our unnormalized target density by currying x and y from the joint.\n",
        "def unnormalized_posterior(w):\n",
        "    #return joint_log_prob(w, xs, ytrues) #the simple smaller data set\n",
        "    return joint_log_prob(x, y.reshape([len(y),1]),w) "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "\u003ctf.Tensor: id\u003d1380262, shape\u003d(), dtype\u003dfloat32, numpy\u003d-14.904734\u003e"
            ]
          },
          "execution_count": 92,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "unnormalized_posterior(w)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "\u003ctf.Tensor: id\u003d1380324, shape\u003d(), dtype\u003dfloat32, numpy\u003d-14.904734\u003e"
            ]
          },
          "execution_count": 93,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "unnormalized_posterior_2 \u003d lambda *args: joint_log_prob(x, y.reshape([len(y),1]), *args)\n",
        "unnormalized_posterior_2(w)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "#### Doing the MCMC (Metropolis)\n",
        "\n",
        "We do a simple random walk mcmc."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 94,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "metropolis\u003dtfp.mcmc.RandomWalkMetropolis(\n",
        "    target_log_prob_fn\u003dunnormalized_posterior_2,\n",
        "    seed\u003d54)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.5/dist-packages/tensorflow_probability/python/mcmc/sample.py:335: UserWarning: Tracing all kernel results by default is deprecated. Set the `trace_fn` argument to None (the future default value) or an explicit callback that traces the values you are interested in.\n",
            "  warnings.warn(\"Tracing all kernel results by default is deprecated. Set \"\n"
          ]
        }
      ],
      "source": [
        "states, kernel_results \u003d tfp.mcmc.sample_chain(\n",
        "        num_results\u003d400,\n",
        "        num_burnin_steps\u003d5,\n",
        "        current_state \u003d w,\n",
        "        kernel\u003dmetropolis)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.5/dist-packages/tensorflow_probability/python/mcmc/sample.py:335: UserWarning: Tracing all kernel results by default is deprecated. Set the `trace_fn` argument to None (the future default value) or an explicit callback that traces the values you are interested in.\n",
            "  warnings.warn(\"Tracing all kernel results by default is deprecated. Set \"\n"
          ]
        }
      ],
      "source": [
        "@tf.function #Much faster, when compiling\n",
        "def run_chain():\n",
        "    states, kernel_results \u003d tfp.mcmc.sample_chain(\n",
        "        num_results\u003d20000,\n",
        "        num_burnin_steps\u003d5,\n",
        "        current_state \u003d w,\n",
        "        kernel\u003dmetropolis)\n",
        "    return(states, kernel_results)\n",
        "\n",
        "states, kernel_results \u003d run_chain()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 97,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[\u003cmatplotlib.lines.Line2D at 0x7f6a47b1e940\u003e]"
            ]
          },
          "execution_count": 97,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(states[200:,1])\n",
        "plt.plot(states[200:,0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1.6224012, 1.0043148, 10.941236)"
            ]
          },
          "execution_count": 98,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "sns.distplot(states[200:,0], norm_hist\u003dTrue, kde\u003dTrue)\n",
        "sns.distplot(states[200:,1], norm_hist\u003dTrue, kde\u003dTrue)\n",
        "a_mean \u003d np.mean(states[200:,0])\n",
        "b_mean \u003d np.mean(states[200:,1])\n",
        "a_mean, b_mean, np.mean(y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 99,
      "metadata": {
        "scrolled": false,
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[\u003cmatplotlib.lines.Line2D at 0x7f6a47a51f60\u003e]"
            ]
          },
          "execution_count": 99,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\u003d\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(x,y, marker\u003d\u0027.\u0027)\n",
        "plt.plot(x_test,a_mean*x_test+b_mean)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "### Critisism "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 107,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(TensorShape([1980, 1]), (100, 1))"
            ]
          },
          "execution_count": 107,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#TODO\n",
        "a_mc \u003d states[200::10,0] #Select every 10 data point due to correlation\n",
        "a_mc.shape\n",
        "b_mc \u003d states[200::10,0]\n",
        "b_mc.shape, x_test.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 160,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# Not sure if I have to add noise\n",
        "y_mc \u003d np.matmul(x_test, a_mc.numpy().transpose()) + b_mc.numpy().transpose() \n",
        "m_mc \u003d y_mc.mean(axis\u003d1)\n",
        "s_mc \u003d y_mc.std(axis\u003d1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 161,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[\u003cmatplotlib.lines.Line2D at 0x7f6a444d07b8\u003e]"
            ]
          },
          "execution_count": 161,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\u003d\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "m_var \u003d np.mean(mus,axis\u003d0)\n",
        "s_var \u003d np.std(mus, axis\u003d0)\n",
        "fig, axes \u003d plt.subplots(1, 1, sharex\u003d\u0027all\u0027)\n",
        "plt.scatter(x,y, marker\u003d\u0027.\u0027)\n",
        "plt.plot(x_test,m_var + 2*s_var, c\u003d\u0027g\u0027)\n",
        "plt.plot(x_test,m_var - 2*s_var, c\u003d\u0027g\u0027)\n",
        "plt.plot(x_test,m_var, c\u003d\u0027b\u0027)\n",
        "plt.title(\u0027Variation Method\u0027)\n",
        "fig, axes \u003d plt.subplots(1, 1, sharex\u003d\u0027all\u0027)\n",
        "plt.title(\u0027MCMC Method\u0027)\n",
        "plt.scatter(x,y, marker\u003d\u0027.\u0027)\n",
        "plt.plot(x_test,m_mc, c\u003d\u0027b\u0027)\n",
        "plt.plot(x_test,m_mc + 2*s_mc, c\u003d\u0027g\u0027)\n",
        "plt.plot(x_test,m_mc - 2*s_mc, c\u003d\u0027g\u0027)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "### Other Sampler: HMC\n",
        "\n",
        "Below is an examples of an other sampler, called Hamiltonian Monte Carlo (HMC). A HMC sampler uses gradient information to sample. It\u0027s not a random walk anymore and hence one can sample higher dimensional random variables."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 146,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# Create an HMC TransitionKernel\n",
        "hmc_kernel \u003d tfp.mcmc.HamiltonianMonteCarlo(\n",
        "  target_log_prob_fn\u003dunnormalized_posterior,\n",
        "  step_size\u003dnp.float32(.1),\n",
        "  num_leapfrog_steps\u003d2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 147,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [],
      "source": [
        "# We wrap sample_chain in tf.function, telling TF to precompile a reusable\n",
        "# computation graph, which will dramatically improve performance.\n",
        "@tf.function\n",
        "def run_chain(initial_state, num_results\u003d1000, num_burnin_steps\u003d500):\n",
        "  return tfp.mcmc.sample_chain(\n",
        "    num_results\u003dnum_results,\n",
        "    num_burnin_steps\u003dnum_burnin_steps,\n",
        "    current_state\u003dinitial_state,\n",
        "    kernel\u003dhmc_kernel,\n",
        "    trace_fn\u003dlambda current_state, kernel_results: kernel_results)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {}
      },
      "source": [
        "initial_state \u003d np.zeros(1 + 1)\n",
        "samples, kernel_results \u003d run_chain(initial_state)\n",
        "print(\"Acceptance rate:\", kernel_results.is_accepted.numpy().mean())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 148,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Acceptance rate: 0.962\n"
          ]
        }
      ],
      "source": [
        "initial_state \u003d np.ones(2, dtype\u003dnp.float32)\n",
        "samples, kernel_results \u003d run_chain(initial_state)\n",
        "print(\"Acceptance rate:\", kernel_results.is_accepted.numpy().mean())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 149,
      "metadata": {
        "pycharm": {}
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[\u003cmatplotlib.lines.Line2D at 0x7f6a567c1ba8\u003e]"
            ]
          },
          "execution_count": 149,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\u003d\n",
            "text/plain": [
              "\u003cFigure size 432x288 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(samples[:,1])\n",
        "plt.plot(samples[:,0])"
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "",
        "kind": "local"
      },
      "name": "Probabilistic_Layers_Regression_oliver.ipynb",
      "provenance": [
        {
          "file_id": "https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_Layers_Regression.ipynb",
          "timestamp": 1554239537358
        },
        {
          "file_id": "1KnuTjdi8udCLZDfe9hufjFg01FXDLYHQ",
          "timestamp": 1550986742534
        }
      ],
      "version": "0.3.2"
    },
    "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"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 1
}