JointDistribution.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "JointDistribution.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMCVzr8xMmrC7BUTuL3c869",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yamada-github-account/LearnBayesNN/blob/master/JointDistribution.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jQKmITk9lMEO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.dates as mdates\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "from tensorflow_probability import distributions as tfd\n",
        "\n",
        "%matplotlib inline"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D6NmdzRdCf-K",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        },
        "outputId": "5a94cc8c-22b5-40d5-de80-375e63afff22"
      },
      "source": [
        "# https://www.hellocybernetics.tech/entry/2019/10/13/220834\n",
        "\n",
        "# テストデータ生成\n",
        "def toy_data():\n",
        "    x = np.random.uniform(0, 5, 30)\n",
        "    y = 5 * x - 3 + np.random.normal(0, 2, 30)\n",
        "    return x, y\n",
        "x_np, y_np = toy_data()\n",
        "\n",
        "plt.plot(x_np, y_np, \"o\")\n",
        "\n",
        "\n",
        "# 変数を Tensor に\n",
        "x = tf.convert_to_tensor(\n",
        "    x_np,\n",
        "    dtype=tf.float32\n",
        ")\n",
        "\n",
        "y = tf.convert_to_tensor(\n",
        "    y_np,\n",
        "    dtype=tf.float32\n",
        ")\n",
        "\n",
        "# 同時分布をコルーティンで記述\n",
        "# TODO: うまく x を渡せずに、グローバル変数として参照してしまっている。要改善\n",
        "Root = tfd.JointDistributionCoroutine.Root\n",
        "def model():\n",
        "    a = yield Root(tfd.Normal(loc=0, scale=10.))\n",
        "    b = yield Root(tfd.Normal(loc=0, scale=10.))\n",
        "    y = yield tfd.Normal(loc=a * x + b, scale=tf.constant(2.0)) # 最後だけRootが不要？\n",
        "\n",
        "\n",
        "joint = tfd.JointDistributionCoroutine(model)\n",
        "\n",
        "joint.sample() # yield した順の a, b, y に対応する Tensor が入っている。 どうして、y だけ、こんなに数多くサンプリングされている？？？"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(<tf.Tensor: shape=(), dtype=float32, numpy=24.326206>,\n",
              " <tf.Tensor: shape=(), dtype=float32, numpy=-1.6130161>,\n",
              " <tf.Tensor: shape=(30,), dtype=float32, numpy=\n",
              " array([108.08908  ,  55.634426 ,   5.9656234, 107.91572  ,  22.117992 ,\n",
              "         18.21659  ,  92.68158  ,  53.118675 , 117.99356  ,  11.869347 ,\n",
              "        111.37376  ,  73.952736 ,  20.325335 , 111.87221  ,  67.547005 ,\n",
              "         64.81824  ,  94.39402  , 110.142105 ,  91.44482  ,   5.3255258,\n",
              "         78.146065 ,  39.434807 , 114.22096  , 115.102936 ,  50.97116  ,\n",
              "        119.26938  ,  72.486946 ,  85.14754  , 116.80966  ,  34.386707 ],\n",
              "       dtype=float32)>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rOUP9-_WJzJC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "034b1ccb-ab78-4aa7-f504-64d3f9813fec"
      },
      "source": [
        "plt.plot(x.numpy(), joint.sample()[-1].numpy(), \"o\")"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fce998115f8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAR1ElEQVR4nO3dYYxc1XnG8eepWcSUJB0oW8tehxqpyFFaCzYaoUSuotYEnBIEKyuiqdrIrZD8JUKgRE7sTy1VJRNZTeBTKwvauiotIHDWlEgYy7iqqFqTWdbUAceCRqAyGLy0XgXKKtjO2w97x9i7szt3ZufOnTv3/5Osnbkzu3M0Hx4O733POY4IAQCK55fyHgAAoDsEOAAUFAEOAAVFgANAQRHgAFBQl/Xzw6655ppYv359Pz8SAApvamrqvYgYXXi9rwG+fv161ev1fn4kABSe7TdbXaeEAgAFRYADQEER4ABQUAQ4ABQUAQ4ABdXXLhQAGCaT0w3tOXhSb8/OaW21oh1bNmhifKxvn0+AA0AXJqcb2rX/uObOnpckNWbntGv/cUnqW4gT4ADQhT0HT14I76a5s+e15+DJCwGe9QydAAeALrw9O7fs9X7M0LmJCQBdWFutLHt9uRl6rxDgANCFHVs2qDKy6pJrlZFV2rFlgyanG2q0maH3AiUUAOhCswyysMYt6UKppJWlZu7dIMABoEsT42OL6tmbHnh+UemkqTlD7xVKKADQQ8uVSHZv3djTLhQCHAB6aKkSyVi10vP+cAIcAHpouZubvUYNHABa6HYRzlI3N7NYnUmAA8ACK12E0+rmZhYooQDAAv1YhNMLBDgALNBumfygoIQCAAusrVZarqRcqsMkr21lmYEDwAKddJI06+WN2TmFPq6XT043Mh8nM3AAQ62b2XEnnSRptpXNCgEOYGitpJskbSdJnvVySigAhlaabpLJ6YY2PfC8rtv5Q2164PmOSx/ttpXNUqoAt121/aTtn9g+YfsLtq+2fcj2a8nPq7IeLAB0Iu2hCyupX/dz5eVCaWfgD0l6NiI+I+kGSSck7ZR0OCKul3Q4eQ4AA6OXhy4sNVOfGB/T7q0bNVatyJrf86TXm1YtpW0N3PavSPqipD+WpIj4SNJHtu+U9DvJ2/ZJ+hdJ38likADQjR1bNlxSA5cunR2nrV+3q6X3a+XlQmlm4NdJmpH0t7anbT9s+0pJqyPiVPKedyStbvXLtrfbrtuuz8zM9GbUAJBCu9lx2vr1oK7MTNOFcpmkz0m6JyKO2n5IC8olERG2o9UvR8ReSXslqVartXwPAGRludlxuxl606CuzEwzA39L0lsRcTR5/qTmA/1d22skKfl5OpshAkA20tav8+w0WU7bAI+IdyT9t+3mf5JulvSqpKclbUuubZN0IJMRAkDO8uw0WU7ahTz3SHrU9uWSfirpTzQf/k/YvlvSm5LuymaIAJCNtAt9+rnHdycc0b+ydK1Wi3q93rfPA4CLLVxW/+FH53Tmw7OL3jdWrejfdm7OYYSt2Z6KiNrC6yylB1AKrWbbS8n75mRaLKUHUAqtWgGXkvfNybQIcAClkHZWPQg3J9MiwAGUwlKz6mplJJdl8L1ADRxAKSy1aOfP7vjNwgT2QgQ4gFIY1FbAlSDAAWQir3Mil5PXplNZIcAB9NxKTsJBetzEBNBzg7p737AhwAH03KDu3jdsCHAAPTeou/cNGwIcQM8N6u59w4abmAB6bhhb9gYRAQ4gE8PWsjeIKKEAQEER4ABQUAQ4ABQUNXAAmRnE5fTDhAAHkAmW02ePAAdKpl+z4uWW0xPgvUGAAyXSz1kxy+mzx01MoET6uckUy+mzR4ADJdLPWTHL6bNHgAMl0s9Z8cT4mHZv3VjY8yaLgBo4UCJLnQuZ1ayY5fTZIsCBEunlJlP0eOePAAdKphezYnq8BwM1cAAd48i0wZBqBm77DUnvSzov6VxE1GxfLelxSeslvSHprog4k80wAQwSerwHQycz8N+NiBsjopY83ynpcERcL+lw8hxACdDjPRhWUkK5U9K+5PE+SRMrHw6AIqDHezCkDfCQ9JztKdvbk2urI+JU8vgdSatb/aLt7bbrtuszMzMrHC6AQUCP92BwRLR/kz0WEQ3bvybpkKR7JD0dEdWL3nMmIq5a7u/UarWo1+srHTMAlIrtqYvK1xekmoFHRCP5eVrSDyTdJOld22uSP75G0uneDRcA0E7bALd9pe1PNh9LulXSjyU9LWlb8rZtkg5kNUgAwGJp2ghXS/qB7eb7/zEinrX9I0lP2L5b0puS7spumACAhdoGeET8VNINLa7/j6SbsxgUAKA9VmICQEER4ABQUAQ4ABQUAQ4ABUWAA0BBEeAAUFAEOAAUFAEOAAXFkWrAgOGsSaRFgAN9kDaUOWsSnaCEAmSsGcqN2TmFPg7lyenGovdy1iQ6QYADGesklDlrEp0gwIGMdRLKnDWJThDgQMY6CWXOmkQnCHAgY61CWZL+7+fnFtXBOWsSnaALBchYM3zv/+dXdObDsxeuz86dbdlhMjE+RmAjFWbgQB9MjI/ply9fPF+iwwQrQYADfUKHCXqNAAf6hA4T9BoBDvQJHSboNW5iAn3SvDHJPifoFQIc6CM6TNBLBDjQAXYKxCAhwIGU2CkQg4abmEBK7BSIQUOAAynRx41BQ4ADKdHHjUFDgAMp0ceNQZM6wG2vsj1t+5nk+XW2j9p+3fbjti/PbphA/tgpEIOmky6UeyWdkPSp5Pl3JX0/Ih6z/deS7pb0Vz0eH5CZbloC6ePGIEk1A7e9TtJXJD2cPLekzZKeTN6yT9JEFgMEstDJOZXAoEpbQnlQ0rcl/SJ5/quSZiPiXPL8LUktpyW2t9uu267PzMysaLBAr9ASiGHQNsBt3y7pdERMdfMBEbE3ImoRURsdHe3mTwA9R0sghkGaGvgmSXfYvk3SFZqvgT8kqWr7smQWvk4S/++JwlhbrajRwaHCwCBqOwOPiF0RsS4i1kv6mqTnI+IPJR2R9NXkbdskHchslECP0RKIYbCSPvDvSPqm7dc1XxN/pDdDArJHSyCGgSOibx9Wq9WiXq/37fMAYBjYnoqI2sLrrMQEgIIiwAGgoAhwACgoAhwACooAB4CCIsABoKAIcAAoKAIcAAqKAAeAgiLAAaCgCHAAKCgCHAAKigAHgIIiwAGgoAhwACgoAhwACooAB4CCIsABoKAIcAAoqMvyHgDKbXK6oT0HT+rt2TmtrVa0Y8sGDhYGUiLAkZvJ6YZ27T+uubPnJUmN2Tnt2n9ckghxIAVKKMjNnoMnL4R309zZ89pz8GROIwKKhQBHbt6enevoOoBLEeDIzdpqpaPrAC5FgCM3O7ZsUGVk1SXXKiOrtGPLhpxGBBQLNzGRm+aNSrpQgO4Q4MjVxPgYgQ10iQBHIdAvDizWtgZu+wrbL9p+2fYrtu9Prl9n+6jt120/bvvy7IeLMmr2izdm5xT6uF98crqR99CAXKW5iflzSZsj4gZJN0r6su3PS/qupO9HxG9IOiPp7uyGiTJbql/8W0+8TIij1NoGeMz7IHk6kvwLSZslPZlc3ydpIpMRovSW6gs/H8FMHKWWqo3Q9irbxySdlnRI0n9Jmo2Ic8lb3pJEQRKZWK4vnJWbKLNUAR4R5yPiRknrJN0k6TNpP8D2dtt12/WZmZkuh4kya9UvfjFWbqKsOlrIExGzko5I+oKkqu1mF8s6SS3/PzYi9kZELSJqo6OjKxosymlifEy7t27UKrvl66zcRFml6UIZtV1NHlck3SLphOaD/KvJ27ZJOpDVIIGJ8TH95V03sHITuEiaPvA1kvbZXqX5wH8iIp6x/aqkx2z/haRpSY9kOE6AlZvAAo6Ivn1YrVaLer3et88DgGFgeyoiaguvs5kVABQUAQ4ABUWAA0BBsZnVkGHTJ6A8CPAhwiHBQLlQQhkiHBIMlAsBPkQ4JBgoF0ooQ2RttaJGi7BeuNScOjkwHJiBD5E0hwRzOAIwPAjwIdLc9GmsWpEljVUr2r114yWza+rkwPCghDJk2h0STJ0cGB7MwEtmqa1X2ZIVKB4CvGTS1MkBFAMllJJhS1ZgeBDgJdSuTg6gGCihAEBBEeAAUFAEOAAUFAEOAAVFgANAQRHgAFBQBDgAFBQBDgAFRYADQEER4ABQUAQ4ABQUAQ4ABUWAA0BBEeAAUFBtA9z2p20fsf2q7Vds35tcv9r2IduvJT+vyn64AICmNDPwc5K+FRGflfR5Sd+w/VlJOyUdjojrJR1OngMA+qRtgEfEqYh4KXn8vqQTksYk3SlpX/K2fZImshokAGCxjk7ksb1e0riko5JWR8Sp5KV3JK1e4ne2S9ouSddee2234xx4k9MNjikD0Fepb2La/oSkpyTdFxE/u/i1iAhJ0er3ImJvRNQiojY6OrqiwQ6qyemGdu0/rsbsnEJSY3ZOu/Yf1+R0I++hARhiqQLc9ojmw/vRiNifXH7X9prk9TWSTmczxMG35+BJzZ09f8m1ubPntefgyZxGBKAM0nShWNIjkk5ExPcueulpSduSx9skHej98Irh7dm5jq4DQC+kmYFvkvR1SZttH0v+3SbpAUm32H5N0peS56W0tlrp6DoA9ELbm5gR8YIkL/Hyzb0dTjHt2LJBu/Yfv6SMUhlZpR1bNuQ4KgDDrqMuFLTW7DahCwVAPw19gPervW9ifIzABtBXQx3gzfa+Zmmj2d4nibAFUHhDHeDLtfetNMBZuAMgb0O9G2FW7X2tFu7c9/gxjf/5cyzeAdA3Qx3gWbX3tZrZS9KZD8+yAhNA3wx1gO/YskGVkVWXXOtFe99yM3hWYALol6EO8InxMe3eulFj1Yosaaxa0e6tG1dcq243g2cFJoB+GOqbmFI27X2tFu5cjBWYAPphqGfgWWnO7KuVkUWvsQITQL8Q4F2aGB/TsT+9VQ/+/o09L9EAQBpDX0LJGiswAeSFGTgAFBQBDgAFRYADQEER4ABQUIW/icmmUgDKqtABznaxAMqs0CUUToMHUGaFDnBOgwdQZgNfQlmuxr22WlGjRVizFwmAMhjoGXirgxMu3m87q+1iAaAIBjrA29W4s9ouFgCKYKBLKGlq3OxFAqCsBnoGntWRaAAwDAY6wKlxA8DSBrqE0iyNsNISABYb6ACXqHEDwFLallBs/43t07Z/fNG1q20fsv1a8vOqbIcJAFgoTQ387yR9ecG1nZIOR8T1kg4nzwEAfdQ2wCPiXyX974LLd0ralzzeJ2mix+MCALTRbRfK6og4lTx+R9Lqpd5oe7vtuu36zMxMlx8HAFhoxW2EERGSYpnX90ZELSJqo6OjK/04AECi2y6Ud22viYhTttdIOp3ml6ampt6z/WaXn1lE10h6L+9BDAC+h3l8D3wHTZ1+D7/e6mK3Af60pG2SHkh+HkjzSxFRqim47XpE1PIeR974HubxPfAdNPXqe0jTRvhPkv5d0gbbb9m+W/PBfYvt1yR9KXkOAOijtjPwiPiDJV66ucdjAQB0YKD3QhkCe/MewIDge5jH98B30NST78HzTSQAgKJhBg4ABUWAA0BBEeAZaLUBWNnY/rTtI7Zftf2K7XvzHlMebF9h+0XbLyffw/15jylPtlfZnrb9TN5jyYvtN2wft33Mdn1Ff4saeO/Z/qKkDyT9fUT8Vt7jyUOywGtNRLxk+5OSpiRNRMSrOQ+tr2xb0pUR8YHtEUkvSLo3Iv4j56HlwvY3JdUkfSoibs97PHmw/YakWkSseEETM/AMLLEBWKlExKmIeCl5/L6kE5JKt7F7zPsgeTqS/CvlrMn2OklfkfRw3mMZFgQ4Mmd7vaRxSUfzHUk+krLBMc1vOXEoIkr5PUh6UNK3Jf0i74HkLCQ9Z3vK9vaV/CECHJmy/QlJT0m6LyJ+lvd48hAR5yPiRknrJN1ku3RlNdu3SzodEVN5j2UA/HZEfE7S70n6RlJy7QoBjswkNd+nJD0aEfvzHk/eImJW0hEtPiClDDZJuiOp/z4mabPtf8h3SPmIiEby87SkH0i6qdu/RYAjE8nNu0cknYiI7+U9nrzYHrVdTR5XJN0i6Sf5jqr/ImJXRKyLiPWSvibp+Yj4o5yH1Xe2r0xu6sv2lZJuldR1txoBnoElNgArm02Svq75mdax5N9teQ8qB2skHbH9n5J+pPkaeGlb6KDVkl6w/bKkFyX9MCKe7faP0UYIAAXFDBwACooAB4CCIsABoKAIcAAoKAIcAAqKAAeAgiLAAaCg/h/Ore5KxStCWQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VoCwH6n1iNI4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# TODO: うまく y を渡せずに、グローバル変数として参照してしまっている。要改善\n",
        "def unnormalized_log_posterior(a, b):\n",
        "    return tf.reduce_mean(joint.log_prob([a, b, y]))"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DVX8NIbgkPmy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 勾配ベースで計算をするメトロポリスヘイスティング法の発展版NUTS\n",
        "kernel = tfp.mcmc.NoUTurnSampler(\n",
        "      target_log_prob_fn=unnormalized_log_posterior,\n",
        "      step_size=0.1,\n",
        ")"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xZrpK1eCk0Vh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        },
        "outputId": "bc64aea2-5560-4946-b4fb-5e3fa0a67a82"
      },
      "source": [
        "# tf.function でデコレートしておかないと遅いらしい\n",
        "@tf.function()\n",
        "def run_chain():\n",
        "    init_state = list(joint.sample()[:-1]) # a, b\n",
        "    chains_states, kernels_results = tfp.mcmc.sample_chain(\n",
        "        num_results=1000,\n",
        "        num_burnin_steps=300,\n",
        "        current_state=init_state,\n",
        "        kernel=kernel\n",
        "    )\n",
        "    return chains_states, kernels_results\n",
        "\n",
        "# Sample from posterior distribution and get diagnostic\n",
        "chain_states, kernel_results = run_chain()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/tensorflow_probability/python/mcmc/sample.py:333: 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"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pnSP4KdIlBJY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "outputId": "740c58e7-87ba-456b-aa9c-2c22935735cb"
      },
      "source": [
        "a = chain_states[0]\n",
        "b = chain_states[1]\n",
        "\n",
        "# a\n",
        "plt.hist(a)\n",
        "plt.show()\n",
        "\n",
        "# b\n",
        "plt.hist(b)\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lObNbfhnwFuBb/ab6par6UFWtrapxpn9t/+eqGpkzpyRndG+U0013vJXpX5VHQlU9BTyZ5PXd0CXASLyZP8PVjNiUTOd7wIVJTu++ly9h+n2zkZHk1d3j2UzPt39uoa8xsn9mL8ltwMXAyiT7gY9U1dZ+U/3CRcC7gUe7eW2AD3d35Y6C1cC27kqFFwHbq2rkLjccYauAu6a/71kBfK6qvtRvpOP8KXBrN/XxHeC9Pec5RvdD8S3A+/vOMlNVPZzkC8AjwGHgG4zenap3JHkV8DPg2sW8YT6yl0JKkhbPaRlJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhpkuUtSg/4fMFze2RyTFS0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-pvV3fMblT7X",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "67a04a60-7118-4ce2-83ef-3a10ca74ea44"
      },
      "source": [
        "# EAP推定 (分布の平均値の利用)\n",
        "\n",
        "x_ = tf.convert_to_tensor(np.linspace(0,5,100), dtype=tf.float32)\n",
        "y_ = tf.reduce_mean(a) * x_ + tf.reduce_mean(b)\n",
        "\n",
        "plt.plot(x_,y_)\n",
        "plt.plot(x,y,\"o\")"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fce982c0a90>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UZ_VkyI8ns05",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "samples_ = tfd.Normal(loc=tf.expand_dims(a, axis=0) * tf.expand_dims(x_, axis=1) + tf.expand_dims(b, axis=0),scale=2.0).sample()"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1GULIIzDYjFD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_expected = tf.reduce_mean(samples_, axis=1)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NoWnvNAocGqz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "393f64db-f262-48fa-e7a1-843d7377dc20"
      },
      "source": [
        "plt.plot(x_, y_expected, \"r\")\n",
        "plt.plot(x_, samples_, \"b\", alpha=0.003 )\n",
        "plt.plot(x, y, \"og\")"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fce98257358>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UleBSbSCcLfb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 11,
      "outputs": []
    }
  ]
}