7_5_bayesian_network_pc_algorithm.ipynb

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  "metadata": {
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "colab": {
      "name": "7_5_bayesian_network_pc_algorithm.ipynb",
      "provenance": [],
      "collapsed_sections": []
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aoxI3DOK9vm2",
        "colab_type": "text"
      },
      "source": [
        "# 7.5 PCアルゴリズムによるベイジアンネットワーク探索の実装\n",
        "\n",
        "本ファイルは、7.5節の実装です。\n",
        "\n",
        "5.3節で使用した人事研修の効果を拡張した模擬データを作成し、因果探索を実施します。"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2XdIDbdlejUk",
        "colab_type": "text"
      },
      "source": [
        "## プログラム実行前の設定など"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XZFKJwcu-_Oj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 乱数のシードを設定\n",
        "import random\n",
        "import numpy as np\n",
        "\n",
        "np.random.seed(1234)\n",
        "random.seed(1234)\n"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hx1idArc_F15",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 使用するパッケージ（ライブラリと関数）を定義\n",
        "# 標準正規分布の生成用\n",
        "from numpy.random import *\n",
        "\n",
        "# グラフの描画用\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# SciPy 平均0、分散1に正規化（標準化）関数\n",
        "import scipy.stats\n",
        "\n",
        "# シグモイド関数をimport\n",
        "from scipy.special import expit\n",
        "\n",
        "# その他\n",
        "import pandas as pd\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AWqP6yeQlI_t",
        "colab_type": "text"
      },
      "source": [
        "## データの作成"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DpnGB2KZ_L8x",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# データ数\n",
        "num_data = 2000\n",
        "\n",
        "# 部下育成への熱心さ\n",
        "x = np.random.uniform(low=-1, high=1, size=num_data)  # -1から1の一様乱数\n",
        "\n",
        "# 上司が「上司向け：部下とのキャリア面談のポイント研修」に参加したかどうか\n",
        "e_z = randn(num_data)  # ノイズの生成\n",
        "z_prob = expit(-5.0*x+5*e_z)\n",
        "Z = np.array([])\n",
        "\n",
        "# 上司が「上司向け：部下とのキャリア面談のポイント研修」に参加したかどうか\n",
        "for i in range(num_data):\n",
        "    Z_i = np.random.choice(2, size=1, p=[1-z_prob[i], z_prob[i]])[0]\n",
        "    Z = np.append(Z, Z_i)\n",
        "\n",
        "# 介入効果の非線形性：部下育成の熱心さxの値に応じて段階的に変化\n",
        "t = np.zeros(num_data)\n",
        "for i in range(num_data):\n",
        "    if x[i] < 0:\n",
        "        t[i] = 0.5\n",
        "    elif x[i] >= 0 and x[i] < 0.5:\n",
        "        t[i] = 0.7\n",
        "    elif x[i] >= 0.5:\n",
        "        t[i] = 1.0\n",
        "\n",
        "e_y = randn(num_data)\n",
        "Y = 2.0 + t*Z + 0.3*x + 0.1*e_y \n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RwfHdcKFzL8o",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 本章からの追加データを生成\n",
        "\n",
        "# Y2：部下当人のチームメンバへの満足度 1から5の5段階\n",
        "Y2 = np.random.choice([1.0, 2.0, 3.0, 4.0, 5.0],\n",
        "                      num_data, p=[0.1, 0.2, 0.3, 0.2, 0.2])\n",
        "\n",
        "# Y3：部下当人の仕事への満足度\n",
        "e_y3 = randn(num_data)\n",
        "Y3 = 4*Y + Y2 + e_y3\n",
        "\n",
        "# ※初版、第2版は20/7/24に変更\n",
        "# Y3 = 3*Y + Y2 + e_y3\n",
        "\n",
        "\n",
        "# Y4：部下当人の仕事のパフォーマンス\n",
        "e_y4 = randn(num_data)\n",
        "Y4 = 3*Y3 + 5 + 2*e_y4 \n"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BHcdUlW9koTa",
        "colab_type": "text"
      },
      "source": [
        "## データをまとめた表を作成し、可視化する"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1EMwdGIIIPrK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "outputId": "1376818e-1c8e-4c34-ad0a-3deaea136d4d"
      },
      "source": [
        "df = pd.DataFrame({'x': x,\n",
        "                   'Z': Z,\n",
        "                   't': t,\n",
        "                   'Y': Y,\n",
        "                   'Y2': Y2,\n",
        "                   'Y3': Y3,\n",
        "                   'Y4': Y4,\n",
        "                   })\n",
        "\n",
        "df.head()  # 先頭を表示\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>Z</th>\n",
              "      <th>t</th>\n",
              "      <th>Y</th>\n",
              "      <th>Y2</th>\n",
              "      <th>Y3</th>\n",
              "      <th>Y4</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.616961</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.286924</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.019469</td>\n",
              "      <td>37.187280</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.244218</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.7</td>\n",
              "      <td>2.864636</td>\n",
              "      <td>3.0</td>\n",
              "      <td>13.608595</td>\n",
              "      <td>45.742923</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.124545</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>2.198515</td>\n",
              "      <td>3.0</td>\n",
              "      <td>12.767678</td>\n",
              "      <td>45.076731</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.570717</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>3.230572</td>\n",
              "      <td>3.0</td>\n",
              "      <td>15.543099</td>\n",
              "      <td>53.400946</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.559952</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>2.459267</td>\n",
              "      <td>5.0</td>\n",
              "      <td>14.878006</td>\n",
              "      <td>48.211738</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          x    Z    t         Y   Y2         Y3         Y4\n",
              "0 -0.616961  1.0  0.5  2.286924  2.0  11.019469  37.187280\n",
              "1  0.244218  1.0  0.7  2.864636  3.0  13.608595  45.742923\n",
              "2 -0.124545  0.0  0.5  2.198515  3.0  12.767678  45.076731\n",
              "3  0.570717  1.0  1.0  3.230572  3.0  15.543099  53.400946\n",
              "4  0.559952  0.0  1.0  2.459267  5.0  14.878006  48.211738"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L6Tb2Hjk9vno",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "4a171cf2-0564-4d2c-fd66-70ac59e5ed92"
      },
      "source": [
        "# グラフで確認\n",
        "plt.scatter(x, Y)\n"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fa4e3a80710>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zpUlt74J0jq-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "72541116-b908-4f1a-f40b-298cedaf5c4f"
      },
      "source": [
        "# グラフで確認\n",
        "plt.scatter(x, Y2)\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fa4e3a61f28>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "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": "UlLscNMF0ndN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "3894d831-d8f8-42d1-d06a-b5dbb86c479f"
      },
      "source": [
        "# グラフで確認\n",
        "plt.scatter(x, Y3)\n"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fa4e34d8b00>"
            ]
          },
          "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": "y04PV60K0p25",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "f91320a6-d7e0-4ed5-ef4b-67184e6b8fe0"
      },
      "source": [
        "# グラフで確認\n",
        "plt.scatter(x, Y4)\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fa4e34c4b00>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "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": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "AeC7Uv29KsXC"
      },
      "source": [
        "## データをビンで区切る"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xp2P-IDT9vql",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "af9db08e-ff27-41a5-9d5a-f9823e14e63e"
      },
      "source": [
        "# ビン区切りの例\n",
        "# cutを使用すると閾値で区切れる\n",
        "# qcutを使用すると同じデータ数になるように区切る\n",
        "s_qcut, bins = pd.cut(df[\"Y\"], 5, labels=[1, 2, 3, 4, 5], retbins=True)\n",
        "\n",
        "print(s_qcut)\n",
        "print(\"=======\")\n",
        "print(bins)\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0       2\n",
            "1       4\n",
            "2       2\n",
            "3       5\n",
            "4       3\n",
            "       ..\n",
            "1995    2\n",
            "1996    2\n",
            "1997    2\n",
            "1998    2\n",
            "1999    2\n",
            "Name: Y, Length: 2000, dtype: category\n",
            "Categories (5, int64): [1 < 2 < 3 < 4 < 5]\n",
            "=======\n",
            "[1.532537   1.92223596 2.30999611 2.69775627 3.08551643 3.47327659]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xozAxa4I2kWo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "outputId": "51efaa04-7856-4dbd-8d5d-abcc086d5ad3"
      },
      "source": [
        "# データを区切る\n",
        "df_bin = df.copy()  # コピーしてビン区切りデータを入れる変数を作成\n",
        "del df_bin[\"t\"]  # 変数tは観測できないので削除\n",
        "\n",
        "# x：部下育成への熱心さ\n",
        "df_bin[\"x\"], x_bins = pd.cut(df[\"x\"], 5, labels=[1, 2, 3, 4, 5], retbins=True)\n",
        "\n",
        "# Z：上司が「上司向け：部下とのキャリア面談のポイント研修」に参加したかどうか\n",
        "# ※qcutではなく、cutで値に応じて分割\n",
        "df_bin[\"Z\"], z_bins = pd.cut(df[\"Z\"], 2, labels=[0, 1], retbins=True)\n",
        "\n",
        "# Y：部下の面談の満足度\n",
        "df_bin[\"Y\"], y_bins = pd.cut(df[\"Y\"], 5, labels=[1, 2, 3, 4, 5], retbins=True)\n",
        "\n",
        "# Y2：部下当人のチームメンバへの満足度 1から5の5段階\n",
        "# # ※qcutではなく、cutで値に応じて分割\n",
        "df_bin[\"Y2\"], y2_bins = pd.cut(\n",
        "    df[\"Y2\"], 5, labels=[1, 2, 3, 4, 5], retbins=True)\n",
        "\n",
        "# Y3：部下当人の仕事への満足度\n",
        "df_bin[\"Y3\"], y3_bins = pd.cut(\n",
        "    df[\"Y3\"], 5, labels=[1, 2, 3, 4, 5], retbins=True)\n",
        "\n",
        "# Y4：部下当人の仕事のパフォーマンス\n",
        "df_bin[\"Y4\"], y4_bins = pd.cut(\n",
        "    df[\"Y4\"], 5, labels=[1, 2, 3, 4, 5], retbins=True)\n",
        "\n",
        "# 確認\n",
        "df_bin.head()\n"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>Z</th>\n",
              "      <th>Y</th>\n",
              "      <th>Y2</th>\n",
              "      <th>Y3</th>\n",
              "      <th>Y4</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   x  Z  Y Y2 Y3 Y4\n",
              "0  1  1  2  2  2  2\n",
              "1  4  1  4  3  3  3\n",
              "2  3  0  2  3  3  3\n",
              "3  4  1  5  3  4  4\n",
              "4  4  0  3  5  4  3"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QD-T2c-VpUHq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#df_bin=df_bin.astype(int)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1TPIeXDg6QDG",
        "colab_type": "text"
      },
      "source": [
        "## PCアルゴリズムを実施"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4TM2J5kq6GOx",
        "colab_type": "text"
      },
      "source": [
        "## pgmpy（Python library for Probabilistic Graphical Models）によるPCアルゴリズム"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "edNNPSLY6u6d",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "65d931a8-7129-4638-e3e0-2786251fdf9b"
      },
      "source": [
        "!pip install pgmpy==0.1.9"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: pgmpy==0.1.9 in /usr/local/lib/python3.6/dist-packages (0.1.9)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wAeHIJiqOF-h",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "outputId": "4297c01b-064d-49cd-d06b-281fe1594e08"
      },
      "source": [
        "from pgmpy.estimators import ConstraintBasedEstimator\n",
        "\n",
        "est = ConstraintBasedEstimator(df_bin)\n",
        "\n",
        "# 0次の独立性の検定\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Z', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y2', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y3', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y4', method=\"chi_square\", tol=0.05))\n",
        "print(\"=====\")\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y2', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y3', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y4', method=\"chi_square\", tol=0.05))\n",
        "print(\"=====\")\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y2', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y3', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y4', method=\"chi_square\", tol=0.05))\n",
        "print(\"=====\")\n",
        "print(est.test_conditional_independence(\n",
        "    'Y2', 'Y3', method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y2', 'Y4', method=\"chi_square\", tol=0.05))\n",
        "print(\"=====\")\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y4', method=\"chi_square\", tol=0.05))\n",
        "print(\"=====\")\n"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "False\n",
            "True\n",
            "False\n",
            "False\n",
            "=====\n",
            "False\n",
            "True\n",
            "False\n",
            "False\n",
            "=====\n",
            "True\n",
            "False\n",
            "False\n",
            "=====\n",
            "False\n",
            "False\n",
            "=====\n",
            "False\n",
            "=====\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sJQ2_9LY8MQ8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "outputId": "f927dd06-728b-4188-e0dc-8a13d033adfc"
      },
      "source": [
        "# 1次の独立性の検定 変数x\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Z', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Z', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Z', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y', ['Z'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y3', ['Z'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y3', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y3', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y4', ['Z'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y4', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y4', ['Y3'], method=\"chi_square\", tol=0.05))\n"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "True\n",
            "True\n",
            "False\n",
            "True\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lo-4p3vBR6tH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "outputId": "a425fa64-758c-4927-c6b1-bfc46d59fe1a"
      },
      "source": [
        "# 1次の独立性の検定 変数Z\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'x', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'x', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'x', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y', ['x'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y3', ['x'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y3', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y3', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y4', ['x'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y4', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y4', ['Y3'], method=\"chi_square\", tol=0.05))\n"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "True\n",
            "False\n",
            "False\n",
            "True\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5ULve2thDTHu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "outputId": "eb1f3154-7f44-43c0-d19a-db4294f9c059"
      },
      "source": [
        "# 1次の独立性の検定 変数Y\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'x', ['Z'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'x', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'x', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Z', ['x'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Z', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Z', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y3', ['x'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y3', ['Z'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y3', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y4', ['x'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y4', ['Z'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y4', ['Y3'], method=\"chi_square\", tol=0.05))\n"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NP1Kr8BjS4Wf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "4a3d8d99-57e5-461a-edef-5dc8b2fe2a6d"
      },
      "source": [
        "# 1次の独立性の検定 変数Y2\n",
        "print(est.test_conditional_independence(\n",
        "    'Y2', 'Y3', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y2', 'Y4', ['Y3'], method=\"chi_square\", tol=0.05))\n"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "5qn5-JxwgJnE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 122
        },
        "outputId": "9f8a7deb-ac1e-4f7e-d7fa-1d218bb8a8a1"
      },
      "source": [
        "# 1次の独立性の検定 変数Y\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y', ['Y2'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y2', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y2', ['Y4'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y4', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y3', 'Y4', ['Y2'], method=\"chi_square\", tol=0.05))\n"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n",
            "False\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "msKigC5iYWH-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "0c679e2a-0cd9-474c-d051-669bedfd41de"
      },
      "source": [
        "# 2020年7月24日追記\n",
        "# 2次の独立性の検定 変数Y\n",
        "\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'x', ['Z', 'Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Z', ['x', 'Y3'], method=\"chi_square\", tol=0.05))\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y3', ['x', 'Z'], method=\"chi_square\", tol=0.05))\n"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "False\n",
            "False\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dFA5qoZ7Ldgg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "0ede5a3e-5b2d-4173-c999-916f2a2b3f8d"
      },
      "source": [
        "# オリエンテーション・フェーズ1での方向づけ\n",
        "# x-Y-Y3\n",
        "print(est.test_conditional_independence(\n",
        "    'x', 'Y3', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "# Z-Y-Y3\n",
        "print(est.test_conditional_independence(\n",
        "    'Z', 'Y3', ['Y'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "# Y-Y3-Y2\n",
        "print(est.test_conditional_independence(\n",
        "    'Y', 'Y2', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "# Y2-Y3-Y4\n",
        "print(est.test_conditional_independence(\n",
        "    'Y2', 'Y4', ['Y3'], method=\"chi_square\", tol=0.05))\n",
        "\n",
        "# Y -> Y3 <- Y2 だけ決まる\n"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "True\n",
            "True\n",
            "False\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kMW1M3YbMi3h",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 122
        },
        "outputId": "6dbc0dd8-2633-4bc9-aa43-1b29b5b4e915"
      },
      "source": [
        "# 最後上の三角形が決まらない\n",
        "# BICを求め、比較\n",
        "from pgmpy.models import BayesianModel\n",
        "from pgmpy.estimators import BicScore\n",
        "\n",
        "model = BayesianModel([('x', 'Z'), ('x', 'Y'), ('Z', 'Y'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])  \n",
        "print(BicScore(df_bin).score(model))\n",
        "\n",
        "model = BayesianModel([('x', 'Z'), ('x', 'Y'), ('Y', 'Z'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])  \n",
        "print(BicScore(df_bin).score(model))\n",
        "\n",
        "model = BayesianModel([('Z', 'x'), ('Z', 'Y'), ('x', 'Y'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])  \n",
        "print(BicScore(df_bin).score(model))\n",
        "\n",
        "model = BayesianModel([('Z', 'x'), ('Z', 'Y'), ('Y', 'x'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])  \n",
        "print(BicScore(df_bin).score(model))\n",
        "\n",
        "model = BayesianModel([('Y', 'x'), ('Y', 'Z'), ('x', 'Z'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])  \n",
        "print(BicScore(df_bin).score(model))\n",
        "\n",
        "model = BayesianModel([('Y', 'x'), ('Y', 'Z'), ('Z', 'x'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])  \n",
        "print(BicScore(df_bin).score(model))"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-11613.498344787251\n",
            "-11613.498344787251\n",
            "-11613.498344787251\n",
            "-11613.498344787251\n",
            "-11613.498344787251\n",
            "-11613.498344787251\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DP8gHiu7lBDi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 最後は限られたデータから無理に因果の方向性を決めようとせず、時間的に考えて、無難な方向性を当てはめる"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HWvE9F0nfWKv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "176822e3-3695-459a-cd7e-4c7406fe46c9"
      },
      "source": [
        "# 2020年7月24日追記\n",
        "# pgmpyでPCアルゴリズムの実行\n",
        "\n",
        "skel, seperating_sets = est.estimate_skeleton(significance_level=0.05)\n",
        "print(\"Undirected edges: \", skel.edges())\n",
        "\n",
        "pdag = est.skeleton_to_pdag(skel, seperating_sets)\n",
        "print(\"PDAG edges:       \", pdag.edges())\n",
        "\n",
        "model = est.pdag_to_dag(pdag)\n",
        "print(\"DAG edges:        \", model.edges())\n"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Undirected edges:  [('x', 'Z'), ('x', 'Y'), ('Z', 'Y'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')]\n",
            "PDAG edges:        [('x', 'Z'), ('x', 'Y'), ('Z', 'x'), ('Z', 'Y'), ('Y', 'x'), ('Y', 'Z'), ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4'), ('Y4', 'Y3')]\n",
            "DAG edges:         [('Z', 'x'), ('Y', 'Y3'), ('Y', 'x'), ('Y', 'Z'), ('Y2', 'Y3'), ('Y3', 'Y4')]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VQs6FwtelB2E",
        "colab_type": "text"
      },
      "source": [
        "## ベイジアンネットワークでの推論"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_OGwPSHbjOV1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 844
        },
        "outputId": "e05110e6-531d-45ab-e742-8ff52eb83bf8"
      },
      "source": [
        "from pgmpy.models import BayesianModel\n",
        "from pgmpy.inference import VariableElimination\n",
        "\n",
        "# モデルを構築\n",
        "model = BayesianModel([('x', 'Z'), ('x', 'Y'), ('Z', 'Y'),\n",
        "                       ('Y', 'Y3'), ('Y2', 'Y3'), ('Y3', 'Y4')])\n",
        "# モデルにデータを与える\n",
        "model.fit(df_bin)\n",
        "\n",
        "# 変数消去アルゴリズムで推論\n",
        "infer = VariableElimination(model)\n",
        "obserbed_data = {'Z': 0, 'Y3': 3}  # 観測できているデータの一例\n",
        "x_dist = infer.query(['x'], evidence=obserbed_data)\n",
        "print(x_dist)\n",
        "print(\"=====================\")\n",
        "obserbed_data = {'Z': 1, 'Y3': 3}  # 観測できているデータの一例\n",
        "x_dist = infer.query(['x'], evidence=obserbed_data)\n",
        "print(x_dist)\n",
        "print(\"=====================\")\n",
        "obserbed_data = {'Z': 1, 'Y3': 5}  # 観測できているデータの一例\n",
        "x_dist = infer.query(['x'], evidence=obserbed_data)\n",
        "print(x_dist)\n"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Finding Elimination Order: : 100%|██████████| 3/3 [00:00<00:00, 866.83it/s]\n",
            "Eliminating: Y4: 100%|██████████| 3/3 [00:00<00:00, 358.06it/s]\n",
            "Finding Elimination Order: : 100%|██████████| 3/3 [00:00<00:00, 628.23it/s]\n",
            "Eliminating: Y4: 100%|██████████| 3/3 [00:00<00:00, 516.39it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "+------+----------+\n",
            "| x    |   phi(x) |\n",
            "+======+==========+\n",
            "| x(1) |   0.0484 |\n",
            "+------+----------+\n",
            "| x(2) |   0.0915 |\n",
            "+------+----------+\n",
            "| x(3) |   0.1958 |\n",
            "+------+----------+\n",
            "| x(4) |   0.2735 |\n",
            "+------+----------+\n",
            "| x(5) |   0.3908 |\n",
            "+------+----------+\n",
            "=====================\n",
            "+------+----------+\n",
            "| x    |   phi(x) |\n",
            "+======+==========+\n",
            "| x(1) |   0.3587 |\n",
            "+------+----------+\n",
            "| x(2) |   0.2370 |\n",
            "+------+----------+\n",
            "| x(3) |   0.2413 |\n",
            "+------+----------+\n",
            "| x(4) |   0.1187 |\n",
            "+------+----------+\n",
            "| x(5) |   0.0444 |\n",
            "+------+----------+\n",
            "=====================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Finding Elimination Order: : 100%|██████████| 3/3 [00:00<00:00, 493.78it/s]\n",
            "Eliminating: Y4: 100%|██████████| 3/3 [00:00<00:00, 472.69it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "+------+----------+\n",
            "| x    |   phi(x) |\n",
            "+======+==========+\n",
            "| x(1) |   0.0070 |\n",
            "+------+----------+\n",
            "| x(2) |   0.0101 |\n",
            "+------+----------+\n",
            "| x(3) |   0.0521 |\n",
            "+------+----------+\n",
            "| x(4) |   0.2781 |\n",
            "+------+----------+\n",
            "| x(5) |   0.6527 |\n",
            "+------+----------+\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UNbNZ8DFuQNF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 以下はファイルをダウンロードしたい場合に使用\n",
        "\n",
        "# from google.colab import files\n",
        "# df_bin.to_csv(\"df_bin.csv\")\n",
        "# files.download('df_bin.csv')\n"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "MGNG7pzi8LI6"
      },
      "source": [
        "以上"
      ]
    }
  ]
}