IDwithMarkovianInput.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNVPmf8a4Vm6fYiIswjFLGP"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4mJJYX-i10L_"
      },
      "outputs": [],
      "source": [
        "!pip install ylearn"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install networkx==2.8"
      ],
      "metadata": {
        "id": "MCiyOvIE2Mm9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install matplotlib==3.5"
      ],
      "metadata": {
        "id": "pLLhYt3m5acF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!pip list"
      ],
      "metadata": {
        "id": "a-_Jt0aXE3eH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from ylearn.causal_model.graph import CausalGraph\n",
        "from ylearn.causal_model import CausalModel\n",
        "# from sklearn.model_selection import train_test_split\n",
        "# from sklearn.linear_model import LogisticRegression\n",
        "# from sklearn.linear_model import LinearRegression"
      ],
      "metadata": {
        "id": "jwOcZJq02Psb"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def markov_to_semimarkov(G):\n",
        "\n",
        "  G_sm = nx.DiGraph()\n",
        "\n",
        "  # Rule 1 ------- Adding all observed nodes to the new graph\n",
        "  for node in G.nodes(data=True):\n",
        "    if node[1]['color'] == 'blue':\n",
        "      G_sm.add_node(node[0])\n",
        "  \n",
        "  # Rule 2 ------- Importing edges between two blue nodes\n",
        "  for edge in G.edges(data=True):\n",
        "    from_node = edge[0]\n",
        "    to_node = edge[1]\n",
        "    from_node_color = G.nodes[from_node]['color']\n",
        "    to_node_color = G.nodes[to_node]['color']\n",
        "    if from_node_color =='blue' and to_node_color =='blue':\n",
        "      G_sm.add_edge(edge[0], edge[1])\n",
        "\n",
        "  # Rule 3 ------- Adding edges for directed paths through grey nodes between two blue nodes\n",
        "  grey_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'grey']  \n",
        "  blue_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'blue']\n",
        "\n",
        "  for source in blue_nodes:\n",
        "    for sink in blue_nodes:\n",
        "      if source == sink or G.has_edge(source, sink):\n",
        "        continue\n",
        "      for path in nx.all_simple_paths(G, source=source, target=sink):\n",
        "        counter = 0\n",
        "        for between_node in path:\n",
        "          if between_node in blue_nodes:\n",
        "            counter += 1\n",
        "        if counter == 2:\n",
        "          G_sm.add_edge(source, sink)\n",
        "          break\n",
        "    \n",
        "  # Rule 4 ------- Extracting the hidden confounders\n",
        "  confounding_list = []\n",
        "\n",
        "  for source in grey_nodes:\n",
        "    potential_confounding = []\n",
        "    for sink in blue_nodes:\n",
        "      for path in nx.all_simple_paths(G, source=source, target=sink):\n",
        "        red_flag = 0\n",
        "        for between_node in path:\n",
        "          if between_node in blue_nodes and between_node != sink:\n",
        "            red_flag = 1\n",
        "            break\n",
        "        if red_flag == 0:\n",
        "          potential_confounding.append(sink)\n",
        "          break\n",
        "    if len(potential_confounding) > 1:\n",
        "      confounding_list.append(potential_confounding)\n",
        "    \n",
        "  # we construct a graph for confounding arcs\n",
        "  G_confounded = nx.Graph()\n",
        "  for item in confounding_list:\n",
        "    for i in range(len(item)):\n",
        "        for j in range(i + 1 , len(item)):\n",
        "          G_confounded.add_edge(item[i], item[j])\n",
        "  # nx.draw(G_confounded, with_labels=True, font_weight='bold', node_size=500)\n",
        "\n",
        "  return G_sm, list(G_confounded.edges())"
      ],
      "metadata": {
        "id": "yib1AxJ72pwG"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating a graph\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_nodes_from([\n",
        "    ('V5', {\"color\": \"grey\"}),\n",
        "    ('V4', {\"color\": \"grey\"}),\n",
        "    ('V3', {\"color\": \"grey\"}),\n",
        "    ('V2', {\"color\": \"blue\"}),\n",
        "    ('V1', {\"color\": \"blue\"}),\n",
        "    ('D', {\"color\": \"blue\"}),\n",
        "])\n",
        "G.add_edge('V5', 'D')\n",
        "G.add_edge('V3', 'V4')\n",
        "G.add_edge('V4', 'V2')\n",
        "G.add_edge('V3', 'V1')\n",
        "G.add_edge('V2', 'V1')\n",
        "G.add_edge('V2', 'D')\n",
        "G.add_edge('V1', 'D')\n",
        "\n",
        "grey_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'grey']\n",
        "\n",
        "nx.draw(G, with_labels=True, font_weight='bold', node_size=1000, node_color = [x[1] for x in G.nodes('color')])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "Fp19Gzyr2xVv",
        "outputId": "5b7ba7b6-e9d5-4a40-fd72-8f0965821422"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "final_graph, confounded_vars = markov_to_semimarkov(G)\n",
        "nx.draw(final_graph, with_labels=True, font_weight='bold', node_size=1000, node_color = 'skyblue')\n",
        "print(confounded_vars)\n",
        "print(grey_nodes)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 552
        },
        "id": "vf32Mk5g6-B7",
        "outputId": "d8e058b0-00cb-48f4-f9d3-6289021fd766"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[('V2', 'V1')]\n",
            "['V5', 'V4', 'V3']\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# function to compute the power set \n",
        "\n",
        "from itertools import chain, combinations\n",
        "\n",
        "def powerset(iterable):\n",
        "    \"powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)\"\n",
        "    s = list(iterable)\n",
        "    return list(chain.from_iterable(combinations(s, r) for r in range(1, len(s)+1)))\n",
        "\n",
        "output = powerset(['V1', 'V2'])\n",
        "print(list(output))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zst8uxcw-vxL",
        "outputId": "2ca32765-bda4-4d4b-a4d5-2166538869e7"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[('V1',), ('V2',), ('V1', 'V2')]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# function\n",
        "\n",
        "# INPUT: Markovian graph (including observed(blue)/unobserved(grey)), Targer, Intervention (node names)\n",
        "# OUTPUT: True/False (for the identifiability), [] a set of all possible adjustment sets\n",
        "\n",
        "def ID_with_markov(G, T, I):\n",
        "\n",
        "  grey_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'grey']\n",
        "  if T in grey_nodes:\n",
        "    print('The target variable (T) cannot be unobserved.')\n",
        "    return False\n",
        "  if I in grey_nodes:\n",
        "    print('The intervention variable (I) cannot be unobserved.')\n",
        "    return False\n",
        "\n",
        "  final_graph, confounded_vars = markov_to_semimarkov(G)\n",
        "  causation = nx.to_dict_of_lists(final_graph.reverse(copy=True))\n",
        "  arcs = confounded_vars\n",
        "  cg = CausalGraph(causation, latent_confounding_arcs=arcs)\n",
        "  cm = CausalModel(cg)\n",
        "\n",
        "  try:\n",
        "    p = cm.id({T}, {I})\n",
        "  except:\n",
        "    print('Based on the current setting the query is not identifiable.')\n",
        "    power_set = powerset(grey_nodes)\n",
        "    adj_sets = []\n",
        "\n",
        "    for grey_set in power_set:\n",
        "      H = G.copy()\n",
        "\n",
        "      grey_list = list(grey_set)\n",
        "      for grey_node in grey_list:\n",
        "        nx.set_node_attributes(H, {grey_node: \"blue\"}, name=\"color\")\n",
        "\n",
        "      final_graph, confounded_vars = markov_to_semimarkov(H)\n",
        "      causation = nx.to_dict_of_lists(final_graph.reverse(copy=True))\n",
        "      arcs = confounded_vars\n",
        "      cg = CausalGraph(causation, latent_confounding_arcs=arcs)\n",
        "      cm = CausalModel(cg)\n",
        "\n",
        "      try:\n",
        "        p = cm.id({T}, {I})\n",
        "      except:\n",
        "        print(\"The query is still not identifiable with \" + str(grey_list) + \" being observed.\")\n",
        "      else:\n",
        "        print(\"The query becomes identifiable if \" + str(grey_list) + \" are observed.\")\n",
        "        adj_sets.append(grey_list)\n",
        "        # p.show_latex_expression()\n",
        "\n",
        "    return False, adj_sets\n",
        "  else:\n",
        "    print(\"Based on the current setting the query is already identifiable.\")\n",
        "    # p.show_latex_expression()\n",
        "    return True, []\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "wMpOhLYA8b4H"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(ID_with_markov(G, 'D', 'V2'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OFSsD3WB5HjW",
        "outputId": "6f25050a-7546-4780-ea82-e4a9bbb03331"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Based on the current setting the query is not identifiable.\n",
            "The query is still not identifiable with ['V5'] being observed.\n",
            "The query becomes identifiable if ['V4'] are observed.\n",
            "The query becomes identifiable if ['V3'] are observed.\n",
            "The query becomes identifiable if ['V5', 'V4'] are observed.\n",
            "The query becomes identifiable if ['V5', 'V3'] are observed.\n",
            "The query becomes identifiable if ['V4', 'V3'] are observed.\n",
            "The query becomes identifiable if ['V5', 'V4', 'V3'] are observed.\n",
            "(False, [['V4'], ['V3'], ['V5', 'V4'], ['V5', 'V3'], ['V4', 'V3'], ['V5', 'V4', 'V3']])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Another Example:\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_nodes_from([\n",
        "    ('V5', {\"color\": \"blue\"}),\n",
        "    ('V4', {\"color\": \"grey\"}),\n",
        "    ('V3', {\"color\": \"grey\"}),\n",
        "    ('V2', {\"color\": \"blue\"}),\n",
        "    ('V1', {\"color\": \"grey\"}),\n",
        "])\n",
        "G.add_edge('V2', 'V3')\n",
        "G.add_edge('V3', 'V4')\n",
        "G.add_edge('V4', 'V5')\n",
        "G.add_edge('V1', 'V5')\n",
        "G.add_edge('V1', 'V2')\n",
        "\n",
        "grey_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'grey']\n",
        "\n",
        "nx.draw(G, with_labels=True, font_weight='bold', node_size=1000, node_color = [x[1] for x in G.nodes('color')])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "2rNNH-Kk0mHH",
        "outputId": "5c82a498-b776-4b64-8aff-739406ad0e08"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(ID_with_markov(G, 'V5', 'V2'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EHsXREig1BqX",
        "outputId": "e13f1ee4-c7b6-426d-d4e3-24c9044c66b5"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Based on the current setting the query is not identifiable.\n",
            "The query becomes identifiable if ['V4'] are observed.\n",
            "The query becomes identifiable if ['V3'] are observed.\n",
            "The query becomes identifiable if ['V1'] are observed.\n",
            "The query becomes identifiable if ['V4', 'V3'] are observed.\n",
            "The query becomes identifiable if ['V4', 'V1'] are observed.\n",
            "The query becomes identifiable if ['V3', 'V1'] are observed.\n",
            "The query becomes identifiable if ['V4', 'V3', 'V1'] are observed.\n",
            "(False, [['V4'], ['V3'], ['V1'], ['V4', 'V3'], ['V4', 'V1'], ['V3', 'V1'], ['V4', 'V3', 'V1']])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Another Example:\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_nodes_from([\n",
        "    ('V5', {\"color\": \"grey\"}),\n",
        "    ('V4', {\"color\": \"grey\"}),\n",
        "    ('V3', {\"color\": \"blue\"}),\n",
        "    ('V2', {\"color\": \"blue\"}),\n",
        "    ('V1', {\"color\": \"grey\"}),\n",
        "])\n",
        "G.add_edge('V5', 'V2')\n",
        "G.add_edge('V5', 'V3')\n",
        "G.add_edge('V4', 'V3')\n",
        "G.add_edge('V2', 'V4')\n",
        "G.add_edge('V1', 'V3')\n",
        "G.add_edge('V1', 'V2')\n",
        "\n",
        "grey_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'grey']\n",
        "\n",
        "nx.draw(G, with_labels=True, font_weight='bold', node_size=1000, node_color = [x[1] for x in G.nodes('color')])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "QdmdUhnJ2oAm",
        "outputId": "2f2063b1-717a-4809-d50b-7ec0dd3ca370"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(ID_with_markov(G, 'V3', 'V2'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0ZsOsyKF3Cgw",
        "outputId": "cf380294-69ec-427f-a5df-727cab88df7b"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Based on the current setting the query is not identifiable.\n",
            "The query is still not identifiable with ['V5'] being observed.\n",
            "The query becomes identifiable if ['V4'] are observed.\n",
            "The query is still not identifiable with ['V1'] being observed.\n",
            "The query becomes identifiable if ['V5', 'V4'] are observed.\n",
            "The query becomes identifiable if ['V5', 'V1'] are observed.\n",
            "The query becomes identifiable if ['V4', 'V1'] are observed.\n",
            "The query becomes identifiable if ['V5', 'V4', 'V1'] are observed.\n",
            "(False, [['V4'], ['V5', 'V4'], ['V5', 'V1'], ['V4', 'V1'], ['V5', 'V4', 'V1']])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Hosipital Example\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_nodes_from([\n",
        "    ('Age', {\"color\": \"blue\"}),\n",
        "    ('Triage', {\"color\": \"grey\"}),\n",
        "    ('Arrival', {\"color\": \"blue\"}),\n",
        "    ('Consultant', {\"color\": \"blue\"}),\n",
        "])\n",
        "G.add_edge('Age', 'Consultant')\n",
        "G.add_edge('Triage', 'Consultant')\n",
        "G.add_edge('Arrival', 'Consultant')\n",
        "G.add_edge('Age', 'Triage')\n",
        "G.add_edge('Arrival', 'Triage')\n",
        "\n",
        "grey_nodes = [n for n,v in G.nodes(data=True) if v['color'] == 'grey']\n",
        "\n",
        "nx.draw(G, with_labels=True, font_weight='bold', node_size=1000, node_color = [x[1] for x in G.nodes('color')])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "uI6ZBIIxGxT-",
        "outputId": "e1382ecd-092c-4b93-cc77-db8e739fc50e"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(ID_with_markov(G, 'Consultant', 'Arrival'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4bvTKWgrHtWp",
        "outputId": "50b84c1e-e28b-4500-95db-ef8b1009d1c1"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Based on the current setting the query is already identifiable.\n",
            "(True, [])\n"
          ]
        }
      ]
    }
  ]
}