Simulating_practical_reasoning.ipynb

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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Simulations from model only implementing Bayes rule and Bayesian practical reasoner model\n",
        "\n",
        "email any Qs to hunter @ priniski at u c l a dot e d u\n"
      ],
      "metadata": {
        "id": "LNQPkp6lT60G"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WT2GdnKSWx9f",
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          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d546306b-8d93-454b-eddc-830ff4a7bc22"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ],
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "cd /content/drive/MyDrive/Motivated Decisions /BDT Model"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tJTetAVsSIkR",
        "outputId": "34a73237-01e3-4cbd-b133-3708707c7b57"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/content/drive/MyDrive/Motivated Decisions /BDT Model\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "cd ../"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HOLA9lqqQIMZ",
        "outputId": "222b8705-990f-4de4-fc4d-7cf439f708d5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/content/drive/MyDrive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "random.seed(420)"
      ],
      "metadata": {
        "id": "rtNMIevjZw6Q"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import scipy\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "from random import randrange\n",
        "from random import choice\n",
        "\n",
        "from scipy.stats import beta, bernoulli\n",
        "\n",
        "\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import seaborn as sns\n",
        "sns.set_theme(style = 'white')"
      ],
      "metadata": {
        "id": "iqNxYNLJSgkw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#we say there is 6 max evidence right (plus 1 for python indexing)\n",
        "MAX_EVIDENCE = 6 ; "
      ],
      "metadata": {
        "id": "ZNyPsBwwn0Ys"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "###########################\n",
        "#PRACTICAL REASONING MODEL#\n",
        "###########################\n",
        "\n",
        "#base = beta-bernoulli, expected value calculation = BDT model. \n",
        "POINTS_OTHER = 2; POINTS_BONUS = 3;\n",
        "N = 4200; samples = 10; #how many trials to run, how many evidence reps to sample\n",
        "\n",
        "#map evidence count to a certainty representation\n",
        "#uniform\n",
        "a = 1; b = 1;\n",
        "\n",
        "#some lists for plotting, to check things check out\n",
        "ev_worlds = []; \n",
        "\n",
        "base_creds = []; base_cred_avgs = []; #the avg will be used for the sampled representation outputs \n",
        "EV_Os = []; EV_Bs = []; EV_samp_Os = []; EV_samp_Bs = [];\n",
        "\n",
        "base_outs = []; base_samp_outs = [];\n",
        "\n",
        "#generate N samples, try varying utility, and see how motivation changes as a function of it. that's a good fig\n",
        "for i in range(N):\n",
        "\n",
        "  #sample a value which will serve as the world state, the true number of facts for bonus\n",
        "  ev_world = np.random.choice(MAX_EVIDENCE + 1)\n",
        "  ev_worlds.append(ev_world)\n",
        "\n",
        "  base_cred = beta.rvs(a + ev_world, b + (MAX_EVIDENCE - ev_world), size = 1)[0]\n",
        "  base_creds.append(base_cred)\n",
        "\n",
        "  #averaged samples\n",
        "  base_cred_avg = np.mean(beta.rvs(a + ev_world, b + (MAX_EVIDENCE - ev_world), size = samples))\n",
        "  base_cred_avgs.append(base_cred_avg)\n",
        "\n",
        "  #These EV variables are the second order beliefs (credences)\n",
        "  EV_O = (1 - base_cred) * POINTS_OTHER;\n",
        "  EV_B = base_cred * POINTS_BONUS;\n",
        "\n",
        "  #will compare against a multiple samples implementation\n",
        "  EV_samp_O = (1 - base_cred_avg) * POINTS_OTHER;\n",
        "  EV_samp_B = base_cred_avg * POINTS_BONUS;\n",
        "\n",
        "  EV_Os.append(EV_O); EV_Bs.append(EV_B);\n",
        "  EV_samp_Os.append(EV_samp_O); EV_samp_Bs.append(EV_samp_B);\n",
        "\n",
        "  #decision output\n",
        "  base_out = np.argmax([EV_O, EV_B])\n",
        "  base_outs.append(base_out)\n",
        "\n",
        "  base_samp_out = np.argmax([EV_samp_O, EV_samp_B])\n",
        "  base_samp_outs.append(base_samp_out)"
      ],
      "metadata": {
        "id": "e66epPRUS1nL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#make into a dataframe\n",
        "prac_df = pd.DataFrame({'ev_world': ev_worlds,\n",
        "                         'base_cred':base_creds,\n",
        "                         'base_cred_avgs': base_cred_avgs,\n",
        "                         'EV_O': EV_Os,\n",
        "                         'EV_B': EV_Bs,\n",
        "                         'EV_samp_O': EV_samp_Os,\n",
        "                         'EV_samp_B': EV_samp_Bs,\n",
        "                         'base_out':base_outs,\n",
        "                         'base_samp_out':base_samp_outs})\n",
        "\n",
        "print(prac_df['base_cred'].mean(), prac_df['base_cred'].var())\n",
        "prac_df.head()"
      ],
      "metadata": {
        "id": "gv2C4omlS-kU",
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          "height": 225
        },
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      "execution_count": null,
      "outputs": [
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          "text": [
            "0.5054224193137001 0.08329598052726238\n"
          ]
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              "   ev_world  base_cred  base_cred_avgs      EV_O      EV_B  EV_samp_O  \\\n",
              "0         4   0.795789        0.656558  0.408422  2.387367   0.686883   \n",
              "1         1   0.436731        0.287993  1.126538  1.310193   1.424013   \n",
              "2         2   0.166757        0.345560  1.666485  0.500272   1.308880   \n",
              "3         6   0.999204        0.899633  0.001591  2.997613   0.200735   \n",
              "4         1   0.289545        0.268013  1.420910  0.868635   1.463975   \n",
              "\n",
              "   EV_samp_B  base_out  base_samp_out  \n",
              "0   1.969675         1              1  \n",
              "1   0.863980         1              0  \n",
              "2   1.036679         0              0  \n",
              "3   2.698898         1              1  \n",
              "4   0.804038         0              0  "
            ],
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    {
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      "source": [
        "prac_df.groupby('ev_world')['base_out'].mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IK88G8oK1xO7",
        "outputId": "d8b2570f-f678-428a-ce75-662fb5fa0d45"
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "ev_world\n",
              "0    0.040853\n",
              "1    0.128664\n",
              "2    0.457990\n",
              "3    0.721582\n",
              "4    0.906143\n",
              "5    0.981818\n",
              "6    1.000000\n",
              "Name: base_out, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "##########################\n",
        "#BAYESIAN REASONING MODEL#\n",
        "##########################\n",
        "\n",
        "#base = beta-bernoulli, expected value calculation = BDT model. \n",
        "POINTS_OTHER = 1; POINTS_BONUS = 1;\n",
        "N = 4200; samples = 10; #how many trials to run, how many evidence reps to sample\n",
        "\n",
        "#map evidence count to a certainty representation\n",
        "#uniform\n",
        "a = 1; b = 1;\n",
        "\n",
        "#some lists for plotting, to check things check out\n",
        "ev_worlds = []; \n",
        "\n",
        "base_creds = []; base_cred_avgs = []; #the avg will be used for the sampled representation outputs \n",
        "EV_Os = []; EV_Bs = []; EV_samp_Os = []; EV_samp_Bs = [];\n",
        "\n",
        "base_outs = []; base_samp_outs = [];\n",
        "\n",
        "#generate N samples, try varying utility, and see how motivation changes as a function of it. that's a good fig\n",
        "for i in range(N):\n",
        "\n",
        "  #sample a value which will serve as the world state, the true number of facts for bonus\n",
        "  ev_world = np.random.choice(MAX_EVIDENCE + 1)\n",
        "  ev_worlds.append(ev_world)\n",
        "\n",
        "  base_cred = beta.rvs(a + ev_world, b + (MAX_EVIDENCE - ev_world), size = 1)[0]\n",
        "  base_creds.append(base_cred)\n",
        "\n",
        "  #averaged samples\n",
        "  base_cred_avg = np.mean(beta.rvs(a + ev_world, b + (MAX_EVIDENCE - ev_world), size = samples))\n",
        "  base_cred_avgs.append(base_cred_avg)\n",
        "\n",
        "  #These EV variables are the second order beliefs (credences)\n",
        "  EV_O = (1 - base_cred) * POINTS_OTHER;\n",
        "  EV_B = base_cred * POINTS_BONUS;\n",
        "\n",
        "  #will compare against a multiple samples implementation\n",
        "  EV_samp_O = (1 - base_cred_avg) * POINTS_OTHER;\n",
        "  EV_samp_B = base_cred_avg * POINTS_BONUS;\n",
        "\n",
        "  EV_Os.append(EV_O); EV_Bs.append(EV_B);\n",
        "  EV_samp_Os.append(EV_samp_O); EV_samp_Bs.append(EV_samp_B);\n",
        "\n",
        "  #decision output\n",
        "  base_out = np.argmax([EV_O, EV_B])\n",
        "  base_outs.append(base_out)\n",
        "\n",
        "  base_samp_out = np.argmax([EV_samp_O, EV_samp_B])\n",
        "  base_samp_outs.append(base_samp_out)"
      ],
      "metadata": {
        "id": "L00YFz0R-V_O"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#make into a dataframe\n",
        "bayes_df = pd.DataFrame({'ev_world': ev_worlds,\n",
        "                         'base_cred':base_creds,\n",
        "                         'base_cred_avgs': base_cred_avgs,\n",
        "                         'EV_O': EV_Os,\n",
        "                         'EV_B': EV_Bs,\n",
        "                         'EV_samp_O': EV_samp_Os,\n",
        "                         'EV_samp_B': EV_samp_Bs,\n",
        "                         'base_out':base_outs,\n",
        "                         'base_samp_out':base_samp_outs})\n",
        "\n",
        "print(bayes_df['base_cred'].mean(), bayes_df['base_cred'].var())\n",
        "bayes_df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        },
        "id": "z71g72_cQBRo",
        "outputId": "adf55cb7-e20b-4d42-bc0b-3955f9f31152"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.4968091579264406 0.0850378641184908\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   ev_world  base_cred  base_cred_avgs      EV_O      EV_B  EV_samp_O  \\\n",
              "0         2   0.285358        0.363114  0.714642  0.285358   0.636886   \n",
              "1         0   0.040960        0.122669  0.959040  0.040960   0.877331   \n",
              "2         2   0.782139        0.341097  0.217861  0.782139   0.658903   \n",
              "3         2   0.749555        0.405603  0.250445  0.749555   0.594397   \n",
              "4         2   0.175179        0.354982  0.824821  0.175179   0.645018   \n",
              "\n",
              "   EV_samp_B  base_out  base_samp_out  \n",
              "0   0.363114         0              0  \n",
              "1   0.122669         0              0  \n",
              "2   0.341097         1              0  \n",
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              "      <th>EV_O</th>\n",
              "      <th>EV_B</th>\n",
              "      <th>EV_samp_O</th>\n",
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              "      <th>base_out</th>\n",
              "      <th>base_samp_out</th>\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "bayes_df.groupby('ev_world')['base_out'].mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S2SxEsui2pnr",
        "outputId": "6d0474b7-6988-47cc-db9c-7a94e4a03a44"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "ev_world\n",
              "0    0.006633\n",
              "1    0.063444\n",
              "2    0.210702\n",
              "3    0.523478\n",
              "4    0.764605\n",
              "5    0.937063\n",
              "6    0.995066\n",
              "Name: base_out, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#https://coolors.co/9cfffa-acf39d-b0c592-a97c73-af3e4d\n",
        "ax = sns.pointplot(x=\"ev_world\", y=\"base_out\", data=prac_df, color = '#011638', label = 'prac')\n",
        "ax.axhline(.5, ls='--')\n",
        "ax = sns.pointplot(x=\"ev_world\", y=\"base_out\", data=bayes_df, color = '#CDCDCD', label = 'bayes')\n",
        "\n",
        "\n",
        "#ax = sns.pointplot(x=\"ev_world\", y=\"base_out\", data=base_df_1_3, color = '#9933ff', label = 'base_df_1_3')\n",
        "#ax = sns.pointplot(x=\"ev_world\", y=\"base_out\", data=base_df_1_1, color = 'black', label = 'base_df_1_1')\n",
        "#decisions\n",
        "#ax = sns.pointplot(x=\"ev_world\", y=\"base_out\", data=base_df, color = '#AF3E4D', label = 'BDT')\n",
        "#ax = sns.pointplot(x=\"ev_world\", y=\"MR_out\", data=MR_df, color = '#ACF39D', label = 'MR')\n",
        "\n",
        "plt.xlabel(\"Evidence Count (out of 6)\")\n",
        "plt.ylabel(\"P(Choosing High Utility Hypothesis)\")\n",
        "\n",
        "plt.yticks([0, .25, .50, .75, 1.0])\n",
        "\n",
        "\n",
        "ax.set(title = 'Distinguishing Practical From Theoretical Rationality')\n",
        "ax.legend([r'Bayesian Practical Reasoner', r'Bayes Rule'], loc = 'upper left', frameon = False, fontsize = 'medium')\n",
        "leg = ax.get_legend()\n",
        "leg.legendHandles[0].set_color('#011638')\n",
        "leg.legendHandles[1].set_color('#CDCDCD')\n",
        "#leg.legendHandles[2].set_color('#9933ff')\n",
        "#leg.legendHandles[3].set_color('black')\n",
        "plt.savefig('PvRDecisions.pdf')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "2gkizPmAPvja",
        "outputId": "3b128df6-6aef-4c1a-8e4f-ab19da2e5197"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}