Day2_DL_probability.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H33oT6raeR9K"
      },
      "source": [
        "# Basic Probability"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T06:01:03.935909Z",
          "start_time": "2019-01-24T06:01:03.924920Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zqMNPrOBeR9N",
        "outputId": "14b4e5b0-5b50-46c4-d97d-32c52f95960c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: mxnet in /usr/local/lib/python3.7/dist-packages (1.9.1)\n",
            "Requirement already satisfied: graphviz<0.9.0,>=0.8.1 in /usr/local/lib/python3.7/dist-packages (from mxnet) (0.8.4)\n",
            "Requirement already satisfied: numpy<2.0.0,>1.16.0 in /usr/local/lib/python3.7/dist-packages (from mxnet) (1.21.6)\n",
            "Requirement already satisfied: requests<3,>=2.20.0 in /usr/local/lib/python3.7/dist-packages (from mxnet) (2.23.0)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests<3,>=2.20.0->mxnet) (2022.6.15)\n",
            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests<3,>=2.20.0->mxnet) (1.24.3)\n",
            "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.7/dist-packages (from requests<3,>=2.20.0->mxnet) (3.0.4)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests<3,>=2.20.0->mxnet) (2.10)\n"
          ]
        }
      ],
      "source": [
        "!pip install mxnet\n",
        "\n",
        "import mxnet as mx\n",
        "from mxnet import nd\n",
        "%matplotlib inline\n",
        "from matplotlib import pyplot as plt\n",
        "from IPython import display\n",
        "display.set_matplotlib_formats('svg')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "srYoAiH4eR9P"
      },
      "source": [
        "Let's define a discrete distribution over 6 outcomes and sample from it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T05:59:38.319382Z",
          "start_time": "2019-01-24T05:59:38.296683Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ED9jCl4DeR9P",
        "outputId": "a2eefd05-2ab4-4639-b6c7-a3459aadc2d7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\n",
              "[3]\n",
              "<NDArray 1 @cpu(0)>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "probabilities = nd.ones(6) / 6\n",
        "nd.random.multinomial(probabilities)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0Z6NtSe2eR9Q"
      },
      "source": [
        "Let's draw from it multiple times."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T05:59:38.339621Z",
          "start_time": "2019-01-24T05:59:38.322810Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "drxH3Cj3eR9R",
        "outputId": "ac81b555-1c72-4863-9d78-5d50d36f8594"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[3 4 5 3 5 3 5 2 3 3]\n",
            "<NDArray 10 @cpu(0)>\n",
            "\n",
            "[[2 2 1 5 0 5 1 2 2 4]\n",
            " [4 3 2 3 2 5 5 0 2 0]\n",
            " [3 0 2 4 5 4 0 5 5 5]\n",
            " [2 4 4 2 3 4 4 0 4 3]\n",
            " [3 0 3 5 4 3 0 2 2 1]]\n",
            "<NDArray 5x10 @cpu(0)>\n"
          ]
        }
      ],
      "source": [
        "print(nd.random.multinomial(probabilities, shape=(10)))\n",
        "print(nd.random.multinomial(probabilities, shape=(5,10)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9AzWKFWOeR9R"
      },
      "source": [
        "Let's see what happens for 1000 samples."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T05:59:39.173110Z",
          "start_time": "2019-01-24T05:59:38.346287Z"
        },
        "id": "j9yA3kOBeR9S"
      },
      "outputs": [],
      "source": [
        "rolls = nd.random.multinomial(probabilities, shape=(1000))\n",
        "counts = nd.zeros((6,1000))\n",
        "totals = nd.zeros(6)\n",
        "for i, roll in enumerate(rolls):\n",
        "    totals[int(roll.asscalar())] += 1\n",
        "    counts[:, i] = totals"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "taHdw3h0eR9S"
      },
      "source": [
        "To start, we can inspect the final tally at the end of $1000$ rolls."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T05:59:39.205568Z",
          "start_time": "2019-01-24T05:59:39.182911Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_yyG9LUqeR9T",
        "outputId": "df78c2a4-da48-4e21-dfb4-395a5d1d2f18"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\n",
              "[0.167 0.168 0.175 0.159 0.158 0.173]\n",
              "<NDArray 6 @cpu(0)>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "totals / 1000"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E9omMO5aeR9U"
      },
      "source": [
        "Let's look at the counts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T05:59:39.234079Z",
          "start_time": "2019-01-24T05:59:39.217890Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uu2fyPlyeR9U",
        "outputId": "093006c0-7f1a-476d-b148-354a06698aed"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\n",
              "[[  0.   0.   0. ... 165. 166. 167.]\n",
              " [  1.   1.   1. ... 168. 168. 168.]\n",
              " [  0.   0.   0. ... 175. 175. 175.]\n",
              " [  0.   0.   0. ... 159. 159. 159.]\n",
              " [  0.   1.   2. ... 158. 158. 158.]\n",
              " [  0.   0.   0. ... 173. 173. 173.]]\n",
              "<NDArray 6x1000 @cpu(0)>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "counts"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XFVYahCjeR9V"
      },
      "source": [
        "Normalizing by the number of tosses, we get:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T05:59:39.274778Z",
          "start_time": "2019-01-24T05:59:39.248788Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8g3_6bm8eR9V",
        "outputId": "352e62ac-2b74-429e-eb52-6d86d779ff8f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[0. 1. 0. 0. 0. 0.]\n",
            "<NDArray 6 @cpu(0)>\n",
            "\n",
            "[0.  0.5 0.  0.  0.5 0. ]\n",
            "<NDArray 6 @cpu(0)>\n",
            "\n",
            "[0.1980198  0.15841584 0.17821783 0.18811882 0.12871288 0.14851485]\n",
            "<NDArray 6 @cpu(0)>\n"
          ]
        }
      ],
      "source": [
        "x = nd.arange(1000).reshape((1,1000)) + 1\n",
        "estimates = counts / x\n",
        "print(estimates[:,0])\n",
        "print(estimates[:,1])\n",
        "print(estimates[:,100])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-01-24T06:01:13.313012Z",
          "start_time": "2019-01-24T06:01:13.138772Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "EUEeb9BgeR9V",
        "outputId": "24573b46-beba-40c2-989a-044f5ff787b7"
      },
      "outputs": [
        {
          "output_type": "display_data",
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              "<Figure size 576x432 with 1 Axes>"
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          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8, 6))\n",
        "for i in range(6):\n",
        "    plt.plot(estimates[i, :].asnumpy(), label=(\"P(die=\" + str(i) +\")\"))\n",
        "\n",
        "plt.axhline(y=0.16666, color='black', linestyle='dashed')\n",
        "plt.legend()   \n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "celltoolbar": "Slideshow",
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
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      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.1"
    },
    "colab": {
      "name": "probability.ipynb",
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}