entropy.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "entropy.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "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/tinhb92/relax_ml/blob/master/entropy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QvppNQ3wyapi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "from matplotlib import pyplot as plt\n",
        "import tensorflow as tf\n",
        "import seaborn as sns\n",
        "sns.set()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wZWW8iBIypmH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def kl_divergence(p, q):\n",
        "    return np.sum(np.where(p != 0, p * np.log(p / q), 0))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zX9yuOiVyrXf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "2b4306f4-c0e6-4781-d1d6-bb5c5a7ca357"
      },
      "source": [
        "x = np.arange(-10, 10, 0.001)\n",
        "p = norm.pdf(x, 0, 2)\n",
        "q = norm.pdf(x, 2, 2)\n",
        "plt.title('KL(P||Q) = %1.3f' % kl_divergence(p, q))\n",
        "plt.plot(x, p)\n",
        "plt.plot(x, q, c='red')"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f288c38bef0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9uGuIN3uOX6Wuwdhqeae1fwWzmZrn/uuO4qJUwp/+hKogH4cPNrZeXpJukAlDktpg79dX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\nJAxBEATBIyJhCIIgCB4RCUMQBEHwyP8D5UqrQstZ7DMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3LGOvCGUzAJQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "085d049b-1681-43d2-fe73-f3bfc44aa033"
      },
      "source": [
        "q = norm.pdf(x, 5, 4)\n",
        "plt.title('KL(P||Q) = %1.3f' % kl_divergence(p, q))\n",
        "plt.plot(x, p)\n",
        "plt.plot(x, q, c='red')"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f2889ab5588>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZKBQKHB0dWb169R0vnAtRF3FJ2fh6OuJkb23uKE2ijasdbVxsiU3K5qE+vuaO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\nQRC88v9vW7ZBONrgvAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vn9eZ9rqzisY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "27579347-521f-409f-c7c5-29d76c2ddaf1"
      },
      "source": [
        "def cross_entropy(predictions, targets, epsilon=1e-12):\n",
        "    \"\"\"\n",
        "    Computes cross entropy between targets (encoded as one-hot vectors)\n",
        "    and predictions. \n",
        "    Input: predictions (N, k) ndarray\n",
        "           targets (N, k) ndarray        \n",
        "    Returns: scalar\n",
        "    \"\"\"\n",
        "    predictions = np.clip(predictions, epsilon, 1. - epsilon)\n",
        "    N = predictions.shape[0]\n",
        "    ce = -np.sum(targets*np.log(predictions+1e-9))/N\n",
        "    return ce\n",
        "\n",
        "predictions = np.array([[0.25,0.25,0.25,0.25],\n",
        "                        [0.01,0.01,0.01,0.96]])\n",
        "targets = np.array([[0,0,0,1],\n",
        "                   [0,0,0,1]])\n",
        "ans = 0.71355817782  #Correct answer\n",
        "x = cross_entropy(predictions, targets)\n",
        "print(np.isclose(x,ans))"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HP5v-oJ9oI4E",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vurf1SaErNKB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "bae6b62a-ba14-46be-ded5-ce8d4531bae8"
      },
      "source": [
        "batch_size, n_classes = 5, 3\n",
        "x = torch.randn(batch_size, n_classes)\n",
        "x.shape"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 3])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5_PfCuTjrOnt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "ceeefe8b-e193-48c1-c2ae-a726edac289d"
      },
      "source": [
        "target = torch.randint(n_classes, size=(batch_size,), dtype=torch.long)\n",
        "target"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2, 0, 1, 0, 0])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iCoWeIRNrfyo",
        "colab_type": "text"
      },
      "source": [
        "softmax + negative likelihood"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wouCdKBnrasu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "589b0e46-72e1-40b9-9e6f-fa639e8e7f5d"
      },
      "source": [
        "def softmax(x): return x.exp() / (x.exp().sum(-1)).unsqueeze(-1)\n",
        "def nl(input, target): return -input[range(target.shape[0]), target].log().mean()\n",
        "\n",
        "pred = softmax(x)\n",
        "loss=nl(pred, target)\n",
        "loss"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.2857)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-NqKHXy_sMW2",
        "colab_type": "text"
      },
      "source": [
        "While mathematically equivalent to log(softmax(x)), doing these two operations separately is slower, and numerically unstable. This function uses an alternative formulation to compute the output and gradient correctly."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RYTX9VzKree3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "245eb1ce-983a-4bca-9537-991b28da5b34"
      },
      "source": [
        "def log_softmax(x): return x - x.exp().sum(-1).log().unsqueeze(-1)\n",
        "def nll(input, target): return -input[range(target.shape[0]), target].mean()\n",
        "\n",
        "pred = log_softmax(x)\n",
        "loss = nll(pred, target)\n",
        "loss"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.2857)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bX8AaMxEsHZ0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "d58d1343-5b5d-4c64-836b-f49408ab4e7c"
      },
      "source": [
        "pred = F.log_softmax(x, dim=-1)\n",
        "loss = F.nll_loss(pred, target)\n",
        "loss"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.2857)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P-5ctP4Msc-x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "c27501c0-2373-4577-c997-7ac87c823c2c"
      },
      "source": [
        "F.cross_entropy(x, target)\n"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.2857)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UHCk5XxcsksP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}