common_loss_functions_in_pytorch.ipynb

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  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F3TxcVyystq0",
        "outputId": "afee31da-c795-4996-f8e4-f4d1a6055049"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE Loss: 0.04500000178813934\n",
            "Binary Cross Entropy Loss: 0.22708065807819366\n",
            "Categorical Cross Entropy Loss: 0.8302483558654785\n",
            "Kullback-Leibler Divergence Loss: 0.08212602138519287\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Example data\n",
        "y_true = torch.tensor([1., 0., 1., 0.])\n",
        "y_pred = torch.tensor([0.9, 0.2, 0.8, 0.3])\n",
        "\n",
        "# 1. Mean Squared Error (MSE) Loss\n",
        "mse_loss = nn.MSELoss()\n",
        "mse_loss_value = mse_loss(y_pred, y_true)\n",
        "print(\"MSE Loss:\", mse_loss_value.item())\n",
        "# Intuition: Measures the average squared difference between predicted and true values.\n",
        "# Math: MSE = 1/N * sum((y_true - y_pred)^2)\n",
        "\n",
        "# 2. Binary Cross Entropy Loss\n",
        "bce_loss = nn.BCELoss()\n",
        "bce_loss_value = bce_loss(y_pred, y_true.float())\n",
        "print(\"Binary Cross Entropy Loss:\", bce_loss_value.item())\n",
        "# Intuition: Measures the average binary cross-entropy between predicted and true values.\n",
        "# Math: BCE = -1/N * sum(y_true * log(y_pred) + (1 - y_true) * log(1 - y_pred))\n",
        "\n",
        "# 3. Categorical Cross Entropy Loss\n",
        "y_true_categorical = torch.tensor([2, 0, 1])\n",
        "y_pred_categorical = torch.tensor([[0.1, 0.2, 0.7],\n",
        "                                   [0.8, 0.1, 0.1],\n",
        "                                   [0.3, 0.4, 0.3]])\n",
        "ce_loss = nn.CrossEntropyLoss()\n",
        "ce_loss_value = ce_loss(y_pred_categorical, y_true_categorical)\n",
        "print(\"Categorical Cross Entropy Loss:\", ce_loss_value.item())\n",
        "# Intuition: Measures the average cross-entropy loss between predicted and true class probabilities.\n",
        "# Math: CE = -1/N * sum(log(y_pred[i][y_true[i]]))\n",
        "\n",
        "# 4. Kullback-Leibler Divergence Loss\n",
        "kl_loss = nn.KLDivLoss(reduction='batchmean')\n",
        "kl_loss_value = kl_loss(torch.log(y_pred), y_true)\n",
        "print(\"Kullback-Leibler Divergence Loss:\", kl_loss_value.item())\n",
        "# Intuition: Measures the average Kullback-Leibler divergence between predicted and true distributions.\n",
        "# Math: KL = 1/N * sum(y_true * log(y_true / y_pred))\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "KL Divergence\n",
        "In the example below, we have a fixed true distribution P and a sequence of approximated distributions Q. Each Q in the sequence represents a progressively diverging distribution from P. We calculate the KL divergence for each Q and store the values in the KL_values list.\n",
        "\n",
        "The code then plots the KL divergence values over iterations. Each point on the plot represents the KL divergence between the corresponding Q and the true distribution P. As the iterations progress, the approximated distributions diverge further from the true distribution, resulting in larger KL divergence values."
      ],
      "metadata": {
        "id": "2NXCiA1k51Uz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Define the true distribution P\n",
        "P = np.array([0.2, 0.3, 0.5])\n",
        "\n",
        "# Define a sequence of approximated distributions Q\n",
        "Q_sequence = [\n",
        "    np.array([0.1, 0.2, 0.7]),\n",
        "    np.array([0.2, 0.4, 0.4]),\n",
        "    np.array([0.3, 0.4, 0.3]),\n",
        "    np.array([0.4, 0.3, 0.3]),\n",
        "    np.array([0.5, 0.2, 0.3])\n",
        "]\n",
        "\n",
        "# Calculate the KL divergence for each Q in the sequence\n",
        "KL_values = []\n",
        "for Q in Q_sequence:\n",
        "    KL = np.sum(P * np.log(P / Q))\n",
        "    KL_values.append(KL)\n",
        "\n",
        "# Plot the KL divergence values\n",
        "iterations = np.arange(len(Q_sequence))\n",
        "plt.plot(iterations, KL_values, marker='o')\n",
        "\n",
        "# Add labels and title to the plot\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('KL Divergence')\n",
        "plt.title('Divergence of Q from P over Iterations')\n",
        "\n",
        "# Display the plot\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "5y2Nq944td8I",
        "outputId": "1613448b-77ee-4b2f-8370-875ca8f704e9"
      },
      "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": "markdown",
      "source": [
        "# NLL\n",
        "\n"
      ],
      "metadata": {
        "id": "bsT20SEz6N3c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# True probability of getting heads\n",
        "true_prob = 0.6\n",
        "\n",
        "# Observed data (coin flips)\n",
        "data = ['H', 'T', 'H', 'T', 'T', 'H', 'H', 'T', 'T', 'T']\n",
        "\n",
        "# Calculate the negative log-likelihood\n",
        "nll = -np.sum(np.log([true_prob if flip == 'H' else 1 - true_prob for flip in data]))\n",
        "\n",
        "# Print the result\n",
        "print(f\"Negative Log-Likelihood: {nll}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6ZengYo-suZG",
        "outputId": "0b098fc7-3a93-439e-d385-d322aee967b9"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Negative Log-Likelihood: 7.541046886308893\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the example below, we have a tensor of true class labels (true_labels) and a tensor of predicted class probabilities (pred_probs). The predicted probabilities are represented as a 2D tensor, where each row corresponds to the predicted probabilities for a specific instance, and each column represents the probabilities for a particular class.\n",
        "\n",
        "We use the nn.NLLLoss function to compute the NLL loss. Since the NLLLoss expects log-probabilities as input, we pass torch.log(pred_probs) to convert the predicted probabilities to log-probabilities. We then compute the NLL loss by comparing the predicted log-probabilities with the true class labels.\n",
        "\n",
        "The resulting NLL loss represents the discrepancy between the predicted class probabilities and the true class labels. A lower NLL loss indicates a better fit between the model's predictions and the true labels.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "xMKFVKX67JXb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "\n",
        "# True class labels\n",
        "true_labels = torch.tensor([2, 1, 0, 3])\n",
        "\n",
        "# Predicted class probabilities\n",
        "pred_probs = torch.tensor([[0.1, 0.2, 0.6, 0.1],\n",
        "                           [0.3, 0.4, 0.1, 0.2],\n",
        "                           [0.7, 0.1, 0.1, 0.1],\n",
        "                           [0.2, 0.2, 0.2, 0.4]])\n",
        "\n",
        "# Define the negative log-likelihood (NLL) loss function\n",
        "loss_fn = nn.NLLLoss()\n",
        "\n",
        "# Compute the NLL loss\n",
        "nll_loss = loss_fn(torch.log(pred_probs), true_labels)\n",
        "\n",
        "# Print the NLL loss\n",
        "print(\"Negative Log-Likelihood (NLL) Loss:\", nll_loss.item())\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OPnvI_4O7IUr",
        "outputId": "b874a8b3-38f4-4432-c04b-311af1536c9a"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Negative Log-Likelihood (NLL) Loss: 0.6750205159187317\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "cZzl9s8w6RM8"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}