{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "ace0c0d8-bc42-4e0b-9005-09f1ef2739f1",
      "metadata": {
        "id": "ace0c0d8-bc42-4e0b-9005-09f1ef2739f1"
      },
      "source": [
        "# Bayes classificator and its behavior\n",
        "\n",
        "\n",
        "\n",
        "## Learning goal\n",
        "\n",
        "The learning goal of this notebook is to gain intuition on how classification problems work. We emphasize how important is to estimate the Bayes classifier for each problem and we do this in a setting that we can know the optimal classifier explicitly.  We will study the performance of this classifier as we change features of classes and the number of classes. The hope is that, with this in mind, we can understand how to increase the performance of classifiers in more general settings.\n",
        "\n",
        "## Overview\n",
        "\n",
        "As discussed in class, for any given classification problem it is essential to estimate the Bayes error rate, which dictates the best performance one can have at the specific problem. For example, it is easier to distinguish clear high-resolution images than to distinguish images taken with a camera made in 1970's. However, there's some samples from a given class that are inherently impossible to distinguish, no matter how good the classifier is (see image below). This is what we refer to when we talk about the Bayes error rate. Those samples will be inevitably misclassified.\n",
        "\n",
        "Then, we'll first acquire some empirical knowledge by classifying samples from a binary Gaussian mixture model. After we are familiar with this problem, we'll reexamine the problem analytically. In the third section, we'll go even further and generalize the problem to  to develop intuition on what happens when samples are drawn from multi-class mixture model. In the final section we again go over analytical results and compare them with our experiments."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c7bfc925-8d68-4932-abec-83d2da4f07e7",
      "metadata": {
        "jupyter": {
          "source_hidden": true
        },
        "id": "c7bfc925-8d68-4932-abec-83d2da4f07e7",
        "outputId": "8b99268c-93a0-4a83-8e20-acfd488d07a5"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define parameters for the two classes (means and standard deviations)\n",
        "mu0 = 0  # Mean for Class 0\n",
        "sigma0 = 1  # Standard deviation for Class 0\n",
        "\n",
        "mu1 = 3  # Mean for Class 1\n",
        "sigma1 = 1  # Standard deviation for Class 1\n",
        "\n",
        "# Generate x values for the plot\n",
        "x = np.linspace(-4, 7, 500)\n",
        "\n",
        "# Calculate the probability density functions (PDFs) for each class\n",
        "pdf0 = norm.pdf(x, mu0, sigma0)\n",
        "pdf1 = norm.pdf(x, mu1, sigma1)\n",
        "\n",
        "# Create the plot\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "# Plot the PDF for Class 0\n",
        "plt.plot(x, pdf0, label='Class 0', color='purple')\n",
        "plt.fill_between(x, 0, pdf0, color='purple', alpha=0.1)\n",
        "\n",
        "# Plot the PDF for Class 1\n",
        "plt.plot(x, pdf1, label='Class 1', color='deeppink')\n",
        "plt.fill_between(x, 0, pdf1, color='deeppink', alpha=0.1)\n",
        "\n",
        "# Find the intersection point (decision boundary)\n",
        "# For two normal distributions with equal variance, the decision boundary is exactly in the middle of the means.\n",
        "# If variances are different, you'd solve norm.pdf(x, mu0, sigma0) = norm.pdf(x, mu1, sigma1)\n",
        "decision_boundary = (mu0 + mu1) / 2\n",
        "# --- MODIFIED PART ---\n",
        "# Instead of axvline, we'll draw a plot line for the decision boundary\n",
        "# Define the y-range for the decision boundary line\n",
        "y_min_boundary = 0  # Start from the x-axis\n",
        "y_max_boundary = np.max(pdf0) * 0.7 # Extend to 70% of the max PDF height (adjust as needed)\n",
        "\n",
        "plt.plot([decision_boundary, decision_boundary], [y_min_boundary, y_max_boundary],\n",
        "         color='gray', linestyle='--', linewidth=0.8, label='Decision Boundary')\n",
        "# --- END MODIFIED PART ---\n",
        "\n",
        "\n",
        "# Highlight the overlap region (misclassification region)\n",
        "x_overlap = np.linspace(decision_boundary, x.max(), 100)\n",
        "pdf0_overlap = norm.pdf(x_overlap, mu0, sigma0)\n",
        "plt.fill_between(x_overlap, 0, pdf0_overlap, color='purple', alpha=0.3, hatch='x', edgecolor='darkblue', linewidth=0.5)\n",
        "\n",
        "x_overlap_left = np.linspace(x.min(), decision_boundary, 100)\n",
        "pdf1_overlap_left = norm.pdf(x_overlap_left, mu1, sigma1)\n",
        "plt.fill_between(x_overlap_left, 0, pdf1_overlap_left, color='deeppink', alpha=0.3, hatch='x', edgecolor='darkred', linewidth=0.5)\n",
        "\n",
        "# Add annotations from the image\n",
        "plt.annotate('Class 1', xy=(mu1 + 1.5, norm.pdf(mu1, mu1, sigma1) * 0.7), xytext=(mu1 + 2, norm.pdf(mu1, mu1, sigma1) * 0.75),\n",
        "             arrowprops=dict(facecolor='black', shrink=0.05, width=0.5, headwidth=5),\n",
        "             horizontalalignment='left', verticalalignment='bottom')\n",
        "\n",
        "plt.annotate('Assigned to class 1', xy=(decision_boundary + 0.5, 0.05), xytext=(decision_boundary + 1, 0.02),\n",
        "             arrowprops=dict(facecolor='black', shrink=0.05, width=0.5, headwidth=5),\n",
        "             horizontalalignment='left', verticalalignment='center')\n",
        "\n",
        "plt.annotate('Assigned to class 0', xy=(decision_boundary - 0.5, 0.05), xytext=(decision_boundary - 2, 0.02),\n",
        "             arrowprops=dict(facecolor='black', shrink=0.05, width=0.5, headwidth=5),\n",
        "             horizontalalignment='right', verticalalignment='center')\n",
        "\n",
        "plt.annotate('Class 0', xy=(mu0 - 1.5, norm.pdf(mu0, mu0, sigma0) * 0.7), xytext=(mu0 - 2, norm.pdf(mu0, mu0, sigma0) * 0.75),\n",
        "             arrowprops=dict(facecolor='black', shrink=0.5, width=0.5, headwidth=5),\n",
        "             horizontalalignment='left', verticalalignment='bottom')\n",
        "\n",
        "# Add the 'Δ' bracket (representing the separation or difference in means)\n",
        "plt.plot([mu0, mu1], [norm.pdf(mu0, mu0, sigma0) * 1.1, norm.pdf(mu1, mu1, sigma1) * 1.1], color='black', linewidth=0.8)\n",
        "plt.plot([mu0, mu0], [norm.pdf(mu0, mu0, sigma0) * 1.05, norm.pdf(mu0, mu0, sigma0) * 1.15], color='black', linewidth=0.8)\n",
        "plt.plot([mu1, mu1], [norm.pdf(mu1, mu1, sigma1) * 1.05, norm.pdf(mu1, mu1, sigma1) * 1.15], color='black', linewidth=0.8)\n",
        "plt.text((mu0 + mu1)/2, norm.pdf(mu0, mu0, sigma0) * 1.1, 'Δ', horizontalalignment='center', verticalalignment='bottom')\n",
        "\n",
        "\n",
        "# Customize the plot\n",
        "plt.title('Bayes Classifier Example (Gaussian Distributions)')\n",
        "plt.xlabel('Feature Value')\n",
        "plt.ylabel('Probability Density')\n",
        "plt.yticks([]) # Remove y-axis ticks as in the original image\n",
        "plt.ylim(bottom=0) # Ensure y-axis starts at 0\n",
        "\n",
        "# Remove top and right spines for a cleaner look\n",
        "plt.gca().spines['top'].set_visible(False)\n",
        "plt.gca().spines['right'].set_visible(False)\n",
        "\n",
        "plt.legend()\n",
        "plt.grid(True, linestyle=':', alpha=0.6)\n",
        "#plt.savefig('Bayes_classifier.png')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6efcb02d-d217-43fe-b204-6711d6413b5c",
      "metadata": {
        "id": "6efcb02d-d217-43fe-b204-6711d6413b5c"
      },
      "source": [
        "## Experiments with two classes\n",
        "\n",
        "Consider a situation where we have a dataset where each data point is sampled from one of two Gaussians (see image above). The Gaussians are separated by a distance $\\Delta$ and their variances are equal (assume this for simplicity for now). We want to understand how well we can classify this as a function of the ratio $\\frac{\\Delta}{\\sigma}$ (which tells us what's the relationship between signal and noise).\n",
        "\n",
        "The classifier we will use is simply the nearest-mean classifier. This uses the training set to compute what's the mean value of each class and then attributes each sample from the training set to the class that has the closest mean to it. For this problem, you can convince yourself that this is actually the best classifier that you can cook up.\n",
        "\n",
        "Use the code below to plot accuracy as a function of the distance $\\Delta$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9cbf8019-373c-4c9e-a5ab-783f909b8e14",
      "metadata": {
        "id": "9cbf8019-373c-4c9e-a5ab-783f909b8e14",
        "outputId": "4de86634-08d3-4b78-8e5e-d2bae006b8c2"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Sweeping Δ/σ ratios: 100%|██████████| 25/25 [00:00<00:00, 907.25it/s]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "from tqdm import tqdm\n",
        "\n",
        "def experiment(delta, sigma, n_train=1000, n_test=500, seed=0):\n",
        "    \"\"\"Runs a single nearest-mean classification experiment and returns the error rate.\"\"\"\n",
        "    rng = np.random.default_rng(seed)\n",
        "\n",
        "    # --- Generate Data ---\n",
        "    # Class 0 centered at -delta/2, Class 1 centered at +delta/2\n",
        "    X_train_0 = rng.normal(loc=-delta / 2, scale=sigma, size=(n_train // 2, 1))\n",
        "    X_train_1 = rng.normal(loc=delta / 2, scale=sigma, size=(n_train // 2, 1))\n",
        "    X_train = np.vstack([X_train_0, X_train_1])\n",
        "    y_train = np.hstack([np.zeros(n_train // 2), np.ones(n_train // 2)])\n",
        "\n",
        "    X_test_0 = rng.normal(loc=-delta / 2, scale=sigma, size=(n_test // 2, 1))\n",
        "    X_test_1 = rng.normal(loc=delta / 2, scale=sigma, size=(n_test // 2, 1))\n",
        "    X_test = np.vstack([X_test_0, X_test_1])\n",
        "    y_test = np.hstack([np.zeros(n_test // 2), np.ones(n_test // 2)])\n",
        "\n",
        "    # --- Nearest-Mean Classifier ---\n",
        "    # 1. Training: Calculate the mean for each class\n",
        "    centroid_0 = X_train[y_train == 0].mean()\n",
        "    centroid_1 = X_train[y_train == 1].mean()\n",
        "\n",
        "    # 2. Prediction: Assign test points to the class of the nearest centroid\n",
        "    decision_boundary = (centroid_0 + centroid_1) / 2\n",
        "    y_pred = (X_test > decision_boundary).flatten().astype(int)\n",
        "\n",
        "    # Calculate accuracy and return the error rate\n",
        "    accuracy = np.mean(y_pred == y_test)\n",
        "    error_rate = 1.0 - accuracy\n",
        "    return error_rate\n",
        "\n",
        "def plot_error_vs_delta_sigma(delta_sigma_ratio_range, sigma, n_seeds, n_train, n_test):\n",
        "    \"\"\"Main function to run simulations and plot the error rate results.\"\"\"\n",
        "\n",
        "    experimental_errors = []\n",
        "    experimental_std_errs = []\n",
        "    theoretical_errs = []\n",
        "\n",
        "    for ratio in tqdm(delta_sigma_ratio_range, desc=\"Sweeping Δ/σ ratios\"):\n",
        "        delta = ratio * sigma\n",
        "\n",
        "        # Run multiple experiments for statistical significance\n",
        "        scores = [experiment(delta, sigma, n_train, n_test, seed=s) for s in range(n_seeds)]\n",
        "        mean_error = np.mean(scores)\n",
        "        std_err = np.std(scores) / np.sqrt(n_seeds)\n",
        "\n",
        "        experimental_errors.append(mean_error)\n",
        "        experimental_std_errs.append(std_err)\n",
        "\n",
        "    # --- Plotting ---\n",
        "    plt.style.use('seaborn-v0_8-whitegrid')\n",
        "    plt.figure(figsize=(10, 6))\n",
        "\n",
        "    # Plot experimental results with error bars\n",
        "    plt.errorbar(delta_sigma_ratio_range, experimental_errors, yerr=experimental_std_errs, fmt='-o',\n",
        "                 capsize=5, markersize=8, color='royalblue', label='Experimental Nearest-Mean Error Rate')\n",
        "\n",
        "\n",
        "    plt.title('Classifier Error Rate vs. Class Separation (Δ/σ)', fontsize=16)\n",
        "    plt.xlabel('Δ/σ (Separation / Standard Deviation)', fontsize=12)\n",
        "    plt.ylabel('Error Rate', fontsize=12)\n",
        "    plt.ylim(-0.05, 0.55)\n",
        "    plt.legend(fontsize=11)\n",
        "    plt.grid(True, which='both', linestyle=':')\n",
        "    plt.show()\n",
        "\n",
        "# --- Run the Simulation ---\n",
        "# Define the range of delta/sigma to test\n",
        "delta_over_sigma_values = np.linspace(0, 6, 25)\n",
        "\n",
        "plot_error_vs_delta_sigma(\n",
        "    delta_sigma_ratio_range=delta_over_sigma_values,\n",
        "    sigma=1.0,         # We can fix sigma=1.0 and vary delta to control the ratio\n",
        "    n_seeds=5,         # Number of runs per data point for averaging\n",
        "    n_train=2000,      # Number of training samples\n",
        "    n_test=1000        # Number of testing samples\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b8659501-f913-49bf-afda-d7eb7349838d",
      "metadata": {
        "id": "b8659501-f913-49bf-afda-d7eb7349838d"
      },
      "source": [
        "\n",
        "\n",
        "1.   Was that what you expected? Why at zero separation the error rate is 0.5 and not 1.0? Explain in your own words why this happens and what's the intuition behind it (look at the figure in the introduction, this should make sense).\n",
        "\n",
        "2. $\\textbf{Optional:}$ play around and use different variances for the Gaussians. Does this change the result? If yes, how?\n",
        "\n",
        "## Some analytics\n",
        "\n",
        "Now, let's derive the analytical result that explains this.\n",
        "\n",
        "### Exercise: Deriving the Bayes Error Rate\n",
        "\n",
        "**Problem Setup:**\n",
        "\n",
        "Consider a one-dimensional classification problem with two classes, Class 0 ($C_0$) and Class 1 ($C_1$), which have equal prior probabilities, $P(C_0) = P(C_1) = 0.5$. The class-conditional probability densities are Gaussian distributions with the same standard deviation, $\\sigma$.\n",
        "\n",
        "- **Class 0:** $p(x|C_0) = \\mathcal{N}(x | \\mu_0, \\sigma^2)$, where $\\mu_0 = -\\Delta/2$\n",
        "- **Class 1:** $p(x|C_1) = \\mathcal{N}(x | \\mu_1, \\sigma^2)$, where $\\mu_1 = +\\Delta/2$\n",
        "\n",
        "Your task is to derive the formula for the minimum possible error rate, known as the Bayes error rate.\n",
        "\n",
        "---\n",
        "\n",
        "#### Step 1: Write Down the Probability Density Functions (PDFs) using the information given.\n",
        "\n",
        "<!-- The PDFs for the two classes are given by the Gaussian formula:\n",
        "$\\mathcal{N}(x | \\mu, \\sigma^2) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\left( - \\frac{(x-\\mu)^2}{2\\sigma^2} \\right)$.\n",
        "\n",
        "Substituting the means for our classes:\n",
        "$$ p(x|C_0) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\left( - \\frac{(x + \\Delta/2)^2}{2\\sigma^2} \\right) $$\n",
        "$$ p(x|C_1) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\left( - \\frac{(x - \\Delta/2)^2}{2\\sigma^2} \\right) $$ -->\n",
        "\n",
        "---\n",
        "\n",
        "#### Step 2: Find the Optimal Decision Boundary\n",
        "\n",
        "The optimal decision boundary, $x^*$, is where the posterior probabilities are equal. Since the priors are equal ($P(C_0) = P(C_1)$), this occurs where the likelihoods intersect: $p(x^*|C_0) = p(x^*|C_1)$. Show that $x^* = 0$.\n",
        "\n",
        "---\n",
        "\n",
        "#### Step 3: Define and Express the Error as an Integral\n",
        "\n",
        "The Bayes error rate is the total probability of misclassification. Due to the symmetry of the problem, this is equal to the probability of misclassifying a sample from Class 0. A sample from Class 0 is misclassified if its value $x$ is greater than the decision boundary $x^*=0$.\n",
        "\n",
        "<!-- $$ P(\\text{error}) = \\int_{x^*}^\\infty p(x|C_0) dx = \\int_{0}^\\infty \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\left( - \\frac{(x + \\Delta/2)^2}{2\\sigma^2} \\right) dx $$ -->\n",
        "\n",
        "---\n",
        "\n",
        "#### Step 4: Solve the Integral via Change of Variables\n",
        "\n",
        "We use a z-score transformation to standardize the variable. Let $z = \\frac{x - \\mu_0}{\\sigma} = \\frac{x + \\Delta/2}{\\sigma}$.\n",
        "\n",
        "<!-- This implies $x = z\\sigma - \\Delta/2$ and $dx = \\sigma dz$.\n",
        "\n",
        "We must also transform the integration limit:\n",
        "$$ \\text{When } x = 0, \\quad z = \\frac{0 + \\Delta/2}{\\sigma} = \\frac{\\Delta}{2\\sigma} $$\n",
        "The integral becomes:\n",
        "$$ P(\\text{error}) = \\int_{\\Delta/(2\\sigma)}^\\infty \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-z^2/2} (\\sigma dz) $$ -->\n",
        "\n",
        "You should arrive at:\n",
        "$$ P(\\text{error}) = \\int_{\\Delta/(2\\sigma)}^\\infty \\frac{1}{\\sqrt{2\\pi}} e^{-z^2/2} dz. $$\n",
        "This integral is the definition of the complementary cumulative distribution function (CDF) of the standard normal distribution, often denoted as the Q-function, $Q(\\Delta/(2\\sigma))$. It is also equal to $1 - \\Phi(\\Delta/(2\\sigma))$, where $\\Phi(\\Delta/(2\\sigma))$ is the standard CDF.\n",
        "\n",
        "---\n",
        "\n",
        "### Final Result to Expect\n",
        "\n",
        "After correctly completing all the steps, you should arrive at the following analytical result for the Bayes error rate:\n",
        "\n",
        "$$ P(\\text{error}) = 1 - \\Phi\\left(\\frac{\\Delta}{2\\sigma}\\right) $$\n",
        "\n",
        "or equivalently, using the Q-function:\n",
        "\n",
        "$$ P(\\text{error}) = Q\\left(\\frac{\\Delta}{2\\sigma}\\right) $$\n",
        "\n",
        "---\n",
        "\n",
        "Now, compare the theoretical result with the experiments that we performed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "92d1f36d-2b0e-458e-b27a-2cb112079a75",
      "metadata": {
        "id": "92d1f36d-2b0e-458e-b27a-2cb112079a75",
        "outputId": "a67eb864-ecb2-4fb5-b03e-c5ccfa49e7fd"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Sweeping Δ/σ ratios: 100%|██████████| 25/25 [00:00<00:00, 771.68it/s]\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def theoretical_error_rate(delta, sigma):\n",
        "    \"\"\"Calculates the theoretical minimum error rate (Bayes error) for two Gaussians.\"\"\"\n",
        "    # The Bayes error is the tail probability at the midpoint.\n",
        "    return 1.0 - norm.cdf(delta / (2 * sigma))\n",
        "\n",
        "def plot_error_vs_delta_sigma(delta_sigma_ratio_range, sigma, n_seeds, n_train, n_test):\n",
        "    \"\"\"Main function to run simulations and plot the error rate results.\"\"\"\n",
        "\n",
        "    experimental_errors = []\n",
        "    experimental_std_errs = []\n",
        "    theoretical_errs = []\n",
        "\n",
        "    for ratio in tqdm(delta_sigma_ratio_range, desc=\"Sweeping Δ/σ ratios\"):\n",
        "        delta = ratio * sigma\n",
        "\n",
        "        # Run multiple experiments for statistical significance\n",
        "        scores = [experiment(delta, sigma, n_train, n_test, seed=s) for s in range(n_seeds)]\n",
        "        mean_error = np.mean(scores)\n",
        "        std_err = np.std(scores) / np.sqrt(n_seeds)\n",
        "\n",
        "        experimental_errors.append(mean_error)\n",
        "        experimental_std_errs.append(std_err)\n",
        "        theoretical_errs.append(theoretical_error_rate(delta, sigma))\n",
        "\n",
        "    # --- Plotting ---\n",
        "    plt.style.use('seaborn-v0_8-whitegrid')\n",
        "    plt.figure(figsize=(10, 6))\n",
        "\n",
        "    # Plot experimental results with error bars\n",
        "    plt.errorbar(delta_sigma_ratio_range, experimental_errors, yerr=experimental_std_errs, fmt='-o',\n",
        "                 capsize=5, markersize=8, color='royalblue', label='Experimental Nearest-Mean Error Rate')\n",
        "\n",
        "    # Plot theoretical curve\n",
        "    plt.plot(delta_sigma_ratio_range, theoretical_errs, '--', color='red',\n",
        "             linewidth=2, label='Theoretical Bayes Error Rate')\n",
        "\n",
        "    plt.title('Classifier Error Rate vs. Class Separation (Δ/σ)', fontsize=16)\n",
        "    plt.xlabel('Δ/σ (Separation / Standard Deviation)', fontsize=12)\n",
        "    plt.ylabel('Error Rate', fontsize=12)\n",
        "    plt.ylim(-0.05, 0.55)\n",
        "    plt.legend(fontsize=11)\n",
        "    plt.grid(True, which='both', linestyle=':')\n",
        "    plt.show()\n",
        "\n",
        "# --- Run the Simulation ---\n",
        "# Define the range of delta/sigma to test\n",
        "delta_over_sigma_values = np.linspace(0, 6, 25)\n",
        "\n",
        "plot_error_vs_delta_sigma(\n",
        "    delta_sigma_ratio_range=delta_over_sigma_values,\n",
        "    sigma=1.0,         # We can fix sigma=1.0 and vary delta to control the ratio\n",
        "    n_seeds=5,         # Number of runs per data point for averaging\n",
        "    n_train=2000,      # Number of training samples\n",
        "    n_test=1000        # Number of testing samples\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b52ac9f9-2f44-4762-b060-f013b264f14f",
      "metadata": {
        "id": "b52ac9f9-2f44-4762-b060-f013b264f14f"
      },
      "source": [
        "## Beyond two Gaussians\n",
        "\n",
        "Now, we propose the question: what if one has many Gaussians to classify, does this affect the behavior or should one expect the same error for the same $\\frac{\\Delta}{\\sigma}$ we saw above?\n",
        "\n",
        "**Problem setup**\n",
        "\n",
        "Consider a $d$-dimensional classification problem with $C$ classes, Class 0 ($C_0$), Class 1 ($C_1$), ..., Class C ($C_C$), which have equal prior probabilities, $P(C_0) = P(C_1) = ... = P(C_C) = \\frac{1}{C}$. The class-conditional probability densities are Gaussian distributions with the same standard deviation, $\\sigma$.\n",
        "\n",
        "- **Class 0:** $p(x|C_0) = \\mathcal{N}(x | \\mu_0, \\sigma^2)$\n",
        "- **Class 1:** $p(x|C_1) = \\mathcal{N}(x | \\mu_1, \\sigma^2)$\n",
        "- $\\vdots$\n",
        "- **Class C:** $p(x|C_C) = \\mathcal{N}(x | \\mu_C, \\sigma^2)$\n",
        "\n",
        "Where we consider that these classes live in a simplex (hence $C \\leq d+1$), so\n",
        "$$|\\mu_i - \\mu_j| = \\Delta, \\forall i,j.$$\n",
        "\n",
        "## Experiments with $C$ Gaussians\n",
        "\n",
        "Your job now is to play with the code below and build intuition on what's happening."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "87eb605e-c870-4428-ae49-168db21c8076",
      "metadata": {
        "id": "87eb605e-c870-4428-ae49-168db21c8076",
        "outputId": "f346cd6a-add8-484c-de2c-f64e3d00118f"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Sweeping C values: 100%|██████████| 6/6 [00:01<00:00,  4.09it/s]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1200x700 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import pandas as pd\n",
        "from sklearn.metrics import f1_score\n",
        "\n",
        "def make_simplex_means(C, d, Delta):\n",
        "    if C > d + 1:\n",
        "        raise ValueError(\"Cannot embed more than d+1 equidistant points in R^d.\")\n",
        "    V = np.eye(C) - np.ones((C, C)) / C\n",
        "    V = V[:, :-1]\n",
        "    norms = np.linalg.norm(V[0] - V[1])\n",
        "    V = V / norms * Delta\n",
        "    if d > V.shape[1]:\n",
        "        V = np.hstack([V, np.zeros((C, d - V.shape[1]))])\n",
        "    return V\n",
        "\n",
        "def generate_data(N, C, d, Delta, sigma, rng):\n",
        "    means = make_simplex_means(C, d, Delta)\n",
        "    X, y = [], []\n",
        "    n_per_class = max(1, N // C)\n",
        "    for c in range(C):\n",
        "        Xc = rng.normal(0, sigma, size=(n_per_class, d)) + means[c]\n",
        "        yc = np.full(n_per_class, c)\n",
        "        X.append(Xc)\n",
        "        y.append(yc)\n",
        "    return np.vstack(X), np.concatenate(y)\n",
        "\n",
        "def experiment(C, N, d, Delta, sigma, n_test=200, seed=0):\n",
        "    rng = np.random.default_rng(seed)\n",
        "    X_train, y_train = generate_data(N, C, d, Delta, sigma, rng)\n",
        "    X_test, y_test = generate_data(n_test, C, d, Delta, sigma, rng)\n",
        "\n",
        "    unique_classes = np.unique(y_train)\n",
        "    centroids = np.array([X_train[y_train == c].mean(axis=0) for c in unique_classes])\n",
        "    sq_dists = np.sum((X_test[:, np.newaxis, :] - centroids[np.newaxis, :, :])**2, axis=2)\n",
        "    y_pred = np.argmin(sq_dists, axis=1)\n",
        "\n",
        "    f1 = f1_score(y_test, y_pred, average=\"macro\", zero_division=0)\n",
        "    error_rate = 1 - f1\n",
        "    return error_rate\n",
        "\n",
        "def run_simulation_for_C(C, d, Delta, sigma, N, n_test, n_seeds):\n",
        "    error_rates = [experiment(C=C, N=N, d=d, Delta=Delta, sigma=sigma,\n",
        "                              n_test=n_test, seed=seed) for seed in range(n_seeds)]\n",
        "    mean_error = np.mean(error_rates)\n",
        "    std_err = np.std(error_rates) / np.sqrt(n_seeds)\n",
        "    return mean_error, std_err\n",
        "\n",
        "def plot_experimental_error(C_values, d, Delta, sigma, N, n_test, n_seeds):\n",
        "    experimental_error_rates = []\n",
        "    experimental_errors_std = []\n",
        "\n",
        "    for C in tqdm(C_values, desc=\"Sweeping C values\"):\n",
        "        mean_error, std_err = run_simulation_for_C(C, d, Delta, sigma, N, n_test, n_seeds)\n",
        "        experimental_error_rates.append(mean_error)\n",
        "        experimental_errors_std.append(std_err)\n",
        "\n",
        "    plt.style.use('seaborn-v0_8-whitegrid')\n",
        "    plt.figure(figsize=(12, 7))\n",
        "\n",
        "    plt.errorbar(C_values, experimental_error_rates, yerr=experimental_errors_std, fmt='-o',\n",
        "                 capsize=5, markersize=8, color='royalblue', label='Experimental Nearest-Mean Error Rate')\n",
        "\n",
        "    title = f'Nearest-Mean Error Rate (N={N}, Δ={Delta}, σ={sigma})'\n",
        "    plt.title(title, fontsize=16)\n",
        "    plt.xlabel('C (Number of Classes)', fontsize=12)\n",
        "    plt.ylabel('Error Rate', fontsize=12)\n",
        "    plt.xticks(C_values)\n",
        "    plt.ylim(-0.05, 1.0)\n",
        "    plt.legend(fontsize=11)\n",
        "    plt.grid(True, which='both', linestyle='--')\n",
        "    plt.show()\n",
        "\n",
        "# --- Run the Comparison ---\n",
        "C_values_to_test = list(range(2, 53, 10))\n",
        "\n",
        "plot_experimental_error(\n",
        "    C_values=C_values_to_test,\n",
        "    d=52,\n",
        "    Delta=3.0,\n",
        "    sigma=1.0,\n",
        "    N=50000,\n",
        "    n_test=2000,\n",
        "    n_seeds=3\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "67d997c3-7907-4e91-aad3-be5f69ed41dc",
      "metadata": {
        "id": "67d997c3-7907-4e91-aad3-be5f69ed41dc"
      },
      "source": [
        "<b> Questions</b>\n",
        "\n",
        "1. Does this behave as you first expected?  List item\n",
        "2. Why does this happen?\n",
        "3. Play with different values of $\\Delta, N, \\sigma, C, d$ and explain what's happening."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "00c0edd1-1b33-4e09-96de-58aa25ecd3ba",
      "metadata": {
        "id": "00c0edd1-1b33-4e09-96de-58aa25ecd3ba"
      },
      "source": [
        "### Exercise: Deriving the Multi-Class Bayes Error Rate\n",
        "\n",
        "**Problem Setup:**\n",
        "We are analyzing a high-dimensional classification problem with $C$ classes. The data for each class $i$ is drawn from a Gaussian distribution, $p(x|C_i) = \\mathcal{N}(x | \\mu_i, \\sigma^2\\mathbb{I}_d)$. The means, $\\mu_i$, are arranged in a regular simplex structure, meaning they are all equidistant from each other. Our goal is to derive the theoretical minimum error rate (the Bayes error rate) for this scenario.\n",
        "\n",
        "---\n",
        "#### Step 1: Define the Misclassification Condition\n",
        "The optimal classifier for this problem is a **nearest-mean classifier**. A data point $x$ originally from Class 0 is misclassified if it is closer to the mean of any other class $j$ than it is to its own mean, $\\mu_0$.\n",
        "\n",
        "Let's define a variable $W_j$ that captures this comparison:\n",
        "$$ W_j = ||x - \\mu_j||^2 - ||x - \\mu_0||^2 $$\n",
        "\n",
        "What's the condition of misclassification?\n",
        "\n",
        "<!--\n",
        "A misclassification occurs if $W_j \\le 0$ for any $j \\neq 0$. Show that for a simplex centered at the origin (where $||\\mu_i||^2$ is the same for all $i$), this simplifies to:\n",
        "$$ W_j = 2x^T(\\mu_0 - \\mu_j) $$\n",
        " -->\n",
        "---\n",
        "#### Step 2: Incorporate the Data's Statistical Properties\n",
        "A data point $x$ from Class 0 can be written as $x = \\mu_0 + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(0, \\sigma^2\\mathbb{I}_d)$ is a random noise vector. Substitute this into the expression for $W_j$ and find the misclassification condition in terms of the data properties.\n",
        "\n",
        "<!-- Using the geometric properties of a regular simplex, it can be shown that $2\\mu_0^T(\\mu_0 - \\mu_j) = \\Delta^2$, where $\\Delta$ is the distance between any two class means. With this, show that the expression for $W_j$ becomes:\n",
        "$$ W_j = \\Delta^2 + 2\\epsilon^T(\\mu_0 - \\mu_j) $$\n",
        "\n",
        "From this, conclude that a misclassification occurs if:\n",
        "$$ \\epsilon^T(\\mu_j - \\mu_0) \\ge \\frac{\\Delta^2}{2} $$ -->\n",
        "\n",
        "---\n",
        "#### Step 3: Standardize the Random Variables\n",
        "Let's define a new set of random variables $Z_j = \\epsilon^T(\\mu_j - \\mu_0)$ for $j=1, \\dots, C-1$. These variables are normally distributed with a mean of 0 and a variance of $\\sigma^2\\Delta^2$.\n",
        "\n",
        "To simplify the math, we standardize these variables. Define $Y_j = \\frac{Z_j}{\\sigma\\Delta}$. What are the mean, variance, and covariance of these new variables, $Y_j$?\n",
        "\n",
        "---\n",
        "#### Step 4: Decompose the Correlated Variables\n",
        "The variables $Y_j$ are correlated. We can represent them as a sum of independent standard normal variables, $S$ and $V_j$, to handle this correlation:\n",
        "$$ Y_j = \\frac{S + V_j}{\\sqrt{2}} $$\n",
        "where $S \\sim \\mathcal{N}(0,1)$ and all $V_j \\sim \\mathcal{N}(0,1)$ are independent.\n",
        "\n",
        "A point is classified correctly if $W_j > 0$ for all $j \\neq 0$, which is equivalent to $Y_j \\le t$, where $t = \\frac{\\Delta}{2\\sigma}$. The probability of a correct classification is therefore $P_{\\text{correct}} = P(\\forall j: Y_j \\le t)$.\n",
        "\n",
        "---\n",
        "#### Step 5: Derive the Final Integral\n",
        "To find the total probability of a correct classification, we must average over all possible values of the shared variable $S$. This is done by conditioning on $S=s$ and then integrating over the distribution of $s$.\n",
        "\n",
        "1.  Given a fixed value $S=s$, what is the probability that a single $Y_j \\le t$? Show that this is equal to $\\Phi(\\sqrt{2}t - s)$, where $\\Phi$ is the CDF of the standard normal distribution.\n",
        "2.  Since all the $V_j$ are independent, what is the probability that *all* $Y_j \\le t$ for $j=1, \\dots, C-1$, conditioned on $S=s$?\n",
        "3.  Finally, write the integral that averages this conditional probability over all possible values of $s$, weighted by the probability density of $s$ (which is $\\phi(s)$, the PDF of a standard normal distribution).\n",
        "\n",
        "This will give you the final expression for the probability of a correct classification. The Bayes error is simply $1 - P_{\\text{correct}}$.\n",
        "\n",
        "### Final Result to Expect\n",
        "After completing the steps, you should arrive at the following integral for the probability of a correct classification:\n",
        "$$ P_{\\text{correct}} = \\int_{-\\infty}^{\\infty} \\phi(s) \\left[ \\Phi(\\sqrt{2}t - s) \\right]^{C-1} ds $$\n",
        "where $t=\\frac{\\Delta}{2\\sigma}$, $\\phi(s)$ is the PDF of the standard normal distribution, and $\\Phi(s)$ is its CDF."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bbdfb32c-4e19-4665-a370-b0d4ca1c430d",
      "metadata": {
        "id": "bbdfb32c-4e19-4665-a370-b0d4ca1c430d",
        "outputId": "da38be47-46bc-40f0-a3a9-70cb8c768f6c"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Sweeping C values: 100%|██████████| 6/6 [00:01<00:00,  3.53it/s]\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1200x700 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from scipy.stats import norm\n",
        "from scipy.integrate import quad\n",
        "\n",
        "def bayes_error(C, Delta, sigma):\n",
        "    \"\"\"Calculates the theoretical minimum error rate for the simplex data model.\"\"\"\n",
        "    t = Delta / (2 * sigma)\n",
        "    m = C - 1\n",
        "    def integrand(s):\n",
        "        return norm.pdf(s) * norm.cdf(np.sqrt(2) * t - s)**m\n",
        "    val, _ = quad(integrand, -np.inf, np.inf)\n",
        "    return 1 - val\n",
        "\n",
        "def plot_experimental_vs_theoretical(C_values, d, Delta, sigma, N, n_test, n_seeds):\n",
        "    experimental_f1_scores = []\n",
        "    experimental_errors = []\n",
        "    theoretical_accuracies = []\n",
        "\n",
        "    for C in tqdm(C_values, desc=\"Sweeping C values\"):\n",
        "        mean_f1, std_err = run_simulation_for_C(C, d, Delta, sigma, N, n_test, n_seeds)\n",
        "        experimental_f1_scores.append(mean_f1)\n",
        "        experimental_errors.append(std_err)\n",
        "        theoretical_accuracies.append(bayes_error(C, Delta, sigma))\n",
        "\n",
        "    plt.style.use('seaborn-v0_8-whitegrid')\n",
        "    plt.figure(figsize=(12, 7))\n",
        "\n",
        "    plt.errorbar(C_values, experimental_f1_scores, yerr=experimental_errors, fmt='-o',\n",
        "                 capsize=5, markersize=8, color='royalblue', label='Experimental Nearest-Mean (Macro F1)')\n",
        "    plt.plot(C_values, theoretical_accuracies, '--', color='red', linewidth=2, label='Theoretical Bayes Accuracy')\n",
        "\n",
        "    title = f'Nearest-Mean Performance vs. Theoretical Limit (N={N}, Δ={Delta}, σ={sigma})'\n",
        "    plt.title(title, fontsize=16)\n",
        "    plt.xlabel('C (Number of Classes)', fontsize=12)\n",
        "    plt.ylabel('Error rate', fontsize=12)\n",
        "    plt.xticks(C_values)\n",
        "    plt.ylim(0, 1.05)\n",
        "    plt.legend(fontsize=11)\n",
        "    plt.grid(True, which='both', linestyle='--')\n",
        "    plt.show()\n",
        "\n",
        "# --- Run the Comparison ---\n",
        "# Note: d must be >= C-1. Here d=102, so C can be up to 103.\n",
        "C_values_to_test = list(range(2, 53, 10))\n",
        "\n",
        "plot_experimental_vs_theoretical(\n",
        "    C_values=C_values_to_test,\n",
        "    d=52,\n",
        "    Delta=3.0,\n",
        "    sigma=1.0,\n",
        "    N=50000,\n",
        "    n_test=2000,\n",
        "    n_seeds=3\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "4941e804-c7d9-4672-91f3-b2c96707c7e2",
      "metadata": {
        "id": "4941e804-c7d9-4672-91f3-b2c96707c7e2"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.4"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}