{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 5 - Bayes theorem, MLE, MAP, naive Bayes and k-NN\n",
    "\n",
    "In this tutorial, we'll look at the Bayesian view of probability and use it to motivate two simple, but very useful classifiers: **naive Bayes** and **k-nearest neighbors**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats\n",
    "from sklearn.datasets import load_iris, make_moons\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.naive_bayes import CategoricalNB, GaussianNB\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in the previous tutorials, we'll use the Iris dataset for the classification examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Features: ['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
      "Target Classes: ['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "print(f\"Features: {iris.feature_names}\")\n",
    "print(f\"Target Classes: {iris.target_names}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayes' theorem\n",
    "\n",
    "Most of probabilistic machine learning rests on a single identity. For two events $A$ and $B$, the conditional probability is:\n",
    "\n",
    "$$\n",
    "P(A, B) = P(A \\mid B) P(B) = P(B \\mid A) P(A)\n",
    "$$\n",
    "\n",
    "Assuming $P(B) > 0$, we can rewrite this to obtain the Bayes' theorem:\n",
    "\n",
    "$$\n",
    "P(A \\mid B) = \\frac{P(B \\mid A) \\, P(A)}{P(B)}.\n",
    "$$\n",
    "\n",
    "It is just a rearrangement of the definition of conditional probability, but the way we read it matters. In machine learning we usually want to reason about an unknown quantity $\\theta$ (a parameter, a class label, ...) given some observed data $D$:\n",
    "\n",
    "$$\n",
    "\\underbrace{P(\\theta \\mid D)}_{\\text{posterior}}\n",
    "= \\frac{\\overbrace{P(D \\mid \\theta)}^{\\text{likelihood}} \\; \\overbrace{P(\\theta)}^{\\text{prior}}}{\\underbrace{P(D)}_{\\text{evidence}}}.\n",
    "$$\n",
    "\n",
    "- The **prior** $P(\\theta)$ encodes what we believed about $\\theta$ before seeing the data.\n",
    "- The **likelihood** $P(D \\mid \\theta)$ tells us how plausible the data is for a given value of $\\theta$.\n",
    "- The **posterior** $P(\\theta \\mid D)$ is the updated belief after seeing the data.\n",
    "- The **evidence** $P(D) = \\sum_\\theta P(D \\mid \\theta) P(\\theta)$ is just a normalising constant; it does not depend on $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: medical testing\n",
    "\n",
    "A standard introductory example: a disease has prevalence $P(\\text{sick}) = 0.01$ in the population. A test is $99\\%$ sensitive ($P(+ \\mid \\text{sick}) = 0.99$) and $95\\%$ specific ($P(- \\mid \\text{healthy}) = 0.95$). What is the probability that you are actually sick if you tested positive?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(sick | +) = 0.1667\n"
     ]
    }
   ],
   "source": [
    "p_sick = 0.01\n",
    "p_pos_given_sick = 0.99\n",
    "p_pos_given_healthy = 1 - 0.95  # 1 - specificity\n",
    "\n",
    "p_pos = p_pos_given_sick * p_sick + p_pos_given_healthy * (1 - p_sick)\n",
    "p_sick_given_pos = p_pos_given_sick * p_sick / p_pos\n",
    "\n",
    "print(f\"P(sick | +) = {p_sick_given_pos:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we see that even with a positive test, the probability of actually being sick is only about 17%. The low prior dominates the update from the likelihood. This is exactly the kind of intuition Bayes' theorem formalises."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum likelihood vs. maximum a-posteriori estimation\n",
    "\n",
    "Suppose we have data $D = \\{x_1, \\dots, x_n\\}$ assumed to come from a parametric distribution $p(x \\mid \\theta)$ and we want to estimate $\\theta$. There are two natural point estimates:\n",
    "\n",
    "**Maximum likelihood estimation (MLE)**: pick the parameter that makes the observed data most likely:\n",
    "\n",
    "$$\n",
    "\\hat\\theta_\\text{MLE} = \\arg\\max_{\\theta} \\; p(D \\mid \\theta) = \\arg\\max_{\\theta} \\; \\prod_{i=1}^n p(x_i \\mid \\theta).\n",
    "$$\n",
    "\n",
    "**Maximum a-posteriori estimation (MAP)**: combine the likelihood with a prior $p(\\theta)$ and pick the mode of the posterior:\n",
    "\n",
    "$$\n",
    "\\hat\\theta_\\text{MAP} = \\arg\\max_{\\theta} \\; p(\\theta \\mid D) = \\arg\\max_{\\theta} \\; p(D \\mid \\theta) \\, p(\\theta).\n",
    "$$\n",
    "\n",
    "Notice that MLE is the special case of MAP with a uniform prior.\n",
    "\n",
    "In practice we maximise the *log* likelihood (or log posterior), turning products into sums and avoiding numerical underflow."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: estimating the bias of a coin\n",
    "\n",
    "Let $\\theta \\in [0, 1]$ be the probability of heads of a biased coin. We flip it $n$ times and observe $k$ heads. The likelihood is binomial:\n",
    "\n",
    "$$\n",
    "p(D \\mid \\theta) = \\binom{n}{k} \\theta^k (1 - \\theta)^{n-k}.\n",
    "$$\n",
    "\n",
    "Setting the derivative of the log-likelihood to zero gives\n",
    "\n",
    "$$\n",
    "\\hat\\theta_\\text{MLE} = \\frac{k}{n}.\n",
    "$$\n",
    "\n",
    "For MAP we need a prior on $\\theta$. We have two requirements:\n",
    "\n",
    "1. The prior has to be supported on $[0, 1]$ (a probability can't be negative or larger than one). This rules out a Gaussian.\n",
    "2. The prior should be flexible enough to express different beliefs: maybe we suspect the coin is fair, maybe we suspect it's biased toward heads, maybe we have no idea at all.\n",
    "\n",
    "The Beta distribution $\\theta \\sim \\mathrm{Beta}(\\alpha, \\beta)$ with $\\alpha, \\beta > 0$ is the natural choice — it is supported on $[0, 1]$ and its two parameters have a very direct interpretation:\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[\\theta] = \\frac{\\alpha}{\\alpha + \\beta}, \\qquad\n",
    "\\mathrm{Var}[\\theta] = \\frac{\\alpha\\beta}{(\\alpha+\\beta)^2 (\\alpha+\\beta+1)}.\n",
    "$$\n",
    "\n",
    "So $\\alpha / (\\alpha+\\beta)$ controls where we think $\\theta$ lies, and $\\alpha + \\beta$ controls how strongly we believe it: large $\\alpha + \\beta$ gives a sharply peaked prior, small values give a vague one. Special cases:\n",
    "\n",
    "- $\\alpha = \\beta = 1$: uniform on $[0,1]$ — \"I have no idea.\" MAP then coincides with MLE.\n",
    "- $\\alpha = \\beta \\gg 1$: peaked at $0.5$ — \"I strongly believe the coin is fair.\"\n",
    "- $\\alpha \\gg \\beta$: skewed toward $1$ — \"I expect mostly heads.\"\n",
    "\n",
    "A useful way to set the parameters is a pseudo-count interpretation: $\\mathrm{Beta}(\\alpha, \\beta)$ behaves as if we had already seen $\\alpha - 1$ heads and $\\beta - 1$ tails before any real data. So if we would only feel confident about a coin's bias after $\\sim 20$ flips, we should pick $\\alpha + \\beta \\approx 20$; if we would need $\\sim 200$, we shoukd pick $\\alpha + \\beta \\approx 200$. This gives us a rule for translating \"how much do I trust my prior?\" into $\\alpha$ and $\\beta$. This is generally a sound approach, picking the prior from something that we know to be realistic.\n",
    "\n",
    "With the Beta in hand the MAP derivation proceeds as before, and we get a happy bonus: the posterior turns out to also be Beta,\n",
    "\n",
    "$$\n",
    "p(\\theta \\mid D) \\propto \\theta^{k + \\alpha - 1} (1 - \\theta)^{n - k + \\beta - 1} = \\mathrm{Beta}(k + \\alpha, ; n - k + \\beta).\n",
    "$$\n",
    "\n",
    "A prior whose family is preserved under Bayesian updating is called conjugate to the likelihood; Beta is conjugate to the binomial. Conjugacy gives our choice of the prior mathematical cleanliness, but isn't required.\n",
    "\n",
    "The mode of $\\mathrm{Beta}(a, b)$ for $a, b > 1$ is $(a - 1) / (a + b - 2)$, so\n",
    "\n",
    "$$\n",
    "\\hat\\theta_\\text{MAP} = \\frac{k + \\alpha - 1}{n + \\alpha + \\beta - 2}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLE estimate of P(heads) = 0.700\n",
      "MAP estimate of P(heads) = 0.567  (with Beta(11,11) prior)\n"
     ]
    }
   ],
   "source": [
    "# Suppose we observe 7 heads out of 10 flips of a coin we suspect is fair.\n",
    "n, k = 10, 7\n",
    "\n",
    "# Prior: Beta(11, 11) -- centred on 0.5, fairly informative (20 pseudo-flips).\n",
    "prior_heads = 10\n",
    "prior_tails = 10\n",
    "alpha, beta = prior_heads + 1, prior_tails + 1\n",
    "\n",
    "theta_mle = k / n\n",
    "theta_map = (k + alpha - 1) / (n + alpha + beta - 2)\n",
    "\n",
    "print(f\"MLE estimate of P(heads) = {theta_mle:.3f}\")\n",
    "print(f\"MAP estimate of P(heads) = {theta_map:.3f}  (with Beta({alpha},{beta}) prior)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualise prior, likelihood and posterior across a range of theta values.\n",
    "theta_grid = np.linspace(0, 1, 500)\n",
    "\n",
    "prior = stats.beta.pdf(theta_grid, alpha, beta)\n",
    "likelihood = stats.binom.pmf(k, n, theta_grid)\n",
    "likelihood = likelihood / np.trapezoid(likelihood, theta_grid)  # normalise for plotting\n",
    "posterior = stats.beta.pdf(theta_grid, k + alpha, n - k + beta)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax.plot(theta_grid, prior, label=f\"prior  Beta({alpha},{beta})\", linestyle=\"--\")\n",
    "ax.plot(theta_grid, likelihood, label=\"likelihood (normalised)\", linestyle=\":\")\n",
    "ax.plot(theta_grid, posterior, label=f\"posterior  Beta({k+alpha},{n-k+beta})\")\n",
    "ax.axvline(theta_mle, color=\"C1\", linestyle=\":\", alpha=0.6, label=f\"MLE = {theta_mle:.2f}\")\n",
    "ax.axvline(theta_map, color=\"C2\", linestyle=\"-.\", alpha=0.6, label=f\"MAP = {theta_map:.2f}\")\n",
    "ax.set_xlabel(r\"$\\theta$ = P(heads)\")\n",
    "ax.set_ylabel(\"density\")\n",
    "ax.set_title(\"Prior, likelihood and posterior for the coin example\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the MAP estimate sits between the MLE (driven only by the data) and the prior mean ($0.5$). As we collect more data the likelihood becomes much sharper than the prior, and the two estimates converge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 1\n",
    "\n",
    "A common task is estimating the mean of a Gaussian when we already have prior knowledge about it. Assume $x_1, \\dots, x_n \\sim \\mathcal{N}(\\mu, \\sigma^2)$ with **known** variance $\\sigma^2$ and a Gaussian prior $\\mu \\sim \\mathcal{N}(\\mu_0, \\tau^2)$.\n",
    "\n",
    "Implement the two functions below:\n",
    "\n",
    "1. `gaussian_mle(samples)` — return $\\hat\\mu_\\text{MLE}$.\n",
    "2. `gaussian_map(samples, sigma_square, mu0, tau_square)` — return $\\hat\\mu_\\text{MAP}$.\n",
    "\n",
    "For the MAP estimate, derive the posterior. Since the Gaussian is its own conjugate prior, the posterior is again Gaussian and its mean (which is also the mode) is\n",
    "\n",
    "$$\n",
    "\\hat\\mu_\\text{MAP}\n",
    "= \\frac{\\frac{n}{\\sigma^2} \\bar x + \\frac{1}{\\tau^2} \\mu_0}{\\frac{n}{\\sigma^2} + \\frac{1}{\\tau^2}}\n",
    "\\; ,\n",
    "$$\n",
    "\n",
    "i.e. a precision-weighted average of the sample mean $\\bar x$ and the prior mean $\\mu_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=  3  MLE=5.671  MAP=2.430  (true mu=5.0)\n",
      "n= 30  MLE=4.639  MAP=4.093  (true mu=5.0)\n",
      "n=300  MLE=5.069  MAP=5.002  (true mu=5.0)\n"
     ]
    }
   ],
   "source": [
    "def gaussian_mle(samples):\n",
    "    return float(np.mean(samples))\n",
    "\n",
    "\n",
    "def gaussian_map(samples, sigma_square, mu0, tau_square):\n",
    "    n = len(samples)\n",
    "    x_bar = np.mean(samples)\n",
    "    precision_data = n / sigma_square\n",
    "    precision_prior = 1 / tau_square\n",
    "    return float((precision_data * x_bar + precision_prior * mu0) / (precision_data + precision_prior))\n",
    "\n",
    "\n",
    "# Truth: mu = 5, sigma^2 = 4. Prior: weakly centred on 0 with tau^2 = 1.\n",
    "true_mu, sigma_square = 5.0, 4.0\n",
    "mu0, tau_square = 0.0, 1.0\n",
    "\n",
    "for n in [3, 30, 300]:\n",
    "    samples = np.random.normal(true_mu, np.sqrt(sigma_square), size=n)\n",
    "    print(f\"n={n:>3d}  MLE={gaussian_mle(samples):.3f}  \"\n",
    "          f\"MAP={gaussian_map(samples, sigma_square, mu0, tau_square):.3f}  (true mu={true_mu})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With only a handful of samples the MAP estimate is heavily pulled toward the prior mean ($0$); as $n$ grows it concentrates on the true mean and matches the MLE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes classifier\n",
    "\n",
    "We can use Bayes' theorem directly to build a classifier. Given a feature vector $\\mathbf{x} = (x_1, \\dots, x_d)$ and a class label $y \\in \\{1, \\dots, K\\}$:\n",
    "\n",
    "$$\n",
    "P(y \\mid \\mathbf{x}) = \\frac{P(\\mathbf{x} \\mid y) \\, P(y)}{P(\\mathbf{x})}.\n",
    "$$\n",
    "\n",
    "To classify, we pick the class with the highest posterior:\n",
    "\n",
    "$$\n",
    "\\hat y = \\arg\\max_{y} \\; P(y \\mid \\mathbf{x}) = \\arg\\max_{y} \\; P(\\mathbf{x} \\mid y) \\, P(y).\n",
    "$$\n",
    "\n",
    "The hard part is modelling the joint $P(\\mathbf{x} \\mid y)$. Naive Bayes makes the **conditional independence assumption**: features are independent given the class. This is rarely true in practice (that's why it's called \"naive\"), but it makes the model simpler to calculate:\n",
    "\n",
    "$$\n",
    "P(\\mathbf{x} \\mid y) \\approx \\prod_{j=1}^{d} P(x_j \\mid y).\n",
    "$$\n",
    "\n",
    "For continuous features (like the Iris measurements) we model each $P(x_j \\mid y)$ as a univariate Gaussian fitted by MLE on the training data — this is **Gaussian naive Bayes**:\n",
    "\n",
    "$$\n",
    "P(x_j \\mid y) = \\frac{1}{\\sqrt{2\\pi \\sigma_{j,y}^2}} \\exp\\!\\left(-\\frac{(x_j - \\mu_{j,y})^2}{2 \\sigma_{j,y}^2}\\right).\n",
    "$$\n",
    "\n",
    "We compare log-posteriors (again, sums are nicer than products):\n",
    "\n",
    "$$\n",
    "\\log P(y \\mid \\mathbf{x}) \\;\\propto\\; \\log P(y) + \\sum_{j=1}^{d} \\log P(x_j \\mid y).\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.95\n",
      "Test accuracy:  1.00\n"
     ]
    }
   ],
   "source": [
    "model_nb_sklearn = GaussianNB()\n",
    "model_nb_sklearn.fit(X_train, y_train)\n",
    "\n",
    "print(f\"Train accuracy: {accuracy_score(y_train, model_nb_sklearn.predict(X_train)):.2f}\")\n",
    "print(f\"Test accuracy:  {accuracy_score(y_test, model_nb_sklearn.predict(X_test)):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 2\n",
    "\n",
    "Implement Gaussian naive Bayes from scratch. Fill in `fit` and `predict` below.\n",
    "\n",
    "- In `fit`, estimate the per-class prior (probability a random sample is of this class), mean and variance for every feature using MLE.\n",
    "- In `predict`, return the class with the highest log-posterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyGaussianNB:\n",
    "    def __init__(self):\n",
    "        self.classes_ = None\n",
    "        self.priors_ = None\n",
    "        self.means_ = None\n",
    "        self.variances_ = None\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        self.classes_ = np.unique(y)\n",
    "        n_classes = len(self.classes_)\n",
    "        n_features = X.shape[1]\n",
    "\n",
    "        self.priors_ = np.zeros(n_classes)\n",
    "        self.means_ = np.zeros((n_classes, n_features))\n",
    "        self.variances_ = np.zeros((n_classes, n_features))\n",
    "\n",
    "        for idx, cls in enumerate(self.classes_):\n",
    "            X_cls = X[y == cls]\n",
    "            self.priors_[idx] = X_cls.shape[0] / X.shape[0]\n",
    "            self.means_[idx] = X_cls.mean(axis=0)\n",
    "            # Add a tiny epsilon for stability.\n",
    "            self.variances_[idx] = X_cls.var(axis=0) + 1e-9\n",
    "\n",
    "    def predict(self, X):\n",
    "        log_priors = np.log(self.priors_)  # shape (n_classes,)\n",
    "        # log-likelihood per sample, class, feature -- then sum over features.\n",
    "        # Broadcasting: X[:, None, :] has shape (n_samples, 1, n_features).\n",
    "        diff = X[:, None, :] - self.means_[None, :, :]\n",
    "        log_likelihood = -0.5 * (np.log(2 * np.pi * self.variances_) + diff**2 / self.variances_)\n",
    "        log_posterior = log_priors + log_likelihood.sum(axis=2)\n",
    "        return self.classes_[np.argmax(log_posterior, axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.95\n",
      "Test accuracy:  1.00\n"
     ]
    }
   ],
   "source": [
    "model_nb_manual = MyGaussianNB()\n",
    "model_nb_manual.fit(X_train, y_train)\n",
    "\n",
    "print(f\"Train accuracy: {accuracy_score(y_train, model_nb_manual.predict(X_train)):.2f}\")\n",
    "print(f\"Test accuracy:  {accuracy_score(y_test, model_nb_manual.predict(X_test)):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discrete features and Laplace smoothing\n",
    "\n",
    "The Iris features are continuous and Gaussian NB worked well. But naive Bayes is also commonly used with **discrete** features, for example, in document classification where each $x_j \\in \\{0, 1\\}$ indicates whether word $j$ appears in the text.\n",
    "\n",
    "For categorical features we estimate $P(x_j = v \\mid y)$ directly from training counts:\n",
    "\n",
    "$$\n",
    "\\hat P(x_j = v \\mid y = c) = \\frac{N_{c, j, v}}{N_c},\n",
    "$$\n",
    "\n",
    "where $N_{c,j,v}$ is the number of training examples with class $c$ and feature value $v$ at position $j$, and $N_c$ is the number of training examples in class $c$. This MLE has a failure mode: if some value $v$ is **never observed** for class $c$ in training, $\\hat P(x_j = v \\mid y = c) = 0$, which makes the *whole* product $\\prod_j P(x_j \\mid y = c)$ collapse to zero. Class $c$ then gets ruled out for any test point with that value, no matter how strong the evidence from the other features.\n",
    "\n",
    "The standard fix is **Laplace smoothing** (also called add-$\\alpha$ / additive smoothing): pretend you saw $\\alpha$ extra examples of every value in every class.\n",
    "\n",
    "$$\n",
    "\\hat P(x_j = v \\mid y = c) = \\frac{N_{c, j, v} + \\alpha}{N_c + \\alpha \\cdot K_j},\n",
    "$$\n",
    "\n",
    "where $K_j$ is the number of possible values of feature $j$. With $\\alpha = 1$ (\"add-one\"), no probability is ever exactly zero. As an aside, this is exactly the **MAP estimate** of $P(x_j \\mid y = c)$ under a symmetric $\\mathrm{Dir}(\\alpha, \\dots, \\alpha)$ prior. As usual, the prior matters most with low data, with enough data the smoothing term is negligible.\n",
    "\n",
    "The cleanest way to see why this matters is a small toy \"spam classifier\" with three binary features (think: presence/absence of three keywords). In the training set below, the third keyword *never* appears in spam — so the MLE assigns it probability zero. A test email containing that keyword then has spam posterior collapse to zero, no matter what the other two features say."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha~=0 (no smoothing)  log P(ham|x)=  -0.00  log P(spam|x)= -24.12  -> ham\n",
      "alpha=1 (Laplace)     log P(ham|x)=  -0.22  log P(spam|x)=  -1.61  -> ham\n"
     ]
    }
   ],
   "source": [
    "# Toy 'spam' dataset: 3 binary features, 2 classes. Crucially, feature 2 is\n",
    "# never 1 for any spam example -- so MLE estimates P(x_2=1 | spam) = 0.\n",
    "X_toy = np.array([\n",
    "    [1, 0, 1],  # ham\n",
    "    [0, 1, 1],  # ham\n",
    "    [1, 1, 1],  # ham\n",
    "    [1, 0, 0],  # spam\n",
    "    [0, 1, 0],  # spam\n",
    "    [1, 1, 0],  # spam\n",
    "])\n",
    "y_toy = np.array([0, 0, 0, 1, 1, 1])  # 0 = ham, 1 = spam\n",
    "class_names = [\"ham\", \"spam\"]\n",
    "\n",
    "# A new email that has feature 2 = 1. Under unsmoothed MLE the spam posterior\n",
    "# becomes zero regardless of the rest of the features.\n",
    "x_new = np.array([[1, 0, 1]])\n",
    "\n",
    "for alpha, label in [(1e-10, \"alpha~=0 (no smoothing)\"), (1.0, \"alpha=1 (Laplace)   \")]:\n",
    "    model = CategoricalNB(alpha=alpha, force_alpha=True, min_categories=2)\n",
    "    model.fit(X_toy, y_toy)\n",
    "    log_probs = model.predict_log_proba(x_new)[0]\n",
    "    pred = class_names[int(model.predict(x_new)[0])]\n",
    "    print(f\"{label}  log P(ham|x)={log_probs[0]:7.2f}  log P(spam|x)={log_probs[1]:7.2f}  -> {pred}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k-nearest neighbors classifier\n",
    "\n",
    "Naive Bayes assumes a parametric family for $P(\\mathbf{x} \\mid y)$. **k-nearest neighbors** (k-NN) takes the opposite, fully *non-parametric* route: it does not assume any shape for the data distribution and stores the entire training set instead.\n",
    "\n",
    "To classify a new point $\\mathbf{x}$:\n",
    "\n",
    "1. Compute the distance from $\\mathbf{x}$ to every training sample (typically Euclidean).\n",
    "2. Pick the $k$ closest training points.\n",
    "3. Predict the most common label among them (majority vote).\n",
    "\n",
    "This can be motivated by Bayes' rule too: the local fraction of class $y$ among the $k$ neighbors is an estimate of $P(y \\mid \\mathbf{x})$. Picking the most common label is then approximately the MAP class.\n",
    "\n",
    "The hyperparameter $k$ controls the bias–variance trade-off:\n",
    "- small $k$ — flexible, low bias, high variance (sensitive to noise);\n",
    "- large $k$ — smoother decision boundary, higher bias, lower variance.\n",
    "\n",
    "Distances are sensitive to feature scaling, so in practice you usually standardise the features before running k-NN. We skip that here because Iris features are already on similar scales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.97\n",
      "Test accuracy:  1.00\n"
     ]
    }
   ],
   "source": [
    "model_knn_sklearn = KNeighborsClassifier(n_neighbors=5)\n",
    "model_knn_sklearn.fit(X_train, y_train)\n",
    "\n",
    "print(f\"Train accuracy: {accuracy_score(y_train, model_knn_sklearn.predict(X_train)):.2f}\")\n",
    "print(f\"Test accuracy:  {accuracy_score(y_test, model_knn_sklearn.predict(X_test)):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 3\n",
    "\n",
    "Implement k-NN from scratch. Use Euclidean distance and break ties by picking the smallest class label (this is what `np.bincount(...).argmax()` does)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyKNN:\n",
    "    def __init__(self, n_neighbors=5):\n",
    "        self.n_neighbors = n_neighbors\n",
    "        self.X_train = None\n",
    "        self.y_train = None\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        # k-NN is a lazy learner -- \"training\" just stores the data.\n",
    "        self.X_train = X\n",
    "        self.y_train = y\n",
    "\n",
    "    def predict(self, X):\n",
    "        # Pairwise Euclidean distances: shape (n_test, n_train).\n",
    "        diff = X[:, None, :] - self.X_train[None, :, :]\n",
    "        distances = np.sqrt((diff ** 2).sum(axis=2))\n",
    "\n",
    "        predictions = np.empty(X.shape[0], dtype=self.y_train.dtype)\n",
    "        for i in range(X.shape[0]):\n",
    "            neighbor_idx = np.argsort(distances[i])[:self.n_neighbors]\n",
    "            neighbor_labels = self.y_train[neighbor_idx]\n",
    "            predictions[i] = np.bincount(neighbor_labels).argmax()\n",
    "        return predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.97\n",
      "Test accuracy:  1.00\n"
     ]
    }
   ],
   "source": [
    "model_knn_manual = MyKNN(n_neighbors=5)\n",
    "model_knn_manual.fit(X_train, y_train)\n",
    "\n",
    "print(f\"Train accuracy: {accuracy_score(y_train, model_knn_manual.predict(X_train)):.2f}\")\n",
    "print(f\"Test accuracy:  {accuracy_score(y_test, model_knn_manual.predict(X_test)):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of $k$\n",
    "\n",
    "Iris is too easy to expose the bias–variance trade-off. To see the trade-off in action we'll switch to the synthetic *two moons* dataset: two interleaved half-circles with Gaussian noise, where the boundary is genuinely fuzzy and $k$ matters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_moons, y_moons = make_moons(n_samples=350, noise=0.3, random_state=1)\n",
    "X_moons_train, X_moons_test = X_moons[:150], X_moons[150:]\n",
    "y_moons_train, y_moons_test = y_moons[:150], y_moons[150:]\n",
    "\n",
    "ks = list(range(1, 51, 2))\n",
    "train_acc, test_acc = [], []\n",
    "for k in ks:\n",
    "    model = MyKNN(n_neighbors=k)\n",
    "    model.fit(X_moons_train, y_moons_train)\n",
    "    train_acc.append(accuracy_score(y_moons_train, model.predict(X_moons_train)))\n",
    "    test_acc.append(accuracy_score(y_moons_test, model.predict(X_moons_test)))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax.plot(ks, train_acc, marker=\"o\", label=\"train accuracy\")\n",
    "ax.plot(ks, test_acc, marker=\"s\", label=\"test accuracy\")\n",
    "ax.set_xlabel(\"k\")\n",
    "ax.set_ylabel(\"accuracy\")\n",
    "ax.set_title(\"k-NN accuracy on the two-moons dataset as a function of k\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $k = 1$ the train accuracy is exactly $1$ (each training point is its own nearest neighbor) but the test accuracy is the worst on the curve — the model has memorised the noise. As $k$ grows the decision boundary smooths out: the training accuracy drops (we are no longer memorising) and the test accuracy improves, peaking somewhere in the middle. Past that peak, $k$ becomes so large that we're averaging over points from the wrong class and accuracy starts to drop again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generative vs. discriminative classifiers\n",
    "\n",
    "Naive Bayes and k-NN are useful representatives of two opposing philosophies of classification.\n",
    "\n",
    "**Generative classifiers** model the *joint* distribution $p(\\mathbf{x}, y) = p(\\mathbf{x} \\mid y) p(y)$ and then use Bayes' theorem to recover the posterior $p(y \\mid \\mathbf{x})$. Once you have the joint, you can do anything with it: sample new $\\mathbf{x}$, detect outliers, fill in missing features by marginalisation. The cost is that you have to commit to a model of $p(\\mathbf{x} \\mid y)$, and a wrong model can hurt classification even when a much simpler discriminative model would have nailed it. Naive Bayes (in any of its variants) is generative - that's exactly why we need to specify a Gaussian / Bernoulli / categorical likelihood per feature.\n",
    "\n",
    "**Discriminative classifiers** model the conditional $p(y \\mid \\mathbf{x})$ (or just the decision boundary) directly, without bothering to model how $\\mathbf{x}$ is distributed. They tend to give better classification accuracy when data is plentiful, but can't generate new data and don't natively handle missing features. Logistic regression is the canonical discriminative classifier. k-NN is a bit of astrange example of this family as well: it doesn't model anything explicitly, but its output is a local non-parametric estimate of $p(y \\mid \\mathbf{x})$, which puts it on the discriminative side in spirit.\n",
    "\n",
    "A useful rule of thumb (Ng & Jordan, 2001): generative models tend to converge faster,but discriminative models eventually win as $n$ grows, because they don't waste capacity modelling $\\mathbf{x}$ and they're robust when the generative assumption (e.g. conditional independence in naive Bayes) is wrong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualising decision boundaries\n",
    "\n",
    "A 2D projection (petal length × petal width) makes the parametric vs. non-parametric distinction very visual. Gaussian NB carves the plane with smooth quadratic curves — that's the shape of the boundary between two Gaussian densities with different means and variances. k-NN produces a piecewise-linear, Voronoi-like boundary that follows the data points instead of any global density model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "feat_idx = [2, 3]  # petal length, petal width\n",
    "X_train_2d = X_train[:, feat_idx]\n",
    "X_test_2d = X_test[:, feat_idx]\n",
    "\n",
    "models_2d = {\n",
    "    \"Gaussian naive Bayes\": GaussianNB().fit(X_train_2d, y_train),\n",
    "    \"k-NN (k=5)\": KNeighborsClassifier(n_neighbors=5).fit(X_train_2d, y_train),\n",
    "}\n",
    "\n",
    "x_min, x_max = X_train_2d[:, 0].min() - 0.5, X_train_2d[:, 0].max() + 0.5\n",
    "y_min, y_max = X_train_2d[:, 1].min() - 0.5, X_train_2d[:, 1].max() + 0.5\n",
    "xx, yy = np.meshgrid(np.linspace(x_min, x_max, 300), np.linspace(y_min, y_max, 300))\n",
    "grid = np.column_stack([xx.ravel(), yy.ravel()])\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 5), sharex=True, sharey=True)\n",
    "for ax, (name, model) in zip(axes, models_2d.items()):\n",
    "    Z = model.predict(grid).reshape(xx.shape)\n",
    "    ax.contourf(xx, yy, Z, alpha=0.3, levels=np.arange(-0.5, 3.5), cmap=\"viridis\")\n",
    "    ax.scatter(X_train_2d[:, 0], X_train_2d[:, 1], c=y_train, edgecolor=\"k\", cmap=\"viridis\", s=40)\n",
    "    ax.set_xlabel(iris.feature_names[feat_idx[0]])\n",
    "    ax.set_ylabel(iris.feature_names[feat_idx[1]])\n",
    "    ax.set_title(name)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "nsn",
   "language": "python",
   "name": "nsn"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
