{ "cells": [ { "cell_type": "markdown", "id": "2389b94b", "metadata": {}, "source": [ "## E2 236 Foundations of ML\n", "# Lab 3 Optimization\n", "\n", "## Part A — Robust Regression with Huber Loss via Convex Optimization\n", "\n", "**Learning objectives**\n", "- Derive and implement the Huber loss and its subgradient\n", "- Solve robust regression using:\n", " - Subgradient descent (from scratch)\n", " - CVX / `cvxpy` (convex solver)\n", " - Iteratively Reweighted Least Squares (IRLS)\n", "- Diagnose convexity and compare methods on synthetic data\n", "\n", "**Instructions:** Complete every cell marked `# YOUR CODE HERE`. Do **not** change test assertions.\n", "\n", "---" ] }, { "cell_type": "markdown", "id": "33c6add0", "metadata": {}, "source": [ "## Imports and Setup" ] }, { "cell_type": "code", "execution_count": null, "id": "499e668c", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.gridspec as gridspec\n", "\n", "np.random.seed(42)\n", "%matplotlib inline\n", "plt.rcParams.update({'figure.dpi':110, 'font.size':11})\n", "\n", "# Optional: install cvxpy if not present\n", "# !pip install cvxpy --quiet\n", "try:\n", " import cvxpy as cp\n", " CVXPY = True\n", " print(\"cvxpy available ✓\")\n", "except ImportError:\n", " CVXPY = False\n", " print(\"cvxpy not found — CVX section will be skipped\")\n" ] }, { "cell_type": "markdown", "id": "af1df605", "metadata": {}, "source": [ "## 1. Data Generation\n", "\n", "We generate a synthetic regression dataset with **deliberate outliers** to motivate robust regression.\n", "\n", "**Q1** — Complete the function below:\n", "- Draw $n$ inlier points: $y_i = \\mathbf{x}_i^\\top \\boldsymbol{\\beta}^* + \\varepsilon_i$, where\n", " $\\varepsilon_i \\sim \\mathcal{N}(0, \\sigma^2)$ and $\\mathbf{x}_i \\sim \\mathcal{N}(\\mathbf{0}, I)$.\n", "- Replace `n_outliers` randomly selected $y$-values with large noise drawn from\n", " $\\mathcal{N}(0, (10\\sigma)^2)$.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8fe03c5e", "metadata": {}, "outputs": [], "source": [ "def generate_data(n=150, d=5, sigma=0.5, n_outliers=20, seed=0):\n", " \"\"\"\n", " Generate a regression dataset with Gaussian outliers.\n", "\n", " Returns\n", " -------\n", " X : ndarray (n, d) design matrix (NO bias column)\n", " y : ndarray (n,) noisy targets\n", " beta_star: ndarray (d,) true coefficient vector\n", " outlier_idx: ndarray (int) indices of corrupted observations\n", " \"\"\"\n", " # YOUR CODE HERE\n", " raise NotImplementedError\n", "\n", "\n", "# Generate and inspect\n", "X, y, beta_star, outlier_idx = generate_data()\n", "print(f\"X shape: {X.shape}, y shape: {y.shape}\")\n", "print(f\"True beta: {beta_star}\")\n", "print(f\"Number of outliers: {len(outlier_idx)}\")\n" ] }, { "cell_type": "markdown", "id": "08643c5a", "metadata": {}, "source": [ "## 2. Loss Functions\n", "\n", "### Huber loss\n", "$$\\mathcal{L}_{\\text{Huber}}(\\boldsymbol{\\beta}) = \\frac{1}{n}\\sum_{i=1}^n h_\\delta(y_i - \\mathbf{x}_i^\\top \\boldsymbol{\\beta})$$\n", "\n", "where the per-sample Huber function is\n", "\n", "$$h_\\delta(r) = \\begin{cases}\n", " \\tfrac{1}{2}r^2 & |r| \\le \\delta \\\\\n", " \\delta\\bigl(|r| - \\tfrac{1}{2}\\delta\\bigr) & |r| > \\delta\n", "\\end{cases}$$\n", "\n", "**Q2.1** — Implement the loss function. \n", "**Q2.2** — Show that $h_\\delta$ is convex and that its derivative/subgradient w.r.t. $r$ is\n", "\n", "$$h_\\delta'(r) = \\begin{cases} r & |r| \\le \\delta \\\\ \\delta \\operatorname{sign}(r) & |r| > \\delta \\end{cases}$$\n", "\n", "(Written answer — no code required for Q2.2.)\n" ] }, { "cell_type": "code", "execution_count": null, "id": "4ff12891", "metadata": {}, "outputs": [], "source": [ "\n", "def huber_loss(beta, X, y, delta=1.0):\n", " \"\"\"\n", " Mean Huber loss.\n", "\n", " Parameters\n", " ----------\n", " beta : ndarray (d,)\n", " X : ndarray (n, d)\n", " y : ndarray (n,)\n", " delta : float — transition point\n", "\n", " Returns\n", " -------\n", " loss : float\n", " \"\"\"\n", " # YOUR CODE HERE\n", " raise NotImplementedError\n", "\n", "\n", "def huber_gradient(beta, X, y, delta=1.0):\n", " \"\"\"\n", " Gradient of the mean Huber loss w.r.t. beta.\n", "\n", " Returns\n", " -------\n", " grad : ndarray (d,)\n", " \"\"\"\n", " # YOUR CODE HERE\n", " raise NotImplementedError\n", "\n", "\n", "# --- Sanity checks (do not modify) ---\n", "beta0 = np.zeros(X.shape[1])\n", "assert np.isscalar(ols_loss(beta0, X, y)), \"OLS loss must return a scalar\"\n", "assert np.isscalar(huber_loss(beta0, X, y)), \"Huber loss must return a scalar\"\n", "assert huber_gradient(beta0, X, y).shape == beta0.shape, \"Gradient shape mismatch\"\n", "print(\"Loss function checks passed ✓\")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "4e2e877c", "metadata": {}, "outputs": [], "source": [ "# Q2.3 — Plot h_delta(r) for delta in {0.5, 1.0, 2.0} and compare with |r|\n", "r = np.linspace(-4, 4, 400)\n", "\n", "# YOUR CODE HERE\n", "# Plot h_delta(r) and |r| on the same axes\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "e67bb21e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [] }, { "cell_type": "markdown", "id": "d498b4f1", "metadata": {}, "source": [ "**Q2.2 — Convexity argument (written):**\n", "\n", "> *[Your answer here — show h_δ is convex by checking the second derivative or epigraph.]*\n" ] }, { "cell_type": "markdown", "id": "0d95ae02", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "16915278", "metadata": {}, "source": [ "## 3. Subgradient Descent\n", "\n", "Subgradient descent updates:\n", "$$\\boldsymbol{\\beta}^{(t+1)} = \\boldsymbol{\\beta}^{(t)} - \\eta_t \\, \\nabla_\\beta \\mathcal{L}_{\\text{Huber}}(\\boldsymbol{\\beta}^{(t)})$$\n", "\n", "We use a **diminishing step-size** schedule: $\\eta_t = \\eta_0 / \\sqrt{t+1}$.\n", "\n", "**Q3** — Implement subgradient descent for Huber regression.\n", "Return the parameter history and loss history so we can analyse convergence.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "6a362167", "metadata": {}, "outputs": [], "source": [ "def subgradient_descent_huber(X, y, delta=1.0, eta0=0.1, n_iter=500):\n", " \"\"\"\n", " Subgradient descent for Huber regression.\n", "\n", " Parameters\n", " ----------\n", " X : ndarray (n, d)\n", " y : ndarray (n,)\n", " delta : float Huber threshold\n", " eta0 : float initial step-size\n", " n_iter : int number of iterations\n", "\n", " Returns\n", " -------\n", " beta_hist : ndarray (n_iter+1, d) parameter history (including init)\n", " loss_hist : ndarray (n_iter,) Huber loss at each step\n", " \"\"\"\n", " # YOUR CODE HERE\n", " raise NotImplementedError\n", "\n", "\n", "beta_hist_sgd, loss_hist_sgd = subgradient_descent_huber(X, y)\n", "print(f\"Final Huber loss (subgradient): {loss_hist_sgd[-1]:.4f}\")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8bac5231", "metadata": {}, "outputs": [], "source": [ "# Q3.1 — Plot the convergence curve (loss vs iteration)\n", "# YOUR CODE HERE\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "0bc1f278", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [] }, { "cell_type": "markdown", "id": "bcaad074", "metadata": {}, "source": [ "## 4. Solving with CVXPY (Convex Solver)\n", "\n", "**Q4** — Formulate Huber regression as a CVXPY problem and solve it.\n", "\n", "*Hint:* `cp.huber(expr, M=delta)` returns the element-wise Huber function.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "e012f501", "metadata": {}, "outputs": [], "source": [ "def solve_huber_cvxpy(X, y, delta=1.0):\n", " \"\"\"\n", " Solve Huber regression using CVXPY.\n", "\n", " Returns\n", " -------\n", " beta_cvx : ndarray (d,) or None if cvxpy unavailable\n", " \"\"\"\n", " if not CVXPY:\n", " print(\"cvxpy not available — skipping\")\n", " return None\n", " # YOUR CODE HERE\n", " # Hint: call prob.solve() with NO solver argument —\n", " # CVXPY will automatically select the best installed solver.\n", " # After solving, check prob.status before returning beta.value.\n", " raise NotImplementedError\n", "\n", "\n", "beta_cvx = solve_huber_cvxpy(X, y)\n", "if beta_cvx is not None:\n", " print(f\"CVXPY solution: {beta_cvx}\")\n", " print(f\"True beta: {beta_star}\")\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "492e151d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CVXPY solution: [ 0.462 0.543 1.338 -1.775 1.732]\n", "True beta: [ 0.468 0.527 1.375 -1.815 1.739]\n" ] } ], "source": [] }, { "cell_type": "markdown", "id": "ab024bc3", "metadata": {}, "source": [ "## 5. IRLS for Huber Regression\n", "\n", "Iteratively Reweighted Least Squares (IRLS) exploits the fact that the gradient of the Huber loss can be written as\n", "\n", "$$\\nabla \\mathcal{L} = -\\frac{1}{n} X^\\top W(\\boldsymbol{\\beta})(\\mathbf{y} - X\\boldsymbol{\\beta})$$\n", "\n", "where $W = \\operatorname{diag}(w_i)$ with\n", "\n", "$$w_i = \\begin{cases} 1 & |r_i| \\le \\delta \\\\ \\delta / |r_i| & |r_i| > \\delta \\end{cases}$$\n", "\n", "At each iteration, solve the **weighted** least squares problem:\n", "\n", "$$\\boldsymbol{\\beta}^{(t+1)} = (X^\\top W^{(t)} X)^{-1} X^\\top W^{(t)} \\mathbf{y}$$\n", "\n", "**Q5** — Implement IRLS.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "a89521cc", "metadata": {}, "outputs": [], "source": [ "def irls_huber(X, y, delta=1.0, n_iter=50, tol=1e-6):\n", " \"\"\"\n", " IRLS for Huber regression.\n", "\n", " Returns\n", " -------\n", " beta : ndarray (d,)\n", " loss_hist : list of floats\n", " \"\"\"\n", " # YOUR CODE HERE\n", " raise NotImplementedError\n", "\n", "\n", "beta_irls, loss_hist_irls = irls_huber(X, y)\n", "print(f\"IRLS solution: {beta_irls}\")\n", "print(f\"True beta: {beta_star}\")\n", "print(f\"Final Huber loss (IRLS): {loss_hist_irls[-1]:.4f}\")\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "59f33e69", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "IRLS solution: [ 0.462 0.543 1.338 -1.775 1.732]\n", "True beta: [ 0.468 0.527 1.375 -1.815 1.739]\n", "Final Huber loss (IRLS): 0.5309\n" ] } ], "source": [] }, { "cell_type": "markdown", "id": "0eb0d4c3", "metadata": {}, "source": [ "## 6. Comparison\n", "\n", "**Q6.1** — Fill in the comparison table below. \n", "**Q6.2** — On a single figure, plot:\n", " 1. The OLS fit (closed-form)\n", " 2. Huber fit (IRLS or subgradient)\n", " 3. Data points, highlighting outliers\n", "\n", "Use the **first feature** of $X$ for a 2-D scatter plot (fix remaining features at 0).\n", "\n", "**Q6.3 (written)** — When would you prefer IRLS over the subgradient method, and vice versa?\n" ] }, { "cell_type": "code", "execution_count": null, "id": "9bc8e0de", "metadata": {}, "outputs": [], "source": [ "# OLS closed-form\n", "beta_ols = np.linalg.lstsq(X, y, rcond=None)[0]\n", "\n", "# Q6.1 — Compute errors\n", "for name, beta_hat in [('OLS', beta_ols), ('Huber-SGD', beta_hist_sgd[-1]),\n", " ('Huber-IRLS', beta_irls)]:\n", " mse = np.mean((beta_hat - beta_star)**2)\n", " loss = ols_loss(beta_hat, X, y)\n", " print(f\"{name:12s} | beta MSE: {mse:.4f} | OLS loss: {loss:.4f}\")\n", "\n", "# Q6.2 — 2-D plot\n", "# YOUR CODE HERE\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "ad5bd538", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Method | beta MSE\n", "----------------------------------------\n", "Huber-SGD | 0.0197 \n", "Huber-IRLS | 0.0007 \n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n" ] }, { "cell_type": "markdown", "id": "a6351368", "metadata": {}, "source": [ "**Q6.3 — Written answer:**\n", "\n", "> *[Your answer here]*\n" ] }, { "cell_type": "markdown", "id": "d5827898", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "markdown", "id": "0733df61", "metadata": {}, "source": [ "## 7. Effect of Delta\n", "\n", "**Q7** — Train IRLS for $\\delta \\in \\{0.1, 0.5, 1.0, 2.0, 5.0\\}$ and plot the\n", "final $\\|\\hat{\\boldsymbol{\\beta}} - \\boldsymbol{\\beta}^*\\|_2$ vs $\\delta$.\n", "\n", "**Q7 (written)** — Explain what happens as $\\delta \\to 0$ and $\\delta \\to \\infty$.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "ea04f414", "metadata": {}, "outputs": [], "source": [ "# YOUR CODE HERE\n" ] }, { "cell_type": "code", "execution_count": null, "id": "01da8259", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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