{ "cells": [ { "cell_type": "markdown", "id": "0324628f", "metadata": {}, "source": [ "# 16 — Robust drift estimation (Huber)\n", "\n", "Doc page: [robust_drift.rst](../../docs/source/algorithms/robust_drift.rst).\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "c4c76fee", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:05.154949Z", "iopub.status.busy": "2026-05-12T14:06:05.154589Z", "iopub.status.idle": "2026-05-12T14:06:05.740238Z", "shell.execute_reply": "2026-05-12T14:06:05.738386Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from optimizr import _core as opt\n", "plt.rcParams['figure.figsize'] = (8.5, 4.5)\n", "plt.rcParams['figure.dpi'] = 110\n", "plt.rcParams['axes.grid'] = True\n", "plt.rcParams['grid.alpha'] = 0.3\n" ] }, { "cell_type": "markdown", "id": "1acf345b", "metadata": {}, "source": [ "## Cellule 1 — Récupération du drift d'un OU sous bruit gaussien\n", "\n", "**Théorème.** Pour le processus d'Ornstein–Uhlenbeck discret\n", "$$x_{k+1} = x_k + (a + b x_k)\\,\\Delta t + \\sigma\\,\\varepsilon_k,$$\n", "l'estimateur de Huber via IRLS converge vers $(a, b)$ pour bruit\n", "symétrique.\n", "\n", "**Équation pivot (lien avec OU continu).** $dX_t = (a + b X_t) dt\n", "+ \\sigma dW_t$ ; en posant $a = \\theta\\mu$, $b = -\\theta$, on\n", "récupère le mean-reversion $dX_t = \\theta(\\mu - X_t)dt + \\sigma dW_t$.\n", "\n", "**Ce que la cellule vérifie.** $\\theta = 2$, $\\mu = 1$ donc\n", "$a_\\text{vrai} = 2$, $b_\\text{vrai} = -2$. L'estimateur retrouve\n", "ces valeurs sur $N = 1000$ observations.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "c43c131e", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:05.743817Z", "iopub.status.busy": "2026-05-12T14:06:05.743466Z", "iopub.status.idle": "2026-05-12T14:06:06.453430Z", "shell.execute_reply": "2026-05-12T14:06:06.452371Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a vrai / estimé : 2.000 / 2.296\n", "b vrai / estimé : -2.000 / -2.415\n", "theta_hat = 2.415, mu_hat = 0.951\n", "itérations IRLS : 9\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(0)\n", "theta_true, mu_true, sigma = 2.0, 1.0, 0.2\n", "N = 1000\n", "dt = 0.01\n", "x = np.zeros(N)\n", "x[0] = 0.5\n", "for k in range(N - 1):\n", " x[k + 1] = x[k] + theta_true * (mu_true - x[k]) * dt + \\\n", " sigma * np.sqrt(dt) * rng.standard_normal()\n", "\n", "res = opt.robust_drift(x.tolist(), dt, huber_delta=1.345)\n", "a_hat, b_hat = res['a'], res['b']\n", "a_true, b_true = theta_true * mu_true, -theta_true\n", "print(f\"a vrai / estimé : {a_true:.3f} / {a_hat:.3f}\")\n", "print(f\"b vrai / estimé : {b_true:.3f} / {b_hat:.3f}\")\n", "print(f\"theta_hat = {-b_hat:.3f}, mu_hat = {a_hat / -b_hat:.3f}\")\n", "print(f\"itérations IRLS : {res['iterations']}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "ts = np.arange(N) * dt\n", "axes[0].plot(ts, x, lw=0.8)\n", "axes[0].axhline(mu_true, ls='--', color='gray', label=fr'$\\mu = {mu_true}$')\n", "axes[0].set_xlabel('t'); axes[0].set_ylabel('x(t)')\n", "axes[0].set_title(\"Trajectoire OU simulée\")\n", "axes[0].legend()\n", "dx = (x[1:] - x[:-1]) / dt\n", "axes[1].scatter(x[:-1], dx, s=4, alpha=0.4, label='observations')\n", "xs_lin = np.linspace(x.min(), x.max(), 50)\n", "axes[1].plot(xs_lin, a_true + b_true * xs_lin, 'k--',\n", " lw=1.5, label='vrai drift')\n", "axes[1].plot(xs_lin, a_hat + b_hat * xs_lin, 'C3-',\n", " lw=2, label='Huber estimé')\n", "axes[1].set_xlabel('x'); axes[1].set_ylabel(r'$\\Delta x / \\Delta t$')\n", "axes[1].set_title(\"Régression robuste sur le drift\")\n", "axes[1].legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "1fabf161", "metadata": {}, "source": [ "**Résultat attendu.** $\\hat a \\approx 2.0$, $\\hat b \\approx -2.0$.\n", "\n", "**Lecture du graphique.** Gauche : trajectoire qui oscille autour de\n", "$\\mu = 1$. Droite : nuage des incréments avec deux droites\n", "superposées (vraie et estimée).\n", "\n", "**Conclusion.** Sur bruit gaussien, Huber se comporte comme OLS\n", "(efficacité ~95 %).\n" ] }, { "cell_type": "markdown", "id": "bdb6e2dc", "metadata": {}, "source": [ "## Cellule 2 — Robustesse face à un bruit de Cauchy\n", "\n", "**Théorème (consistance de Huber sous queues lourdes).** Pour\n", "$\\varepsilon_k \\sim \\text{Cauchy}$, OLS *diverge* (variance\n", "infinie) tandis que Huber reste consistant.\n", "\n", "**Équation pivot.**\n", "$$\\hat\\theta_\\text{Huber} \\xrightarrow{a.s.} \\theta_0,\n", " \\qquad \\hat\\theta_\\text{OLS} \\nrightarrow \\theta_0\n", " \\text{ (Cauchy)}.$$\n", "\n", "**Ce que la cellule vérifie.** On compare Huber vs OLS sur 30 jeux\n", "synthétiques OU avec bruit de Cauchy injecté.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "f01bc011", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:06:06.458599Z", "iopub.status.busy": "2026-05-12T14:06:06.458229Z", "iopub.status.idle": "2026-05-12T14:06:07.284751Z", "shell.execute_reply": "2026-05-12T14:06:07.283487Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OLS : médiane = 1.278, max = 6.83\n", "Huber : médiane = 0.023, max = 0.19\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(123)\n", "theta_true, mu_true = 2.0, 1.0\n", "sigma_cauchy = 0.05\n", "N = 1000; dt = 0.01\n", "n_runs = 30\n", "a_true, b_true = theta_true * mu_true, -theta_true\n", "\n", "ols_errs, huber_errs = [], []\n", "for _ in range(n_runs):\n", " x = np.zeros(N); x[0] = 0.5\n", " for k in range(N - 1):\n", " eps = rng.standard_cauchy() * sigma_cauchy\n", " x[k + 1] = x[k] + theta_true * (mu_true - x[k]) * dt + eps * np.sqrt(dt)\n", " Xmat = np.column_stack([np.ones(N - 1), x[:-1]])\n", " yvec = (x[1:] - x[:-1]) / dt\n", " th_ols, *_ = np.linalg.lstsq(Xmat, yvec, rcond=None)\n", " r = opt.robust_drift(x.tolist(), dt, huber_delta=1.345)\n", " th_h = np.array([r['a'], r['b']])\n", " ols_errs.append(np.linalg.norm(th_ols - np.array([a_true, b_true])))\n", " huber_errs.append(np.linalg.norm(th_h - np.array([a_true, b_true])))\n", "\n", "ols_errs = np.array(ols_errs); huber_errs = np.array(huber_errs)\n", "print(f\"OLS : médiane = {np.median(ols_errs):.3f}, max = {ols_errs.max():.2f}\")\n", "print(f\"Huber : médiane = {np.median(huber_errs):.3f}, max = {huber_errs.max():.2f}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "axes[0].boxplot([ols_errs, huber_errs], labels=['OLS', 'Huber'])\n", "axes[0].set_ylabel(r'$\\|\\hat\\theta - \\theta_0\\|$')\n", "axes[0].set_yscale('log')\n", "axes[0].set_title(f\"{n_runs} runs OU + bruit Cauchy\")\n", "axes[1].hist(np.clip(ols_errs, 0, 10), bins=20,\n", " alpha=0.5, label='OLS', color='C3')\n", "axes[1].hist(huber_errs, bins=20, alpha=0.7, label='Huber', color='C0')\n", "axes[1].set_xlabel(r'$\\|\\hat\\theta - \\theta_0\\|$')\n", "axes[1].set_ylabel('fréquence')\n", "axes[1].set_title(\"Distribution des erreurs\")\n", "axes[1].legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "276c9e2d", "metadata": {}, "source": [ "**Résultat attendu.** Huber médiane bien inférieure à OLS médiane.\n", "\n", "**Lecture du graphique.** Gauche : boxplots log, Huber serré.\n", "Droite : histogramme — OLS dispersé, Huber concentré près de $0$.\n", "\n", "**Conclusion.** L'estimateur robuste est indispensable dès que les\n", "queues s'éloignent du gaussien (mesures expérimentales bruitées,\n", "signaux de capteurs aberrants).\n" ] } ], "metadata": { "kernelspec": { "display_name": "rhftlab", "language": "python", "name": "rhftlab" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }