{ "cells": [ { "cell_type": "markdown", "id": "52cce656", "metadata": {}, "source": [ "# Calibrated GLM Posteriors: R-VGA vs. Laplace\n", "\n", "`BayesianGLM` supports non-conjugate likelihoods (logistic, Poisson) by approximating the posterior with a Gaussian. The default strategy is the **Laplace approximation**: find the MAP estimate and match the curvature there. It is fast and usually fine, but for the logit link it has a known bias: the posterior it produces is **too narrow**, and it centers on the mode of a skewed posterior rather than the mean.\n", "\n", "The intuition: the logistic Fisher weight $\\sigma'(\\eta) = \\sigma(\\eta)(1-\\sigma(\\eta))$ peaks at $\\eta = 0$. Laplace evaluates it at a single point (the mode). The **R-VGA** approximation (Lambert, Bonnabel & Bach, 2022) instead averages the curvature over the current posterior, $\\mathbb{E}_q[\\sigma'(\\eta)]$, accounting for the parameter uncertainty the point estimate ignores.\n", "\n", "Per coordinate and per update, the difference is percent-level. It matters anyway, for two compounding reasons:\n", "\n", "1. **Recursion**: a bandit updates one observation at a time, and each update's posterior becomes the next update's prior. A slightly over-shrunk posterior feeds an over-shrunk prior into every subsequent step.\n", "2. **Dimension**: Thompson sampling draws *all* $p$ coefficients jointly. Small per-coordinate underestimation multiplies across coordinates into a meaningfully under-dispersed sample.\n", "\n", "In this notebook we measure both effects: first against the exact (numerically integrated) posterior of a streaming logistic model, then as cumulative regret in a contextual bandit. See the [GLM math reference](../math/glm.rst) for the derivations." ] }, { "cell_type": "code", "execution_count": 1, "id": "ed9cf8de", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T01:06:35.452625Z", "iopub.status.busy": "2026-06-13T01:06:35.451850Z", "iopub.status.idle": "2026-06-13T01:06:36.675025Z", "shell.execute_reply": "2026-06-13T01:06:36.674170Z" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.special import expit\n", "\n", "from bayesianbandits import BayesianGLM, LaplaceApproximator, RVGAApproximator\n", "\n", "rng = np.random.default_rng(3)" ] }, { "cell_type": "markdown", "id": "e668523c", "metadata": {}, "source": [ "## Part 1: Tracking the exact posterior through 150 online updates\n", "\n", "With a single coefficient we can compute the exact posterior on a grid. We stream 150 Bernoulli observations (true weight $w = 1.5$, standard normal prior) through both approximators **one at a time** via `partial_fit`, exactly how a bandit consumes data, and compare each one's posterior to the exact posterior of all data seen so far." ] }, { "cell_type": "code", "execution_count": 2, "id": "c44dd70e", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T01:06:36.678445Z", "iopub.status.busy": "2026-06-13T01:06:36.677855Z", "iopub.status.idle": "2026-06-13T01:06:40.100423Z", "shell.execute_reply": "2026-06-13T01:06:40.099541Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After 150 single-observation updates:\n", " Laplace: mean = 1.245 sd = 0.2156 (sd -9.0% vs exact)\n", " R-VGA: mean = 1.330 sd = 0.2251 (sd -5.0% vs exact)\n", " Exact: mean = 1.303 sd = 0.2368\n" ] } ], "source": [ "TRUE_W = 1.5\n", "N_OBS = 150\n", "\n", "x = rng.standard_normal(N_OBS)\n", "y = rng.binomial(1, expit(TRUE_W * x)).astype(np.float64)\n", "\n", "w_grid = np.linspace(-2.0, 6.0, 8001)\n", "\n", "\n", "def exact_moments(k):\n", " \"\"\"Mean and sd of the exact posterior given the first k observations.\"\"\"\n", " eta = np.outer(w_grid, x[:k])\n", " log_post = np.sum(y[:k] * eta - np.logaddexp(0.0, eta), axis=1) - 0.5 * w_grid**2\n", " p = np.exp(log_post - log_post.max())\n", " p /= np.trapezoid(p, w_grid)\n", " mean = np.trapezoid(w_grid * p, w_grid)\n", " sd = np.sqrt(np.trapezoid((w_grid - mean) ** 2 * p, w_grid))\n", " return mean, sd, p\n", "\n", "\n", "models = {\n", " \"Laplace\": BayesianGLM(alpha=1.0, link=\"logit\", approximator=LaplaceApproximator()),\n", " \"R-VGA\": BayesianGLM(alpha=1.0, link=\"logit\", approximator=RVGAApproximator()),\n", "}\n", "\n", "sd_history = {name: np.empty(N_OBS) for name in models}\n", "exact_sd_history = np.empty(N_OBS)\n", "\n", "for k in range(N_OBS):\n", " exact_sd_history[k] = exact_moments(k + 1)[1]\n", " for name, model in models.items():\n", " model.partial_fit(x[k : k + 1].reshape(1, 1), y[k : k + 1])\n", " sd_history[name][k] = 1.0 / np.sqrt(model.cov_inv_[0, 0])\n", "\n", "exact_mean, exact_sd, exact_density = exact_moments(N_OBS)\n", "print(f\"After {N_OBS} single-observation updates:\")\n", "for name, model in models.items():\n", " sd = sd_history[name][-1]\n", " print(\n", " f\" {name:>8}: mean = {model.coef_[0]:.3f} sd = {sd:.4f}\"\n", " f\" (sd {100 * (sd - exact_sd) / exact_sd:+.1f}% vs exact)\"\n", " )\n", "print(f\" {'Exact':>8}: mean = {exact_mean:.3f} sd = {exact_sd:.4f}\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "002d165a", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T01:06:40.103355Z", "iopub.status.busy": "2026-06-13T01:06:40.102744Z", "iopub.status.idle": "2026-06-13T01:06:40.491406Z", "shell.execute_reply": "2026-06-13T01:06:40.490287Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def gaussian_pdf(w, mean, sd):\n", " return np.exp(-0.5 * ((w - mean) / sd) ** 2) / (sd * np.sqrt(2 * np.pi))\n", "\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(13, 4.5))\n", "\n", "ax1.plot(exact_sd_history, \"k-\", linewidth=2, label=\"Exact\")\n", "ax1.plot(sd_history[\"Laplace\"], \"C3--\", linewidth=2, label=\"Laplace\")\n", "ax1.plot(sd_history[\"R-VGA\"], \"C2-.\", linewidth=2, label=\"R-VGA\")\n", "ax1.set_xlabel(\"observations\")\n", "ax1.set_ylabel(\"posterior sd\")\n", "ax1.set_title(\"Posterior width during online updates\")\n", "ax1.legend()\n", "\n", "ax2.plot(w_grid, exact_density, \"k-\", linewidth=2.5, label=\"Exact posterior\")\n", "for name, color, style in [(\"Laplace\", \"C3\", \"--\"), (\"R-VGA\", \"C2\", \"-.\")]:\n", " model = models[name]\n", " sd = sd_history[name][-1]\n", " ax2.plot(\n", " w_grid,\n", " gaussian_pdf(w_grid, model.coef_[0], sd),\n", " color=color,\n", " linestyle=style,\n", " linewidth=2,\n", " label=f\"{name} (mean {model.coef_[0]:.2f}, sd {sd:.3f})\",\n", " )\n", "ax2.axvline(TRUE_W, color=\"gray\", linestyle=\":\", alpha=0.7)\n", "ax2.set_xlim(0.4, 2.4)\n", "ax2.set_xlabel(\"w\")\n", "ax2.set_ylabel(\"density\")\n", "ax2.set_title(f\"Posterior after {N_OBS} observations\")\n", "ax2.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "004efe0a", "metadata": {}, "source": [ "The Laplace posterior runs consistently below the exact width throughout the stream, and its mean sits below the exact mean (it tracks the mode of a right-skewed posterior). R-VGA tracks both noticeably better with the same per-update cost structure.\n", "\n", "The gaps look small in one dimension. But a Thompson sampler draws all coefficients of the model jointly: if each coordinate's sd is a few percent short, the joint draw is systematically less exploratory than the data justifies, every round, with the deficit compounding through the recursion. Part 2 measures what that costs.\n", "\n", "## Part 2: Cumulative regret under Thompson sampling\n", "\n", "We build a 5-arm contextual bandit with binary rewards: arm $a$ pays out with probability $\\sigma(\\mathbf{x}^\\top \\mathbf{w}_a)$ for a context $\\mathbf{x}$ with 4 features. All arms share one `BayesianGLM` through `LipschitzContextualAgent` with a block-sparse arm featurizer, so the model has $5 \\times 4 = 20$ coefficients and updates one observation at a time.\n", "\n", "The two agents are identical except for the `approximator`." ] }, { "cell_type": "code", "execution_count": 4, "id": "606ebd6c", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T01:06:40.494200Z", "iopub.status.busy": "2026-06-13T01:06:40.493674Z", "iopub.status.idle": "2026-06-13T01:06:40.500232Z", "shell.execute_reply": "2026-06-13T01:06:40.499356Z" } }, "outputs": [], "source": [ "from bayesianbandits import (\n", " Arm,\n", " FunctionArmFeaturizer,\n", " LipschitzContextualAgent,\n", " ThompsonSampling,\n", ")\n", "\n", "N_ARMS = 5\n", "N_FEATURES = 4 # intercept + 3 user features\n", "P = N_ARMS * N_FEATURES\n", "\n", "# Fixed true weights per arm\n", "weight_rng = np.random.default_rng(7)\n", "TRUE_WEIGHTS = weight_rng.normal(0.0, 1.0, (N_ARMS, N_FEATURES))\n", "\n", "\n", "def block_sparse_featurizer(X, action_tokens):\n", " \"\"\"Arm a gets the user features in the a-th block of a K*d vector.\"\"\"\n", " n_contexts = X.shape[0]\n", " result = np.zeros((n_contexts, P, len(action_tokens)))\n", " for i, token in enumerate(action_tokens):\n", " result[:, token * N_FEATURES : (token + 1) * N_FEATURES, i] = X\n", " return result\n", "\n", "\n", "arm_featurizer = FunctionArmFeaturizer(block_sparse_featurizer)\n", "\n", "\n", "def make_agent(approximator, seed):\n", " return LipschitzContextualAgent(\n", " arms=[Arm(action_token=i) for i in range(N_ARMS)],\n", " learner=BayesianGLM(alpha=1.0, link=\"logit\", approximator=approximator),\n", " policy=ThompsonSampling(),\n", " arm_featurizer=arm_featurizer,\n", " random_seed=np.random.default_rng(seed),\n", " )" ] }, { "cell_type": "markdown", "id": "bb343651", "metadata": {}, "source": [ "We run 300 rounds per simulation and 50 paired simulations: within each simulation, both agents see the same context sequence and the same reward randomness, so the per-simulation regret difference isolates the effect of the approximator. Regret each round is the gap between the best arm's payout probability and the chosen arm's." ] }, { "cell_type": "code", "execution_count": 5, "id": "8ea327b0", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T01:06:40.503072Z", "iopub.status.busy": "2026-06-13T01:06:40.502574Z", "iopub.status.idle": "2026-06-13T01:07:04.031071Z", "shell.execute_reply": "2026-06-13T01:07:04.030034Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean cumulative regret after 300 rounds (50 paired sims):\n", " Laplace: 34.4\n", " R-VGA: 32.3\n", " Paired difference: 2.1 ± 0.4 (s.e.) = 6% lower\n" ] } ], "source": [ "N_ROUNDS = 300\n", "N_SIMS = 50\n", "\n", "regret = {\n", " \"Laplace\": np.empty((N_SIMS, N_ROUNDS)),\n", " \"R-VGA\": np.empty((N_SIMS, N_ROUNDS)),\n", "}\n", "\n", "for sim in range(N_SIMS):\n", " sim_rng = np.random.default_rng(1000 + sim)\n", " contexts = np.column_stack(\n", " [np.ones(N_ROUNDS), sim_rng.standard_normal((N_ROUNDS, N_FEATURES - 1))]\n", " )\n", " reward_draws = sim_rng.random((N_ROUNDS, N_ARMS)) # shared across agents\n", "\n", " agents = {\n", " \"Laplace\": make_agent(LaplaceApproximator(), seed=sim),\n", " \"R-VGA\": make_agent(RVGAApproximator(), seed=sim),\n", " }\n", "\n", " for name, agent in agents.items():\n", " for t in range(N_ROUNDS):\n", " context = contexts[[t]]\n", " probs = expit(TRUE_WEIGHTS @ contexts[t])\n", "\n", " (action,) = agent.pull(context)\n", " regret[name][sim, t] = probs.max() - probs[action]\n", "\n", " reward = float(reward_draws[t, action] < probs[action])\n", " agent.select_for_update(action).update(context, np.array([reward]))\n", "\n", "final = {name: np.cumsum(r, axis=1)[:, -1] for name, r in regret.items()}\n", "diff = final[\"Laplace\"] - final[\"R-VGA\"]\n", "se = diff.std(ddof=1) / np.sqrt(N_SIMS)\n", "pct = 100 * diff.mean() / final[\"Laplace\"].mean()\n", "print(f\"Mean cumulative regret after {N_ROUNDS} rounds ({N_SIMS} paired sims):\")\n", "print(f\" Laplace: {final['Laplace'].mean():.1f}\")\n", "print(f\" R-VGA: {final['R-VGA'].mean():.1f}\")\n", "print(f\" Paired difference: {diff.mean():.1f} ± {se:.1f} (s.e.) = {pct:.0f}% lower\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "560102d0", "metadata": { "execution": { "iopub.execute_input": "2026-06-13T01:07:04.034968Z", "iopub.status.busy": "2026-06-13T01:07:04.033636Z", "iopub.status.idle": "2026-06-13T01:07:04.221447Z", "shell.execute_reply": "2026-06-13T01:07:04.220622Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 4.5))\n", "for name, color in [(\"Laplace\", \"C3\"), (\"R-VGA\", \"C2\")]:\n", " cum = np.cumsum(regret[name], axis=1)\n", " mean = cum.mean(axis=0)\n", " se_t = cum.std(axis=0, ddof=1) / np.sqrt(N_SIMS)\n", " ax.plot(mean, color=color, linewidth=2, label=name)\n", " ax.fill_between(\n", " np.arange(N_ROUNDS), mean - se_t, mean + se_t, color=color, alpha=0.2\n", " )\n", "\n", "ax.set_xlabel(\"round\")\n", "ax.set_ylabel(\"cumulative regret\")\n", "ax.set_title(f\"Thompson sampling, {N_ARMS} arms, p = {P} (mean ± s.e., {N_SIMS} sims)\")\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d9878504", "metadata": {}, "source": [ "The agents behave identically in the earliest rounds, where both posteriors are dominated by the prior. The gap opens as data accumulates: the Laplace agent's slightly overconfident posterior commits to arms earlier than the evidence justifies, and some of those commitments are wrong. The improvement is a steady single-digit percentage rather than a dramatic one, which is the honest size of this effect at $p = 20$; it comes essentially for free, and it grows with dimension as the joint draw involves more under-dispersed coordinates.\n", "\n", "## Practical guidance\n", "\n", "- **Drop-in usage**: `BayesianGLM(approximator=RVGAApproximator())`. The default uses an analytical probit approximation for the logit link; pass `use_probit=False` for Gauss-Hermite quadrature when you want maximum accuracy.\n", "- **Cost**: each iteration additionally computes predictive variances. For dense models this is $O(p^2 n)$, negligible once the $O(p^3)$ Cholesky dominates.\n", "- **Log link**: the expected weight $\\mathbb{E}[e^\\eta] = e^{m + v/2}$ is computed in closed form (no quadrature). Note the correction direction flips for the log link: expected curvature is *larger* than point curvature, so R-VGA gives narrower posteriors than Laplace for Poisson models.\n", "- **Large sparse batches**: for `sparse=True`, batches larger than `batch_size` (default 2048) are processed as sequential minibatch updates to bound memory. This is R-VGA's native recursive mode; see the [GLM math reference](../math/glm.rst) for details.\n" ] } ], "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": "3.10.16" } }, "nbformat": 4, "nbformat_minor": 5 }