arXiv subjects

Kenyon Ng

Publications and source records attributed to Kenyon Ng.

7 recordsLinked to original sources

arXiv2026

PFN-TS: Thompson Sampling for Contextual Bandits via Prior-Data Fitted Networks

Thompson sampling is a widely used strategy for contextual bandits: at each round, it samples a reward function from a Bayesian posterior and acts greedily under that sample. Prior-data fitted networks (PFNs), such as TabPFN v2+ and TabICL v2, are attractive candidates for this purpose because they approximate Bayesian posterior predictive distributions in a single forward pass. However, PFNs predict noisy future rewards, while Thompson sampling requires uncertainty over the latent mean reward function. We propose PFN-TS, a Thompson sampling algorithm that converts PFN posterior predictives into mean-reward samples using a subsampled predictive central limit theorem. The method estimates posterior variance from a geometric grid of $O(\log n)$ dataset prefixes rather than the full $O(n)$ predictive sequence used in previous predictive-sequence approaches, and reuses TabICL's cached representations across rounds. We prove consistency of the subsampled variance estimator and give a Bayesian regret bound that decomposes PFN-TS regret into exact posterior-sampling regret under the PFN prior plus approximation terms. Empirically, PFN-TS achieves the best average rank across nonlinear synthetic and OpenML classification-to-bandit benchmarks, remains competitive on linear and BART-generated rewards, and attains the highest estimated policy value in an offline mobile-health evaluation. Code is available at https://anonymous.4open.science/r/PFN_TS-36ED/.

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arXiv2026

Uncertainty Decomposition for Bayes-Filtered Transformers via Bayesian Predictive Inference

Bayes-filtered transformers are transformers meta-learned on sequences from a prior predictive distribution to approximate the corresponding posterior predictive distribution. They output total predictive uncertainty in a single forward pass but never explicitly represent a posterior distribution, making the standard route to separating aleatoric from epistemic uncertainty unavailable. We address this challenge through the lens of Bayesian predictive inference (BPI). Our main result is a predictive Central Limit Theorem (CLT) for supervised settings under conditions that are among the weakest known in the BPI literature. The CLT characterises the posterior of the limiting predictive distribution given an observed context as asymptotically Gaussian; the variance of this Gaussian quantifies epistemic uncertainty. We apply the framework to TabPFN, a Bayes-filtered transformer that is a state-of-the-art foundation model for tabular prediction. The resulting credible bands achieve near-nominal frequentist coverage as context length grows, and the decomposition largely matches standard desiderata: epistemic uncertainty shrinks with context length and is highest in sparsely observed regions within the span of the context data, while aleatoric uncertainty dominates near decision boundaries where classes overlap.

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arXiv2025

TabMGP: Martingale Posterior with TabPFN

Bayesian inference provides principled uncertainty quantification but is often limited by the challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these requirements with a predictive rule. In addition, the MGP focuses inference on parameters defined through a loss function. This framework is especially resonant in the era of foundation transformers; practitioners increasingly leverage models like TabPFN for their state-of-the-art capabilities, yet often require epistemic uncertainty for a scientific estimand $\theta$ that need not parameterise the implicit latent model. The MGP provides a mechanism to recover these posterior distributions. We introduce TabMGP, an MGP built on TabPFN for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both handcrafted MGP constructions and standard Bayesian baselines.

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arXiv2025

Expectation-Propagation for Bayesian Empirical Likelihood Inference

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical likelihood offers a semi-parametric alternative by replacing the parametric likelihood with a profile empirical likelihood defined through moment constraints, thereby avoiding explicit distributional assumptions. Despite these advantages, Bayesian empirical likelihood faces substantial computational challenges, including the need to solve a constrained optimization problem for each likelihood evaluation and difficulties with non-convex posterior support, particularly in small-sample settings. This paper introduces a variational approach based on expectation-propagation to approximate the Bayesian empirical-likelihood posterior, balancing computational cost and accuracy without altering the target posterior via adjustments such as pseudo-observations. Empirically, we show that our approach can achieve a superior cost-accuracy trade-off relative to existing methods, including Hamiltonian Monte Carlo and variational Bayes. Theoretically, we show that the approximation and the Bayesian empirical-likelihood posterior are asymptotically equivalent.

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arXiv2024

Pathwise Gradient Variance Reduction with Control Variates in Variational Inference

Variational inference in Bayesian deep learning often involves computing the gradient of an expectation that lacks a closed-form solution. In these cases, pathwise and score-function gradient estimators are the most common approaches. The pathwise estimator is often favoured for its substantially lower variance compared to the score-function estimator, which typically requires variance reduction techniques. However, recent research suggests that even pathwise gradient estimators could benefit from variance reduction. In this work, we review existing control-variates-based variance reduction methods for pathwise gradient estimators to assess their effectiveness. Notably, these methods often rely on integrand approximations and are applicable only to simple variational families. To address this limitation, we propose applying zero-variance control variates to pathwise gradient estimators. This approach offers the advantage of requiring minimal assumptions about the variational distribution, other than being able to sample from it.

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arXiv2024

Temperature Optimization for Bayesian Deep Learning

The Cold Posterior Effect (CPE) is a phenomenon in Bayesian Deep Learning (BDL), where tempering the posterior to a cold temperature often improves the predictive performance of the posterior predictive distribution (PPD). Although the term `CPE' suggests colder temperatures are inherently better, the BDL community increasingly recognizes that this is not always the case. Despite this, there remains no systematic method for finding the optimal temperature beyond grid search. In this work, we propose a data-driven approach to select the temperature that maximizes test log-predictive density, treating the temperature as a model parameter and estimating it directly from the data. We empirically demonstrate that our method performs comparably to grid search, at a fraction of the cost, across both regression and classification tasks. Finally, we highlight the differing perspectives on CPE between the BDL and Generalized Bayes communities: while the former primarily emphasizes the predictive performance of the PPD, the latter prioritizes the utility of the posterior under model misspecification; these distinct objectives lead to different temperature preferences.

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arXiv2019

A flexible sequential Monte Carlo algorithm for parametric constrained regression

An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This algorithm is based on Sequential Monte Carlo-Simulated Annealing and only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing the enforcement of various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. The algorithm is illustrated by fitting rational function and B-spline regression models subject to a monotonicity constraint. An implementation of the algorithm using R is freely available on GitHub.

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