arXiv subjects

Matthew A. Fisher

Publications and source records attributed to Matthew A. Fisher.

7 recordsLinked to original sources

arXiv2026

A Distributional Optimisation Perspective on Combining Models in Deep Learning

Combining predictions from different models can improve performance at machine learning tasks, but the training of the individual models and the rule used to combine them are typically chosen separately, and by ad hoc means. Recent advances in distributional optimisation (i.e. where the optimisation occurs over the set of probability distributions) offer an opportunity for principled joint training, viewing the collection of models as a discrete distribution whose support points are to be optimised, but the potential of these methods is not well-understood. In this paper we (1) cast two standard combination strategies - ensembles and low-rank adapter averaging - as entropy-regularised distributional optimisation, observing that the resulting objective is convex in the ensemble case but not in the adapter-averaging case, so that existing convergence guarantees for mean field Langevin dynamics transfer only to the former; (2) assess existing and novel algorithms for this task, including a functional variant of variational gradient descent; and (3) report an empirical study spanning synthetic classification tasks and fine-tuning of large language models on a commonsense reasoning benchmark.

cs.LG↗

arXiv2026

Overcoming Model Misspecification in Bayesian Inference of Molecular Signalling Networks

Bayesian inference of molecular signalling networks usually relies on tractability of the marginal likelihood, enabling the set of possible networks to be efficiently explored. As such, linear models with independent errors and conjugate priors are routinely used. However, the dynamics of molecular signalling are nonlinear, and relevant confounders are often unobserved; failure to account for these complexities will almost certainly lead to over-confident inferences in the standard Bayesian framework. To confront this reality, we develop a post-Bayesian approach to inference of molecular signalling networks, guided by the principle that uncertainty should not vanish when the statistical model is misspecified, even in the infinite-data limit. Technically, we extend the predictively-oriented (PrO) posterior of McLatchie et al. (2025) to the setting of latent variable models, empirically investigating the properties of PrO posteriors in the challenging network inference context.

stat.AP↗

arXiv2026

Detecting Model Misspecification in Bayesian Inverse Problems via Variational Gradient Descent

Bayesian inference is optimal when the statistical model is well-specified, while outside this setting Bayesian inference can catastrophically fail; accordingly a wealth of post-Bayesian methodologies have been proposed. Predictively oriented (PrO) approaches lift the statistical model $P_θ$ to an (infinite) mixture model $\int P_θ\; \mathrm{d}Q(θ)$ and fit this predictive distribution via minimising an entropy-regularised objective functional. In the well-specified setting one expects the mixing distribution $Q$ to concentrate around the true data-generating parameter in the large data limit, while such singular concentration will typically not be observed if the model is misspecified. Our contribution is to demonstrate that one can empirically detect model misspecification by comparing the standard Bayesian posterior to the PrO `posterior' $Q$, providing a novel and widely-applicable diagnostic tool for the standard Bayesian workflow. To operationalise this, we present an efficient numerical algorithm based on variational gradient descent. A simulation study, and a more detailed case study involving a Bayesian inverse problem in seismology, confirm that model misspecification can be automatically detected using this framework.

stat.ME↗

arXiv2025

Harnessing the Power of Reinforcement Learning for Adaptive MCMC

Sampling algorithms drive probabilistic machine learning, and recent years have seen an explosion in the diversity of tools for this task. However, the increasing sophistication of sampling algorithms is correlated with an increase in the tuning burden. There is now a greater need than ever to treat the tuning of samplers as a learning task in its own right. In a conceptual breakthrough, Wang et al (2025) formulated Metropolis-Hastings as a Markov decision process, opening up the possibility for adaptive tuning using Reinforcement Learning (RL). Their emphasis was on theoretical foundations; realising the practical benefit of Reinforcement Learning Metropolis-Hastings (RLMH) was left for subsequent work. The purpose of this paper is twofold: First, we observe the surprising result that natural choices of reward, such as the acceptance rate, or the expected squared jump distance, provide insufficient signal for training RLMH. Instead, we propose a novel reward based on the contrastive divergence, whose superior performance in the context of RLMH is demonstrated. Second, we explore the potential of RLMH and present adaptive gradient-based samplers that balance flexibility of the Markov transition kernel with learnability of the associated RL task. A comprehensive simulation study using the posteriordb benchmark supports the practical effectiveness of RLMH.

stat.CO↗

arXiv2025

Fast Approximate Solution of Stein Equations for Post-Processing of MCMC

Bayesian inference is conceptually elegant, but calculating posterior expectations can entail a heavy computational cost. Monte Carlo methods are reliable and supported by strong asymptotic guarantees, but do not leverage smoothness of the integrand. Solving Stein equations has emerged as a possible alternative, providing a framework for numerical approximation of posterior expectations in which smoothness can be exploited. However, existing numerical methods for Stein equations are associated with high computational cost due to the need to solve large linear systems. This paper considers the combination of iterative linear solvers and preconditioning strategies to obtain fast approximate solutions of Stein equations.

stat.CO↗

arXiv2021

GaussED: A Probabilistic Programming Language for Sequential Experimental Design

Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many of the actual computations performed in such software are identical. Motivated by the diverse problems that can in principle be solved with common code, this paper presents GaussED, a simple probabilistic programming language coupled to a powerful experimental design engine, which together automate sequential experimental design for approximating a (possibly nonlinear) quantity of interest in Gaussian processes models. Using a handful of commands, GaussED can be used to: solve linear partial differential equations, perform tomographic reconstruction from integral data and implement Bayesian optimisation with gradient data.

stat.CO↗

arXiv2020

Measure Transport with Kernel Stein Discrepancy

Measure transport underpins several recent algorithms for posterior approximation in the Bayesian context, wherein a transport map is sought to minimise the Kullback--Leibler divergence (KLD) from the posterior to the approximation. The KLD is a strong mode of convergence, requiring absolute continuity of measures and placing restrictions on which transport maps can be permitted. Here we propose to minimise a kernel Stein discrepancy (KSD) instead, requiring only that the set of transport maps is dense in an $L^2$ sense and demonstrating how this condition can be validated. The consistency of the associated posterior approximation is established and empirical results suggest that KSD is competitive and more flexible alternative to KLD for measure transport.

stat.CO↗