Schedule 2025/26

Here is the schedule for the 2025/26 academic year.

Michaelmas Term

Date Speaker Title Links
11 Dec 2025 Zheyang Shen Newcastle University A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives
▶ Abstract
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an explicit unnormalised density for the target. To mitigate this difficulty, we introduce a novel measure of suboptimality called 'gradient discrepancy', and in particular a 'kernel' gradient discrepancy (KGD) that can be explicitly computed. In the standard Bayesian context, KGD coincides with the kernel Stein discrepancy (KSD), and we obtain a novel characterisation of KSD as measuring the size of a variational gradient. Outside this familiar setting, KGD enables novel sampling algorithms to be developed and compared, even when unnormalised densities cannot be obtained. To illustrate this point several novel algorithms are proposed and studied, including a natural generalisation of Stein variational gradient descent, with applications to mean-field neural networks and predictively oriented posteriors presented. On the theoretical side, our principal contribution is to establish sufficient conditions for desirable properties of KGD, such as continuity and convergence control.

Lent Term

Date Speaker Title Links
15 Jan 2026 Hefin Lambley University of Warwick Autoencoders in function space
▶ Abstract
We propose function-space versions of autoencoders—machine-learning methods for dimension reduction and generative modelling—in both their deterministic (FAE) and variational (FVAE) forms. Formulating autoencoder objectives in function space enables training and evaluation with data discretised at arbitrary resolutions, leading to new applications such as inpainting, superresolution, and generative modelling. We discuss the technical challenges of formulating autoencoders in infinite dimension. A key issue is that FVAE's variational inference is often ill defined, unlike in finite dimensions, limiting its applicability. We then explore specific problem classes where FVAE remains useful. We contrast this with the FAE objective, which remains well defined in many situations where FVAE fails, making it a robust and versatile alternative. We demonstrate both methods on scientific data sets, including Navier--Stokes fluid flow simulations. This is joint work with Justin Bunker and Mark Girolami (Cambridge), Andrew M. Stuart (Caltech) and T. J. Sullivan (Warwick).
 arXiv
22 Jan 2026 Yuga Iguchi Lancaster University
29 Jan 2026 William Laplante University College London Conjugate Generalised Bayesian Inference for Discrete Doubly Intractable Problems
▶ Abstract
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation of the posterior through specialised and typically expensive MCMC methods. In this paper, we provide a computationally efficient alternative in the form of a novel generalised Bayesian posterior that allows for conjugate inference within the class of exponential family models for discrete data. We derive theoretical guarantees to characterise the asymptotic behaviour of the generalised posterior, supporting its use for inference. The method is evaluated on a range of challenging intractable exponential family models, including the Conway-Maxwell-Poisson graphical model of multivariate count data, autoregressive discrete time series models, and Markov random fields such as the Ising and Potts models. The computational gains are significant; in our experiments, the method is between 10 and 6000 times faster than state-of-the-art Bayesian computational methods.
 arXiv
5 Feb 2026 Chris Sherlock Lancaster University
12 Feb 2026 Abiel Talwar Lancaster University
19 Feb 2026 Matthias Sachs Lancaster University
26 Feb 2026 Jonas Latz University of Manchester Sparse Techniques for Regression in Deep Gaussian Processes
▶ Abstract
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. GPs suffer when the amount of training data is large or when the underlying function contains multiscale features that are difficult to represent by an isotropic kernel. The training of GPs with large scale data is often performed through inducing point approximations (also known as sparse GP regression), where the size of the covariance matrices in GP regression is reduced considerably through a greedy search on the data set. Deep Gaussian processes have recently been introduced as hierarchical models that resolve multi-scale features by composing multiple Gaussian processes. Whilst GPs can be trained through a simple analytical formula, deep GPs require a sampling or, more usual, a variational approximation. Variational approximations lead to large-scale stochastic, non-convex optimisation problems and the resulting approximation tends to represent uncertainty incorrectly. In this work, we combine variational learning with MCMC to develop a particle-based expectation-maximisation method to simultaneously find inducing points within the large-scale data (variationally) and accurately train the Gaussian processes (sampling-based). The result is a highly efficient and accurate methodology for deep GP training on large scale data. We test the method on standard benchmark problems. Joint work with Aretha Teckentrup and Simon Urbainczyk.
 Paper 1 Paper 2
5 Mar 2026 Paul Fearnhead Lancaster University
12 Mar 2026 Chen Qi Aalto University
19 Mar 2026 Liam Llamazares-Elias Lancaster University
23 Apr 2026 Rui Zhang Lancaster University
30 Apr 2026 Masha Naslidnyk University College London Kernel Quantile Embeddings and Associated Probability Metrics
▶ Abstract
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful non-parametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings (KMEs) to represent distributions as mean functions in RKHS . However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs), along with a consistent estimator. We then use KQEs to construct a family of distances that (i) are probability metrics under weaker kernel conditions than MMD ;(ii) recover a kernelised form of the sliced Wasserstein distance; and(iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations. Our findings demonstrate the value of representing distributions in Hilbert space beyond simple mean functions, paving the way for new avenues of research.
 arXiv

Summer Term

Date Speaker Title Links
7 May 2026 Connie Trojan Lancaster University
14 May 2026 Chris Nemeth Lancaster University
21 May 2026 Gabriel Diaz-Aylwin Lancaster University
28 May 2026 Edwin Fong University of Hong Kong Quantile Martingale Posteriors
▶ Abstract
In this talk, we introduce a novel Bayesian nonparametric method for quantile estimation/regression based on the martingale posterior (MP) framework. The core idea of the MP is that posterior sampling is equivalent to predictive imputation, which allows us to break free of the stringent likelihood-prior specification. We demonstrate that a recursive estimate of a smooth quantile function, subject to a martingale condition, is entirely sufficient for full nonparametric Bayesian inference. We term the resulting posterior distribution as the quantile martingale posterior (QMP), which arises from an implicit generative predictive distribution. Associated with the QMP is an expedient, MCMC-free and parallelizable posterior computation scheme, which can be further accelerated with an asymptotic approximation based on a Gaussian process. Furthermore, the well-known issue of monotonicity in quantile estimation is naturally alleviated through increasing rearrangement due to the connections to the Bayesian bootstrap, and the QMP has a particularly tractable form that allows for comprehensive theoretical study.
 arXiv
4 Jun 2026 Tiffany Vlaar University of Glasgow
Date Speaker Title Links
11 Dec 2025 Zheyang Shen Newcastle University A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives
▶ Abstract
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an explicit unnormalised density for the target. To mitigate this difficulty, we introduce a novel measure of suboptimality called 'gradient discrepancy', and in particular a 'kernel' gradient discrepancy (KGD) that can be explicitly computed. In the standard Bayesian context, KGD coincides with the kernel Stein discrepancy (KSD), and we obtain a novel characterisation of KSD as measuring the size of a variational gradient. Outside this familiar setting, KGD enables novel sampling algorithms to be developed and compared, even when unnormalised densities cannot be obtained. To illustrate this point several novel algorithms are proposed and studied, including a natural generalisation of Stein variational gradient descent, with applications to mean-field neural networks and predictively oriented posteriors presented. On the theoretical side, our principal contribution is to establish sufficient conditions for desirable properties of KGD, such as continuity and convergence control.
Date Speaker Title Links
15 Jan 2026 Hefin Lambley University of Warwick Autoencoders in function space
▶ Abstract
We propose function-space versions of autoencoders—machine-learning methods for dimension reduction and generative modelling—in both their deterministic (FAE) and variational (FVAE) forms. Formulating autoencoder objectives in function space enables training and evaluation with data discretised at arbitrary resolutions, leading to new applications such as inpainting, superresolution, and generative modelling. We discuss the technical challenges of formulating autoencoders in infinite dimension. A key issue is that FVAE's variational inference is often ill defined, unlike in finite dimensions, limiting its applicability. We then explore specific problem classes where FVAE remains useful. We contrast this with the FAE objective, which remains well defined in many situations where FVAE fails, making it a robust and versatile alternative. We demonstrate both methods on scientific data sets, including Navier--Stokes fluid flow simulations. This is joint work with Justin Bunker and Mark Girolami (Cambridge), Andrew M. Stuart (Caltech) and T. J. Sullivan (Warwick).
 arXiv
22 Jan 2026 Yuga Iguchi Lancaster University
29 Jan 2026 William Laplante University College London Conjugate Generalised Bayesian Inference for Discrete Doubly Intractable Problems
▶ Abstract
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation of the posterior through specialised and typically expensive MCMC methods. In this paper, we provide a computationally efficient alternative in the form of a novel generalised Bayesian posterior that allows for conjugate inference within the class of exponential family models for discrete data. We derive theoretical guarantees to characterise the asymptotic behaviour of the generalised posterior, supporting its use for inference. The method is evaluated on a range of challenging intractable exponential family models, including the Conway-Maxwell-Poisson graphical model of multivariate count data, autoregressive discrete time series models, and Markov random fields such as the Ising and Potts models. The computational gains are significant; in our experiments, the method is between 10 and 6000 times faster than state-of-the-art Bayesian computational methods.
 arXiv
5 Feb 2026 Chris Sherlock Lancaster University
12 Feb 2026 Abiel Talwar Lancaster University
19 Feb 2026 Matthias Sachs Lancaster University
26 Feb 2026 Jonas Latz University of Manchester Sparse Techniques for Regression in Deep Gaussian Processes
▶ Abstract
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. GPs suffer when the amount of training data is large or when the underlying function contains multiscale features that are difficult to represent by an isotropic kernel. The training of GPs with large scale data is often performed through inducing point approximations (also known as sparse GP regression), where the size of the covariance matrices in GP regression is reduced considerably through a greedy search on the data set. Deep Gaussian processes have recently been introduced as hierarchical models that resolve multi-scale features by composing multiple Gaussian processes. Whilst GPs can be trained through a simple analytical formula, deep GPs require a sampling or, more usual, a variational approximation. Variational approximations lead to large-scale stochastic, non-convex optimisation problems and the resulting approximation tends to represent uncertainty incorrectly. In this work, we combine variational learning with MCMC to develop a particle-based expectation-maximisation method to simultaneously find inducing points within the large-scale data (variationally) and accurately train the Gaussian processes (sampling-based). The result is a highly efficient and accurate methodology for deep GP training on large scale data. We test the method on standard benchmark problems. Joint work with Aretha Teckentrup and Simon Urbainczyk.
 Paper 1 Paper 2
5 Mar 2026 Paul Fearnhead Lancaster University
12 Mar 2026 Chen Qi Aalto University
19 Mar 2026 Liam Llamazares-Elias Lancaster University
23 Apr 2026 Rui Zhang Lancaster University
30 Apr 2026 Masha Naslidnyk University College London Kernel Quantile Embeddings and Associated Probability Metrics
▶ Abstract
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful non-parametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings (KMEs) to represent distributions as mean functions in RKHS . However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs), along with a consistent estimator. We then use KQEs to construct a family of distances that (i) are probability metrics under weaker kernel conditions than MMD ;(ii) recover a kernelised form of the sliced Wasserstein distance; and(iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations. Our findings demonstrate the value of representing distributions in Hilbert space beyond simple mean functions, paving the way for new avenues of research.
 arXiv
Date Speaker Title Links
7 May 2026 Connie Trojan Lancaster University
14 May 2026 Chris Nemeth Lancaster University
21 May 2026 Gabriel Diaz-Aylwin Lancaster University
28 May 2026 Edwin Fong University of Hong Kong Quantile Martingale Posteriors
▶ Abstract
In this talk, we introduce a novel Bayesian nonparametric method for quantile estimation/regression based on the martingale posterior (MP) framework. The core idea of the MP is that posterior sampling is equivalent to predictive imputation, which allows us to break free of the stringent likelihood-prior specification. We demonstrate that a recursive estimate of a smooth quantile function, subject to a martingale condition, is entirely sufficient for full nonparametric Bayesian inference. We term the resulting posterior distribution as the quantile martingale posterior (QMP), which arises from an implicit generative predictive distribution. Associated with the QMP is an expedient, MCMC-free and parallelizable posterior computation scheme, which can be further accelerated with an asymptotic approximation based on a Gaussian process. Furthermore, the well-known issue of monotonicity in quantile estimation is naturally alleviated through increasing rearrangement due to the connections to the Bayesian bootstrap, and the QMP has a particularly tractable form that allows for comprehensive theoretical study.
 arXiv
4 Jun 2026 Tiffany Vlaar University of Glasgow

Michaelmas Term

Date Speaker Title Links
4 Dec 2025 Giorgos Vasdekis Sampling with time-changed Markov processes
▶ Abstract
We introduce a framework of time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms in the context of multimodal distributions and rare event simulation. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent function. We apply this framework to several Markov processes from the MCMC literature, such as Langevin diffusions and piecewise deterministic Markov processes, obtaining novel modifications of classical algorithms and also re-discovering known MCMC algorithms. We prove theoretical properties of the time-changed process under suitable conditions on the base process, focusing on connecting the stationary distributions and qualitative convergence properties such as geometric and uniform ergodicity, as well as a functional central limit theorem. Time permitting, we will compare our approach with the framework of space transformations, clarifying the similarities between the approaches. This is joint work with Andrea Bertazzi.
 Slides
20 Nov 2025 Lanya Yang Lancaster University Exchangeable Particle Gibbs for Markov Jump Processes
▶ Abstract
Inference in stochastic reaction-network models—such as the SEIR epidemic model or the Lotka–Volterra predator–prey system—is crucial for understanding the dynamics of interacting systems in epidemiology, ecology, and systems biology. These models are typically represented as Markov jump processes (MJPs) with intractable likelihoods. As a result, particle Markov chain Monte Carlo (particle MCMC) methods, particularly the Particle Gibbs (PG) sampler, have become standard tools for Bayesian inference. However, PG suffers from severe particle degeneracy, especially in high-dimensional state spaces, leading to poor mixing and inefficiency. In this talk, I focus on improving the efficiency of particle MCMC methods for inference in reaction networks by addressing the degeneracy problem. Building on recent work on the Exchangeable Particle Gibbs (xPG) sampler for continuous-state diffusions, this project develops a novel version of xPG tailored to discrete-state reaction networks, where randomness is driven by Poisson processes rather than Brownian motion. The proposed method retains the exchangeability framework of xPG while adapting it to the structural and computational challenges specific to reaction networks.
 Slides
30 Oct 2025 Rui Zhang Lancaster University A Dynamic Perspective of Matern Gaussian Processes
▶ Abstract
The ubiquitous Gaussian process (GP) models in statistics and machine learning (Williams and Rasmussen; 2006) are static by default, either using the weight-space or function-space views (Kanagawa et al.; 2025), where the observation and test locations have no unilateral dependency order, and this also explains the cubic scalability in computational costs for GP regressions. On the other hand, the dynamic view of Gaussian processes, while only available for a class of GP models, reformulates the dependency structure unilaterally (Whittle; 1954) to enable sequential inferences for GP regressions with computational costs that could scale linearly (Hartikainen and Sarkka;2010; Sarkka and Hartikainen; 2012) with little to no approximation. This talk explores this dynamic perspective of (Matern) Gaussian processes and some consequences of this perspective.
 Slides HTML Slides
16 Oct 2025 Henry Moss Lancaster University GPGreen: Linear Operator Learning with Gaussian Processes
4 Sep 2025 Rafael Izbicki Federal University of São Carlos, Brazil Simulation‑Based Calibration of Confidence Sets for Statistical Models arXiv
7 Aug 2025 Jixiang Qing Imperial College London Bayesian Optimization Over Graphs With Shortest-Path Encodings arXiv
Date Speaker Title Links
4 Dec 2025 Giorgos Vasdekis Sampling with time-changed Markov processes
▶ Abstract
We introduce a framework of time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms in the context of multimodal distributions and rare event simulation. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent function. We apply this framework to several Markov processes from the MCMC literature, such as Langevin diffusions and piecewise deterministic Markov processes, obtaining novel modifications of classical algorithms and also re-discovering known MCMC algorithms. We prove theoretical properties of the time-changed process under suitable conditions on the base process, focusing on connecting the stationary distributions and qualitative convergence properties such as geometric and uniform ergodicity, as well as a functional central limit theorem. Time permitting, we will compare our approach with the framework of space transformations, clarifying the similarities between the approaches. This is joint work with Andrea Bertazzi.
 Slides
20 Nov 2025 Lanya Yang Lancaster University Exchangeable Particle Gibbs for Markov Jump Processes
▶ Abstract
Inference in stochastic reaction-network models—such as the SEIR epidemic model or the Lotka–Volterra predator–prey system—is crucial for understanding the dynamics of interacting systems in epidemiology, ecology, and systems biology. These models are typically represented as Markov jump processes (MJPs) with intractable likelihoods. As a result, particle Markov chain Monte Carlo (particle MCMC) methods, particularly the Particle Gibbs (PG) sampler, have become standard tools for Bayesian inference. However, PG suffers from severe particle degeneracy, especially in high-dimensional state spaces, leading to poor mixing and inefficiency. In this talk, I focus on improving the efficiency of particle MCMC methods for inference in reaction networks by addressing the degeneracy problem. Building on recent work on the Exchangeable Particle Gibbs (xPG) sampler for continuous-state diffusions, this project develops a novel version of xPG tailored to discrete-state reaction networks, where randomness is driven by Poisson processes rather than Brownian motion. The proposed method retains the exchangeability framework of xPG while adapting it to the structural and computational challenges specific to reaction networks.
 Slides
30 Oct 2025 Rui Zhang Lancaster University A Dynamic Perspective of Matern Gaussian Processes
▶ Abstract
The ubiquitous Gaussian process (GP) models in statistics and machine learning (Williams and Rasmussen; 2006) are static by default, either using the weight-space or function-space views (Kanagawa et al.; 2025), where the observation and test locations have no unilateral dependency order, and this also explains the cubic scalability in computational costs for GP regressions. On the other hand, the dynamic view of Gaussian processes, while only available for a class of GP models, reformulates the dependency structure unilaterally (Whittle; 1954) to enable sequential inferences for GP regressions with computational costs that could scale linearly (Hartikainen and Sarkka;2010; Sarkka and Hartikainen; 2012) with little to no approximation. This talk explores this dynamic perspective of (Matern) Gaussian processes and some consequences of this perspective.
 Slides HTML Slides
16 Oct 2025 Henry Moss Lancaster University GPGreen: Linear Operator Learning with Gaussian Processes
4 Sep 2025 Rafael Izbicki Federal University of São Carlos, Brazil Simulation‑Based Calibration of Confidence Sets for Statistical Models arXiv
7 Aug 2025 Jixiang Qing Imperial College London Bayesian Optimization Over Graphs With Shortest-Path Encodings arXiv