arXiv subjects

Simon Maskell

Publications and source records attributed to Simon Maskell.

At least 19 recordsLinked to original sources

arXiv2026

Investigating Batch Inference in a Sequential Monte Carlo Framework for Neural Networks

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational inference - is computationally efficient when using mini-batch stochastic gradient descent as subsets of the data are used for likelihood and gradient evaluations, though the approach relies on the selection of a variational distribution which sufficiently matches the form of the posterior. Particle-based methods such as Markov chain Monte Carlo and Sequential Monte Carlo (SMC) do not assume a parametric family for the posterior by typically require higher computational cost. These sampling methods typically use the full-batch of data for likelihood and gradient evaluations, which contributes to this computational expense. We explore several methods of gradually introducing more mini-batches of data (data annealing) into likelihood and gradient evaluations of an SMC sampler. We find that we can achieve up to $6\times$ faster training with minimal loss in accuracy on benchmark image classification problems using NNs.

cs.LG↗

arXiv2025

Improved Disease Outbreak Detection from Out-of-sequence measurements Using Markov-switching Fixed-lag Particle Filters

Particle filters (PFs) have become an essential tool for disease surveillance, as they can estimate hidden epidemic states in nonlinear and non-Gaussian models. In epidemic modelling, population dynamics may be governed by distinct regimes such as endemic or outbreak phases which can be represented using Markov-switching state-space models. In many real-world surveillance systems, data often arrives with delays or in the wrong temporal order, producing out-of-sequence (OOS) measurements that pertain to past time points rather than the current one. While existing PF methods can incorporate OOS measurements through particle reweighting, these approaches are limited in their ability to fully adjust past latent trajectories. To address this, we introduce a Markov-switching fixed-lag particle filter (FL-PF) that resimulates particle trajectories within a user-specified lag window, allowing OOS measurements to retroactively update both state and model estimates. By explicitly reevaluating historical samples, the FL-PF improves the accuracy and timeliness of outbreak detection and reduces false alarms. We also show how to compute the log-likelihood within the FL-PF framework, enabling parameter estimation using Sequential Monte Carlo squared (SMC$^2$). Together, these contributions extend the applicability of PFs to surveillance systems where retrospective data are common, offering a more robust framework for monitoring disease outbreaks and parameter inference.

stat.AP↗

arXiv2025

Towards Scalable Proteomics: Opportunistic SMC Samplers on HTCondor

Quantitative proteomics plays a central role in uncovering regulatory mechanisms, identifying disease biomarkers, and guiding the development of precision therapies. These insights are often obtained through complex Bayesian models, whose inference procedures are computationally intensive, especially when applied at scale to biological datasets. This limits the accessibility of advanced modelling techniques needed to fully exploit proteomics data. Although Sequential Monte Carlo (SMC) methods offer a parallelisable alternative to traditional Markov Chain Monte Carlo, their high-performance implementations often rely on specialised hardware, increasing both financial and energy costs. We address these challenges by introducing an opportunistic computing framework for SMC samplers, tailored to the demands of large-scale proteomics inference. Our approach leverages idle compute resources at the University of Liverpool via HTCondor, enabling scalable Bayesian inference without dedicated high-performance computing infrastructure. Central to this framework is a novel Coordinator-Manager-Follower architecture that reduces synchronisation overhead and supports robust operation in heterogeneous, unreliable environments. We evaluate the framework on a realistic proteomics model and show that opportunistic SMC delivers accurate inference with weak scaling, increasing samples generated under a fixed time budget as more resources join. To support adoption, we release CondorSMC, an open-source package for deploying SMC samplers in opportunistic computing environments.

q-bio.QM↗

arXiv2025

Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals

When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo Squared (SMC$^2$) is well-suited for high-performance computing (HPC) environments. The design of the proposal distribution within SMC$^2$ can improve accuracy and exploration of the posterior as poor proposals may lead to high variance in importance weights and particle degeneracy. The Metropolis-Adjusted Langevin Algorithm (MALA) uses gradient information so that particles preferentially explore regions of higher probability. In this paper, we extend this idea by incorporating second-order information, specifically the Hessian of the log-target. While second-order proposals have been explored previously in particle Markov Chain Monte Carlo (p-MCMC) methods, we are the first to introduce them within the SMC$^2$ framework. Second-order proposals not only use the gradient (first-order derivative), but also the curvature (second-order derivative) of the target distribution. Experimental results on synthetic models highlight the benefits of our approach in terms of step-size selection and posterior approximation accuracy when compared to other proposals.

stat.ML↗

arXiv2025

Assessing the Impact of Vaccination on Rotavirus Transmission Dynamics Using Bayesian Inference

The introduction of the rotavirus vaccine in the United Kingdom (UK) in 2013 led to a noticeable decline in laboratory reports in subsequent years. To assess the impact of vaccination on rotavirus transmissibility we calibrated a stochastic compartmental epidemiological model using Sequential Monte Carlo (SMC) methods. Our analysis focuses on estimating the time-varying transmissibility parameter and documenting its evolution before and after vaccine rollout. We observe distinct periods of increasing and decreasing transmissibility, reflecting the dynamic response of rotavirus spread to immunization efforts. These findings improve our understanding of vaccination-driven shifts in disease transmission and provide a quantitative framework for evaluating long-term epidemiological trends.

q-bio.PE↗

arXiv2025

Humble your Overconfident Networks: Unlearning Overfitting via Sequential Monte Carlo Tempered Deep Ensembles

Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) proposals into SMC, enabling efficient mini-batch based sampling. Our resulting SMCSGHMC algorithm outperforms standard stochastic gradient descent (SGD) and deep ensembles across image classification, out-of-distribution (OOD) detection, and transfer learning tasks. We further show that SMCSGHMC mitigates overfitting and improves calibration, providing a flexible, scalable pathway for converting pretrained neural networks into well-calibrated Bayesian models.

stat.ML↗

arXiv2025

Efficient MCMC Sampling with Expensive-to-Compute and Irregular Likelihoods

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.

stat.ML↗

arXiv2025

Utilising Gradient-Based Proposals Within Sequential Monte Carlo Samplers for Training of Partial Bayesian Neural Networks

Partial Bayesian neural networks (pBNNs) have been shown to perform competitively with fully Bayesian neural networks while only having a subset of the parameters be stochastic. Using sequential Monte Carlo (SMC) samplers as the inference method for pBNNs gives a non-parametric probabilistic estimation of the stochastic parameters, and has shown improved performance over parametric methods. In this paper we introduce a new SMC-based training method for pBNNs by utilising a guided proposal and incorporating gradient-based Markov kernels, which gives us better scalability on high dimensional problems. We show that our new method outperforms the state-of-the-art in terms of predictive performance and optimal loss. We also show that pBNNs scale well with larger batch sizes, resulting in significantly reduced training times and often better performance.

cs.LG↗

arXiv2025

Poisson multi-Bernoulli mixture filter for trajectory measurements

This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM (TM-PMBM) filter, propagates a PMBM density on the set of target states. In prediction, the filter obtains the PMBM density on the set of trajectories over the last two time steps. This density is then updated with the set of trajectory measurements. After the update step, the PMBM posterior on the set of two-step trajectories is marginalised to obtain a PMBM density on the set of target states. The filter provides a closed-form solution for multi-target filtering based on sets of trajectory measurements, estimating the set of target states at the end of each time window. Additionally, the paper proposes computationally lighter alternatives to the TM-PMBM filter by deriving a Poisson multi-Bernoulli (PMB) density through Kullback-Leibler divergence minimisation in an augmented space with auxiliary variables. The performance of the proposed filters are evaluated in a simulation study.

eess.SP↗

arXiv2025

Incorporating the ChEES Criterion into Sequential Monte Carlo Samplers

Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the parameter space of interest if the additional hyper-parameters are chosen well. The No-U-Turn Sampler (NUTS) is a variant of HMC which is extremely effective at selecting these hyper-parameters but is slow to run and is not suited to GPU architectures. An alternative to NUTS, Change in the Estimator of the Expected Square HMC (ChEES-HMC) was shown not only to run faster than NUTS on GPU but also sample from posteriors more efficiently. Sequential Monte Carlo (SMC) samplers are another sampling method which instead output weighted samples from the posterior. They are very amenable to parallelisation and therefore being run on GPUs while having additional flexibility in their choice of proposal over MCMC. We incorporate (ChEEs-HMC) as a proposal into SMC samplers and demonstrate competitive but faster performance than NUTS on a number of tasks.

stat.CO↗

arXiv2025

An Entropic Metric for Measuring Calibration of Machine Learning Models

Understanding the confidence with which a machine learning model classifies an input datum is an important, and perhaps under-investigated, concept. In this paper, we propose a new calibration metric, the Entropic Calibration Difference (ECD). Based on existing research in the field of state estimation, specifically target tracking (TT), we show how ECD may be applied to binary classification machine learning models. We describe the relative importance of under- and over-confidence and how they are not conflated in the TT literature. Indeed, our metric distinguishes under- from over-confidence. We consider this important given that algorithms that are under-confident are likely to be 'safer' than algorithms that are over-confident, albeit at the expense of also being over-cautious and so statistically inefficient. We demonstrate how this new metric performs on real and simulated data and compare with other metrics for machine learning model probability calibration, including the Expected Calibration Error (ECE) and its signed counterpart, the Expected Signed Calibration Error (ESCE).

cs.LG↗

arXiv2024

Bayesian Wideband Signal Detection via Source Signal Marginalization and RJMCMC

Consider an array receiving unknown wideband signals from an unknown number of sources $k$. Wideband signals can occupy arbitrarily wide bandwidths, rendering demodulation-based approaches inapplicable, a common situation in settings involving acoustic signals. Here, we aim to determine $k$ given $N$ noisy array-valued measurements, a task known as the "detection problem," for which Bayesian model comparison is a common approach. To render Bayesian inference tractable, it is typically necessary to marginalize the source signals. Unfortunately, for wideband signals, naive marginalization has an unaffordable time complexity of $\mathcal{O}(N^3 k^3)$. As a result, fully Bayesian signal detection has yet to be demonstrated in wideband settings. In this work, we propose a wideband signal model that allows for computationally tractable marginalization of the source signals. We begin from the canonical model of linear time-invariant (LTI) signal propagation, which is then augmented into a circular convolution, all without loss of generality. This allows for efficient computation in the frequency domain, where the resulting linear system admits a decomposition into a sparse matrix we refer to as a \textit{stripe matrix decomposition}. Exploiting this sparsity pattern reduces the time complexity of computing the marginal likelihood to $\mathcal{O}(N k^3)$. These computational improvements enable efficient posterior inference via reversible-jump Markov chain Monte Carlo (RJMCMC). In this work, we use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than RJMCMC. Detection of the latent source signals can then be performed in a fully Bayesian manner using samples drawn by NRJMCMC. We evaluate our procedure by comparing it against generalized likelihood ratio testing (GLRT) and information criteria.

eess.SP↗

arXiv2024

Enhanced SMC$^2$: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals

Sequential Monte Carlo Squared (SMC$^2$) is a Bayesian method which can infer the states and parameters of non-linear, non-Gaussian state-space models. The standard random-walk proposal in SMC$^2$ faces challenges, particularly with high-dimensional parameter spaces. This study outlines a novel approach by harnessing first-order gradients derived from a Common Random Numbers - Particle Filter (CRN-PF) using PyTorch. The resulting gradients can be leveraged within a Langevin proposal without accept/reject. Including Langevin dynamics within the proposal can result in a higher effective sample size and more accurate parameter estimates when compared with the random-walk. The resulting algorithm is parallelized on distributed memory using Message Passing Interface (MPI) and runs in $\mathcal{O}(\log_2N)$ time complexity. Utilizing 64 computational cores we obtain a 51x speed-up when compared to a single core. A GitHub link is given which provides access to the code.

stat.ML↗

arXiv2023

An $\mathcal{O}(\log_2N)$ SMC$^2$ Algorithm on Distributed Memory with an Approx. Optimal L-Kernel

Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC$^2$) are two methods that use an unbiased estimate of the log-likelihood obtained from a particle filter (PF) to evaluate the target distribution. P-MCMC constructs a single Markov chain which is sequential by nature so cannot be readily parallelized using Distributed Memory (DM) architectures. This is in contrast to SMC$^2$ which includes processes, such as importance sampling, that are described as \textit{embarrassingly parallel}. However, difficulties arise when attempting to parallelize resampling. None-the-less, the choice of backward kernel, recycling scheme and compatibility with DM architectures makes SMC$^2$ an attractive option when compared with p-MCMC. In this paper, we present an SMC$^2$ framework that includes the following features: an optimal (in terms of time complexity) $\mathcal{O}(\log_2N)$ parallelization for DM architectures, an approximately optimal (in terms of accuracy) backward kernel, and an efficient recycling scheme. On a cluster of $128$ DM processors, the results on a biomedical application show that SMC$^2$ achieves up to a $70\times$ speed-up vs its sequential implementation. It is also more accurate and roughly $54\times$ faster than p-MCMC. A GitHub link is given which provides access to the code.

stat.AP↗

arXiv2023

Non-Myopic Sensor Control for Target Search and Track Using a Sample-Based GOSPA Implementation

This paper is concerned with sensor management for target search and track using the generalised optimal subpattern assignment (GOSPA) metric. Utilising the GOSPA metric to predict future system performance is computationally challenging, because of the need to account for uncertainties within the scenario, notably the number of targets, the locations of targets, and the measurements generated by the targets subsequent to performing sensing actions. In this paper, efficient sample-based techniques are developed to calculate the predicted mean square GOSPA metric. These techniques allow for missed detections and false alarms, and thereby enable the metric to be exploited in scenarios more complex than those previously considered. Furthermore, the GOSPA methodology is extended to perform non-myopic (i.e. multi-step) sensor management via the development of a Bellman-type recursion that optimises a conditional GOSPA-based metric. Simulations for scenarios with missed detections, false alarms, and planning horizons of up to three time steps demonstrate the approach, in particular showing that optimal plans align with an intuitive understanding of how taking into account the opportunity to make future observations should influence the current action. It is concluded that the GOSPA-based, non-myopic search and track algorithm offers a powerful mechanism for sensor management.

math.OC↗

arXiv2023

Bayesian Decision Trees Inspired from Evolutionary Algorithms

Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) because they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo (MCMC) with an accept-reject mechanism and sample using naive proposals to proceed to the next iteration, which can be slow because of the burn-in time needed. We can reduce the burn-in period by proposing a more sophisticated way of sampling or by designing a different numerical Bayesian approach. In this paper, we propose a replacement of the MCMC with an inherently parallel algorithm, the Sequential Monte Carlo (SMC), and a more effective sampling strategy inspired by the Evolutionary Algorithms (EA). Experiments show that SMC combined with the EA can produce more accurate results compared to MCMC in 100 times fewer iterations.

cs.LG↗

arXiv2023

Bayesian Estimation for Bell State Rotations

This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation from a sequence of Bell state measurements and we demonstrate that the resultant improvement over the optimal single qubit case approaches the $\sqrt{2}$ factor that is consistent with the Heisenberg limit. We also demonstrate how the accuracy of the estimation method is a function of the purity of mixed states.

quant-ph↗

arXiv2023

Parallel Approaches to Accelerate Bayesian Decision Trees

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC. Unfortunately, this can be slow, especially when considering large volumes of data. It is hard to parallelise the accept-reject component of the MCMC. None-the-less, we propose two methods for exploiting parallelism in the MCMC: in the first, we replace the MCMC with another numerical Bayesian approach, the Sequential Monte Carlo (SMC) sampler, which has the appealing property that it is an inherently parallel algorithm; in the second, we consider data partitioning. Both methods use multi-core processing with a HighPerformance Computing (HPC) resource. We test the two methods in various study settings to determine which method is the most beneficial for each test case. Experiments show that data partitioning has limited utility in the settings we consider and that the use of the SMC sampler can improve run-time (compared to the sequential implementation) by up to a factor of 343.

stat.CO↗