9 papers
Sampling from Neural Operator Priors to Solve Partial Differential Equations
Andrew Millard, Joshua Murphy, Zheng Zhao
Guided sampling with sparse observations and PDE residuals has recently been combined with neural operator priors to solve partial differential equations in function space, their n…
Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Sampling
Andrew Millard, Zheng Zhao, Henrik Pedersen
Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. Ho…
Particle-Guided Diffusion for Gas-Phase Reaction Kinetics
Andrew Millard, Henrik Pedersen
Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful r…
Position: Stop Preaching and Start Practising Data Frugality for Responsible Development of AI
Sophia N. Wilson, Andrew Millard, Guðrún Fjóla Guðmundsdóttir +2
This position paper argues that the machine learning community must move from preaching to practising data frugality for responsible artificial intelligence (AI) development. For t…
Investigating Batch Inference in a Sequential Monte Carlo Framework for Neural Networks
Andrew Millard, Joshua Murphy, Peter Green +1
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 approxima…
Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals
Joshua Murphy, Conor Rosato, Andrew Millard +3
When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. T…
Humble your Overconfident Networks: Unlearning Overfitting via Sequential Monte Carlo Tempered Deep Ensembles
Andrew Millard, Zheng Zhao, Joshua Murphy +1
Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluation…
Utilising Gradient-Based Proposals Within Sequential Monte Carlo Samplers for Training of Partial Bayesian Neural Networks
Andrew Millard, Joshua Murphy, Simon Maskell +1
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. Us…
Incorporating the ChEES Criterion into Sequential Monte Carlo Samplers
Andrew Millard, Joshua Murphy, Daniel Frisch +1
Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, su…