Note:

Hybrid

Abstract:

An informal observation, made by several authors, is that the adaptive design of a Markov transition kernel has the flavour of a reinforcement learning task. Yet, to-date it has remained unclear how to actually exploit modern reinforcement learning technologies for adaptive MCMC. The aim of this work is to set out a general framework, called Reinforcement Learning Metropolis--Hastings, that is theoretically supported and empirically validated. Our principal focus is on learning fast-mixing Metropolis--Hastings transition kernels, which we cast as deterministic policies and optimise via a policy gradient. Control of the learning rate provably ensures conditions for ergodicity are satisfied. The methodology is used to construct a gradient-free sampler that out-performs a popular gradient-free adaptive Metropolis--Hastings algorithm on ≈90% of tasks in the PosteriorDB benchmark.

Note:

Hybrid

Abstract:

There is increasing appetite for analysing populations of network data due to the fast-growing body of applications demanding such methods. While methods exist to provide readily interpretable summaries of heterogeneous network populations, these are often descriptive or ad hoc, lacking any formal justification. In contrast, principled analysis methods often provide results difficult to relate back to the applied problem of interest. Motivated by two complementary applied examples, we develop a Bayesian framework to appropriately model complex heterogeneous network populations, while also allowing analysts to gain insights from the data and make inferences most relevant to their needs. The first application involves a study in computer science measuring human movements across a university. The second analyses data from neuroscience investigating relationships between different regions of the brain. While both applications entail analysis of a heterogeneous population of networks, network sizes vary considerably. We focus on the problem of clustering the elements of a network population, where each cluster is characterised by a network representative. We take advantage of the Bayesian machinery to simultaneously infer the cluster membership, the representatives, and the community structure of the representatives, thus allowing intuitive inferences to be made. The implementation of our method on the human movement study reveals interesting movement patterns of individuals in clusters, readily characterised by their network representative. For the brain networks application, our model reveals a cluster of individuals with different network properties of particular interest in neuroscience. The performance of our method is additionally validated in extensive simulation studies.

Note:

Hybrid

Abstract:

Flexible survival models have seen increasing popularity for the estimation of mean survival in the presence of a high degree of administrative censoring where survival curves need to be extrapolated beyond final observed event times. This increased flexibility, however, often introduces challenging model selection problems that have limited their wider application. In this talk I will focus on two such models, the polyhazard model and the piecewise exponential model. We introduce new prior structures that allow for the joint inference of parameters and structural quantities. Posterior sampling is achieved using bespoke MCMC schemes based on Piecewise Deterministic Markov Processes that utilise and extend existing methods for these samplers to target transdimensional posterior distributions. This is a joint work with Samuel Livingstone and Gianluca Baio.