14:00 – 15:00 Robin Mitra
Title: Bayesian model-based clustering for populations of network data
Abstract: There is increasing appetite for analysing multiple 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, whilst 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. 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.
15:30 – 16:30 Aki Nishimura
Title: Zigzag path connects two Monte Carlo paradigms: Hamiltonian counterparts to piecewise deterministic Markov processes
Abstract: Zigzag and other piecewise deterministic Markov process samplers have attracted significant interest for their non-reversibility and other appealing properties for Bayesian computation. Hamiltonian Monte Carlo is another state-of-the-art sampler, exploiting fictitious momentum to guide Markov chains through complex target distributions.
In this talk, we first establish a remarkable connection between the zigzag sampler and a variant of Hamiltonian Monte Carlo based on Laplace-distributed momentum. The position-velocity component of the corresponding Hamiltonian dynamics travels along a zigzag path paralleling the Markovian zigzag process; however, the dynamics is non-Markovian as the momentum component encodes non-immediate pasts. In the limit of increasingly frequent momentum refreshments in which we preserve its direction but re-sample magnitude, we prove that Hamiltonian zigzag converges strongly to its Markovian counterpart. This theoretical insight in particular explains the two zigzags’ relative performance on target distributions with highly correlated parameters, which we demonstrate on a 11,235-dimensional truncated Gaussian target arising from Bayesian phylogenetic multivariate probit model applied to an HIV virus dataset.
We then proceed to construct a Hamiltonian counterpart to the bouncy particle sampler (BPS), further strengthening the connection between the two paradigms. We achieve this by turning BPS’s Poisson schedule for velocity switch events into a deterministic one dictated by an auxiliary “inertia” parameter. The resulting Hamiltonian BPS constitutes an efficient sampler on log-concave targets and straightforwardly accommodates parameter constraints. We demonstrate its competitive performance in the posterior computation under Bayesian sparse logistic regression model applied to a large-scale observational study consisting of 72,489 patients and 22,175 clinical covariates.
Refreshments available between 15:00 – 15:30