13:30 – 14:30 – Dr. Nikolas Nusken (King’s College London)
Title: Transport meets Variational Inference: Controlled Monte Carlo Diffusions
Abstract: Connecting optimal transport and variational inference, this talk is about a principled and systematic framework for score-based sampling and generative modelling centred around forward and reverse-time stochastic differential equations. In particular, I will discuss the novel Controlled Monte Carlo Diffusion (CMCD) methodology for Bayesian computation, a score-based annealing technique that crucially adapts both forward and backward dynamics in a diffusion model. Time permitting, we will discuss relationships between the EM-algorithm and iterative proportional fitting (IPF) for Schroedinger bridges, as well as connections to the Jarzinsky and Crooks identities from statistical physics. This is joint work with F. Vargas, S. Padhy and D. Blessing.
15:00 – 16:00 – Dr. Lachlan Astfalck (Univ. Western Australia)
Title: Debiasing Welch’s Method for Spectral Density Estimation
Abstract: Most non-parametric spectral estimation methodologies are based on transformations of the periodogram, a biased and statistically inconsistent estimator to the true spectral density. To enforce consistency, we average partitions of the periodogram; although, doing so increases the bias. Consequently, we become increasingly certain in an estimate that is increasingly wrong. This is particularly seen in Welch’s estimator, the most widespread estimator for non-parametric spectral density estimation in the engineering and physical sciences. In this seminar we show, by extending some recent results, how to debias Welch’s estimate whilst retaining optimal convergence guarantees. This results in a non-parametric estimator to the spectral density that is optimally convergent in RMSE, a property, until now, absent in the literature. We show results for efficient computation and demonstrate application across a range of oceanographic and hydrodynamic datasets.
Refreshments available between 14:30 – 15:00