30th May 2024 - Alessandro Barp (UCL and the Alan Turing Institute)

Title: Controlling convergence of distributions with kernel discrepancies
Abstract: Kernel discrepancies, such as the maximum mean discrepancy (MMD) and kernel Stein discrepancy (KSD), have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. While kernel-based discrepancies are more computational tractable than the classical distances of probability theory, their successful application in each of the above setting requires them to: (i) separate a target distribution from other probability measures or even (ii) control weak convergence to the target.
In this seminar I will introduce kernels, motivate their associated MMDs and KSDs, which respectively leverage the target’s topological and differential information, and discuss some of the results on convergence control we obtained in [1-3].
[1] Simon-Gabriel, Carl-Johann, et al. "Metrizing weak convergence with maximum mean discrepancies." Journal of Machine Learning Research 24.184 (2023): 1-20
[2] Barp, Alessandro, et al. "Targeted separation and convergence with kernel discrepancies." To appear in Journal of Machine Learning Research (2024)
[3] Kanagawa, Heishiro, et al. "Controlling moments with kernel Stein discrepancies." Submitted to Annals Of Statistics.