Room: Engineering Building 2B025

8:30-9:00 Arrivals

9:00-10:30 Bayesian Optimization and Beyond Henry Moss, University of Lancaster

10:30-11:00 Coffee Break

11:00-12:30 Multi-task Gaussian processes Arthur Leroy, INRAE

12:30-13:45 Lunch

13:45-15:30 Lab Session 2

15:30-16:00 Coffee Break

16:00-17:00 From Spectral Kernels to Latent Variable Models: Random Fourier Features, Expressive Kernels, and Flow-Based Inference Pablo M Olmos, Universidad Carlos III Madrid

Abstracts

From Spectral Kernels to Latent Variable Models: Random Fourier Features, Expressive Kernels, and Flow-Based Inference

Random Fourier features (RFFs) are a cornerstone tool for scaling Gaussian process models, turning an intractable kernel matrix inversion into a cheap, low-rank computation. This lecture builds the idea from the ground up. We begin with Bochner's theorem and its generalizations, which establish a duality between kernels and their spectral densities, and show how this duality yields unbiased Monte Carlo estimators of stationary—and, more recently, nonstationary—kernels. From there, we treat the spectral density itself as an object to be learned: by parameterizing it as a mixture and optimizing it from data, we obtain highly expressive kernels in the supervised setting while retaining scalable RFF approximations. In the second half, we carry these ideas into the unsupervised regime through Gaussian process latent variable models (GPLVMs), where the inputs are themselves unknown and must be inferred. We discuss variational inference for these models and show how normalizing flows can be used to enrich the variational posterior—both over the latent variables and over the spectral points driving the RFF construction—leading to more flexible, efficient, and better-regularized inference. Throughout, the aim is to give a unified spectral perspective connecting kernel design, scalability, and modern variational techniques.