Kernel Methods for Machine Learning and Dynamical Systems

Explore advanced kernel methods and their applications in machine learning and dynamical systems through this comprehensive symposium featuring 14 specialized presentations. Delve into cutting-edge research on approximation of matrix-valued functions with contraction metrics, kernel two-sample tests for functional data, and Gaussian processes for time series forecasting. Learn about random feature models for input-output maps between function spaces and kernel analog forecasting techniques for multiscale problems. Examine variably scaled discontinuous kernels (VSDK) through a detailed three-part presentation covering basics and applications. Discover how to learn patterns with kernels and extract kernels from patterns, while exploring parameter learning with unknown observation functions. Investigate practical applications including Gaussian process learning for power systems and kernel flows for regression problems. Study consistency in hierarchical parameter learning through empirical Bayes and kernel flow approaches, and understand sparse Cholesky factorization using Kullback-Leibler minimization. Gain insights from leading researchers presenting their latest findings in kernel methods, functional analysis, and their intersection with dynamical systems theory.