Atmosphere Ocean Science Student Seminar
Kernel Methods for Forecasting Dynamical Systems
Speaker: Romeo Alexander, PhD Candidate, Courant Institute
Location: Warren Weaver Hall 1314
Date: Friday, November 2, 2018, 3:45 p.m.
Kernel methods are a collection of non-parametric prediction techniques that exploit the internal geometric structures of the dynamical system. Such methods are ideally suited to non-linearly generated high-dimensional data, or otherwise data whose governing equations are either unknown or computationally intractable. This talk will explore the application of two such methods, kernel principal component regression (KPCR) and kernel ridge regression (KRR), in the context of several illustrative examples, including the classical Lorenz-63 model, as well as real climate data from the tropical atmosphere. This talk will also examine the theoretical limit of prediction of such kernel methods through the perspective of functional analysis, especially the theory of Reproducing Kernel Hilbert Spaces (RKHS), the main takeaway being that such methods can only perform as well as the conditional expectation function that is inherent to the system. Extensions of kernel forecasting to the related problems of conditional probability estimation and classification will also be shown.