# Seminars

# Atmosphere Ocean Science Student Seminar

#### Kernel Regression for Dynamical Systems Forecasting

**Speaker:**
Romeo Alexander, PhD Candidate

**Location:**
Warren Weaver Hall 1314

**Date:**
Friday, March 29, 2019, 3:30 p.m.

**Synopsis:**

This talk will provide an overview of kernel regression techniques in the forecasting of dynamically generated time series data. A general learning framework will be presented that reveals connections to classical i.i.d learning theory and highlights the unique considerations that must be made for dynamical systems. Error decomposition into model bias, sample variance, and the intrinsic error of the conditional expectation function,will be presented as the starting point for the construction of algorithms and proofs of convergence. A brief overview of the theory of Reproducing Kernel Hilbert Spaces, Spectral Theory, and Mercer Kernels will be provided, in addition to a comparison of the two classic kernel regressional gorithms - kernel ridge regression and kernel principal component regression. The bias-variance trade-off will be illustrated by using the Gaussian and polynomial kernel regression for periodic flow on a circle. Mean-square error analysis of Gaussian kernel regression for the Lorenz-63 dynamical system will also be shown, demonstrating the impact that the choice of covariate variable can have on intrinsic error. Applications to climate systems will also be shown, with an emphasis on how the learning theory framework can aid in separating statistical effects from physical phenomena.