Multiresolution Gaussian Processes

TL;DR

This paper introduces a multiresolution Gaussian process model that captures both long-range dependencies and abrupt changes in data, enabling efficient inference and application to brain activity analysis.

Contribution

It presents a hierarchical multiresolution GP model with analytical marginalization, allowing efficient inference of complex dependencies and change points in data.

Findings

Effective modeling of long-range dependencies and abrupt changes.

Analytical marginalization enables efficient inference.

Successful application to MEG brain activity data.

Abstract

We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the conditional likelihood of the observations given the partition tree. This property allows for efficient inference of the partition itself, for which we employ graph-theoretic techniques. We apply the multiresolution GP to the analysis of Magnetoencephalography (MEG) recordings of brain activity.