GP Kernels for Cross-Spectrum Analysis

Abstract Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, Wilson and Adams (2013) proposed the spectral mixture (SM) kernel to model the spectral density of a single task in a Gaussian process framework. In this paper, we develop a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. We demonstrate the expressive capabilities of the CSM kernel through implementation of a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel. Results are presented for measured multi-region electrophysiological data

Approximate inference in related multi-output Gaussian Process Regression

In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs. Using a prior known relation between outputs, joint auto- and cross-covariance functions can be constructed. Realizations from these joint-covariance functions give outputs that are consistent with the prior relation. One issue with gaussian process regression is efficient inference when scaling upto large datasets. In this paper we use approximate inference techniques upon multi-output kernels enforcing relationships between outputs. Results of the proposed methodology for theoretical data and real world applications are presented. The main contribution of this paper is the application and validation of our methodology on a dataset of real aircraft fight tests, while imposing knowledge of aircraft physics into the model

Adding Flight Mechanics to Flight Loads Surrogate Model using Multi-Output Gaussian Processes

In this paper analytical methods to formally incorporate knowledge of physics-based equations between multiple outputs in a Gaussian Process (GP) model are presented. In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs. Using a general framework for constructing auto- and cross-covariance functions that are consistent with the physical laws, physics-based relationships among several outputs can be imposed. Results of the proposed methodology for simulated data and measurement from flight tests are presented. The main contribution of this paper is the application and validation of our methodology on a dataset of flight tests, while imposing knowledge of flight mechanics into the model