Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering

Simo Sarkka, Arno Solin, Jouni Hartikainen
2013 IEEE Signal Processing Magazine  
G aussian process-based machine learning is a powerful Bayesian paradigm for nonparametric nonlinear regression and classification. In this article, we discuss connections of Gaussian process regression with Kalman filtering and present methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models. This formulation allows for use of computationally efficient infinite-dimensional Kalman filtering and smoothing methods, or more general
more » ... sian filtering and smoothing methods, which reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The implication of this is that the use of machinelearning models in signal processing becomes computationally feasible, and it opens the possibility to combine machinelearning techniques with signal processing methods.
doi:10.1109/msp.2013.2246292 fatcat:4sxpmbcndbezxiopzs733xicqe