Accurate Kernel Learning for Linear Gaussian Markov Processes using a Scalable Likelihood Computation

TL;DR

This paper introduces an exact and scalable likelihood computation method for Linear Gaussian Markov processes, improving efficiency for complex models and sparse data, and evaluates kernel learning accuracy with practical experiments.

Contribution

It presents a novel scalable likelihood computation technique that enhances kernel learning for complex and sparsely sampled Linear Gaussian Markov processes.

Findings

Posterior mean with a reference prior improves accuracy for complex models.

Maximum likelihood estimator is computationally efficient for dense sampling.

Experimental validation on speleothem data confirms estimator behaviors.

Abstract

We report an exact likelihood computation for Linear Gaussian Markov processes that is more scalable than existing algorithms for complex models and sparsely sampled signals. Better scaling is achieved through elimination of repeated computations in the Kalman likelihood, and by using the diagonalized form of the state transition equation. Using this efficient computation, we study the accuracy of kernel learning using maximum likelihood and the posterior mean in a simulation experiment. The posterior mean with a reference prior is more accurate for complex models and sparse sampling. Because of its lower computation load, the maximum likelihood estimator is an attractive option for more densely sampled signals and lower order models. We confirm estimator behavior in experimental data through their application to speleothem data.