Kernels for time series with irregularly-spaced multivariate observations

TL;DR

This paper introduces a new class of positive semi-definite kernels for irregularly-spaced multivariate time series, enabling effective kernel-based analysis and prediction, validated through Gaussian process modeling and classification tasks.

Contribution

It proposes a general framework for constructing positive semi-definite kernels for irregular multivariate time series using vector kernels, filling a gap in existing methods.

Findings

The proposed kernels are positive semi-definite and broadly applicable.

The Gaussian process-based prediction strategy achieves competitive generalization error.

The kernel performs well in time series classification tasks.

Abstract

Time series are an interesting frontier for kernel-based methods, for the simple reason that there is no kernel designed to represent them and their unique characteristics in full generality. Existing sequential kernels ignore the time indices, with many assuming that the series must be regularly-spaced; some such kernels are not even psd. In this manuscript, we show that a "series kernel" that is general enough to represent irregularly-spaced multivariate time series may be built out of well-known "vector kernels". We also show that all series kernels constructed using our methodology are psd, and are thus widely applicable. We demonstrate this point by formulating a Gaussian process-based strategy - with our series kernel at its heart - to make predictions about test series when given a training set. We validate the strategy experimentally by estimating its generalisation error on multiple datasets and comparing it to relevant baselines. We also demonstrate that our series kernel may be used for the more traditional setting of time series classification, where its performance is broadly in line with alternative methods.