Kernels for time series with irregularly-spaced multivariate observations
This work addresses a gap in kernel methods for time series analysis, particularly for irregularly-spaced multivariate data, though it appears incremental as it builds on existing vector kernels.
The authors tackled the problem of representing irregularly-spaced multivariate time series with kernel methods, which lacked general-purpose kernels, by constructing a series kernel from vector kernels that ensures positive semi-definiteness. They demonstrated its application in Gaussian process predictions and classification, achieving generalization error estimates comparable to baselines on multiple datasets.
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.