Classification of Sparse and Irregularly Sampled Time Series with Mixtures of Expected Gaussian Kernels and Random Features

This paper presents a kernel-based framework for classification of sparse and irregularly sampled time series. The properties of such time series can result in substantial uncertainty about the values of the underlying temporal processes, while making the data difficult to deal with using standard classification methods that assume fixed-dimensional feature spaces. To address these challenges, we propose to first re-represent each time series through the Gaussian process (GP) posterior it induces under a GP regression model. We then define kernels over the space of GP posteriors and apply standard kernel-based classification. Our primary contributions are (i) the development of a kernel between GPs based on the mixture of kernels between their finite marginals, (ii) the development and analysis of extensions of random Fourier features for scaling the proposed kernel to large-scale data, and (iii) an extensive empirical analysis of both the classification performance and scalability of our proposed approach.