Kernel embeddings of longitudinal data

Abstract

Longitudinal data is the repeated observations of individuals through time. They often exhibit rich statistical qualities, such as skew or multimodality, that are difficult to capture using traditional parametric methods. To tackle this, we build a non-parametric Markov transition model for longitudinal data. Our approach uses kernel mean embeddings to learn a transition model that can express complex statistical features. We also propose an approximate data subsampling technique based on kernel herding and random Fourier features that allows our method to scale to large longitudinal data sets. We demonstrate our approach on two real world data sets.