Normalizing Kalman Filters for Multivariate Time Series Analysis

This paper tackles the modelling of large, complex and multivariate time series panels in a probabilistic setting. To this extent, we present a novel approach reconciling classical state space models with deep learning methods. By augmenting state space models with normalizing flows, we mitigate imprecisions stemming from idealized assumptions in state space models. The resulting model is highly flexible while still retaining many of the attractive properties of state space models, e.g., uncertainty and observation errors are properly accounted for, inference is tractable, sampling is efficient and good generalization performance is observed, even in low data regimes. We demonstrate competitiveness against state-of-the-art deep learning methods on the tasks of forecasting real world data and handling varying levels of missing data. * Equal contribution. † Work done while at Amazon. 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada.