Interpretable Latent Variables in Deep State Space Models

We introduce a new version of deep state-space models (DSSMs) that combines a recurrent neural network with a state-space framework to forecast time series data. The model estimates the observed series as functions of latent variables that evolve non-linearly through time. Due to the complexity and non-linearity inherent in DSSMs, previous works on DSSMs typically produced latent variables that are very difficult to interpret. Our paper focus on producing interpretable latent parameters with two key modifications. First, we simplify the predictive decoder by restricting the response variables to be a linear transformation of the latent variables plus some noise. Second, we utilize shrinkage priors on the latent variables to reduce redundancy and improve robustness. These changes make the latent variables much easier to understand and allow us to interpret the resulting latent variables as random effects in a linear mixed model. We show through two public benchmark datasets the resulting model improves forecasting performances.