Sparse Linear Dynamical System with Its Application in Multivariate Clinical Time Series

Linear Dynamical System (LDS) is an elegant mathematical framework for mod-eling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may not be able to model the complexities of a time series, while a large number of hidden states can lead to overfitting. In this paper, we study methods that impose an `1 regularization on the transition matrix of an LDS model to alleviate the problem of choosing the optimal number of hidden states. We incorporate a generalized gradient descent method into the Maximum a Posteriori (MAP) framework and use Expectation Maximization (EM) to iteratively achieve sparsity on the transi-tion matrix of an LDS model. We show that our Sparse Linear Dynamical System (SLDS) improves the predictive performance when compared to ordinary LDS on a multivariate clinical time series dataset.