LAMORE: A Stable, Scalable Approach to Latent Vector Autoregressive Modeling of Categorical Time Series

Abstract

Latent vector autoregressive models for categorical time series have a wide range of potential applications from marketing research to healthcare analytics. However, a brute-force particle filter implementation of the Expectation-Maximization (EM) algorithm often fails to estimate the maximum likelihood parameters due to the Monte Carlo approximation of the E-step and multiple local optima of the log-likelihood function. This paper proposes two auxiliary techniques that help stabilize and calibrate the estimated parameters. These two techniques, namely \textit{asymptotic} mean regularization and \textit{low-resolution} augmentation, do not require any additional parameter tuning, and can be implemented by modifying the brute-force EM algorithm. Experiments with simulated data show that the proposed techniques effectively stabilize the parameter estimation process. Also, experimental results using Medicare and MIMIC-II datasets illustrate various potential applications of the proposed model and methods.