Characterizing A Database of Sequential Behaviors with Latent Dirichlet Hidden Markov Models

TL;DR

This paper introduces LDHMMs, a hierarchical generative model for sequential behaviors that captures sequence-level and database-level parameters, improving behavior modeling and classification accuracy.

Contribution

The paper presents LDHMMs, a novel hierarchical model for sequences, with an efficient variational EM algorithm for learning, outperforming existing models in behavior analysis.

Findings

LDHMMs achieve better log-likelihood scores.

LDHMMs deliver competitive sequence classification results.

The model effectively captures hierarchical sequence structures.

Abstract

This paper proposes a generative model, the latent Dirichlet hidden Markov models (LDHMM), for characterizing a database of sequential behaviors (sequences). LDHMMs posit that each sequence is generated by an underlying Markov chain process, which are controlled by the corresponding parameters (i.e., the initial state vector, transition matrix and the emission matrix). These sequence-level latent parameters for each sequence are modeled as latent Dirichlet random variables and parameterized by a set of deterministic database-level hyper-parameters. Through this way, we expect to model the sequence in two levels: the database level by deterministic hyper-parameters and the sequence-level by latent parameters. To learn the deterministic hyper-parameters and approximate posteriors of parameters in LDHMMs, we propose an iterative algorithm under the variational EM framework, which consists of E and M steps. We examine two different schemes, the fully-factorized and partially-factorized forms, for the framework, based on different assumptions. We present empirical results of behavior modeling and sequence classification on three real-world data sets, and compare them to other related models. The experimental results prove that the proposed LDHMMs produce better generalization performance in terms of log-likelihood and deliver competitive results on the sequence classification problem.