State-Sharing Sparse Hidden Markov Models for Personalized Sequences

Hidden Markov Model (HMM) is a powerful tool that has been widely adopted in sequence modeling tasks, such as mobility analysis, healthcare informatics, and online recommendation. However, using HMM for modeling personalized sequences remains a challenging problem: training a unified HMM with all the sequences often fails to uncover interesting personalized patterns; yet training one HMM for each individual inevitably suffers from data scarcity. We address this challenge by proposing a state-sharing sparse hidden Markov model (S3HMM) that can uncover personalized sequential patterns without suffering from data scarcity. This is achieved by two design principles: (1) all the HMMs in the ensemble share the same set of latent states; and (2) each HMM has its own transition matrix to model the personalized transitions. The result optimization problem for S3HMM becomes nontrivial, because of its two-layer hidden state design and the non-convexity in parameter estimation. We design a new Expectation-Maximization algorithm based, which treats the difference of convex programming as a sub-solver to optimize the non-convex function in the M-step with convergence guarantee. Our experimental results show that, S3HMM can successfully uncover personalized sequential patterns in various applications and outperforms baselines significantly in downstream prediction tasks.