Learning continuous-time hidden Markov models for event data

Yu Ying Liu, Alexander Moreno, Shuang Li, Fuxin Li, Le Song, James M. Rehg

Research output: Chapter in Book/Report/Conference proceedingChapter


The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive modeling tool for mHealth data that takes the form of events occurring at irregularly-distributed continuous time points. However, the lack of an efficient parameter learning algorithm for CT-HMM has prevented its widespread use, necessitating the use of very small models or unrealistic constraints on the state transitions. In this paper, we describe recent advances in the development of efficient EM-based learning methods for CT-HMM models. We first review the structure of the learning problem, demonstrating that it consists of two challenges: (1) the estimation of posterior state probabilities and (2) the computation of end-state conditioned expectations. The first challenge can be addressed by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by exploiting computational methods traditionally used for continuous-time Markov chains and adapting them to the CT-HMM domain. We describe three computational approaches and analyze the tradeoffs between them. We evaluate the resulting parameter learning methods in simulation and demonstrate the use of models with more than 100 states to analyze disease progression using glaucoma and Alzheimer's Disease datasets.

Original languageEnglish (US)
Title of host publicationMobile Health
Subtitle of host publicationSensors, Analytic Methods, and Applications
EditorsJames M Rehg, Susan A Murphy, Santosh Kumar
Number of pages27
ISBN (Electronic)9783319513942
ISBN (Print)9783319513935
StatePublished - Jul 12 2017
Externally publishedYes

ASJC Scopus subject areas

  • General Medicine
  • General Computer Science


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