title: Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression.
abstract: The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer's disease dataset.
authors.affiliation: College of Computing Georgia Institute of Technology Atlanta, GA.
authors.forename: Yu-Ying
authors.initials: YY
authors.lastname: Liu
authors.affiliation: College of Computing Georgia Institute of Technology Atlanta, GA.
authors.forename: Shuang
authors.initials: S
authors.lastname: Li
authors.affiliation: College of Computing Georgia Institute of Technology Atlanta, GA.
authors.forename: Fuxin
authors.initials: F
authors.lastname: Li
authors.affiliation: College of Computing Georgia Institute of Technology Atlanta, GA.
authors.forename: Le
authors.initials: L
authors.lastname: Song
authors.affiliation: College of Computing Georgia Institute of Technology Atlanta, GA.
authors.forename: James M
authors.initials: JM
authors.lastname: Rehg