Learning Continuous-Time Hidden Markov Models for Event Data

@inproceedings{Liu2017LearningCH,
  title={Learning Continuous-Time Hidden Markov Models for Event Data},
  author={Yu-Ying Liu and Alexander Moreno and Shuang Li and Fuxin Li and Le Song and James M. Rehg},
  booktitle={Mobile Health - Sensors, Analytic Methods, and Applications},
  year={2017}
}
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… 
Efficient Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling
TLDR
This paper presents the first complete characterization of efficient EM-based learning methods for CT-HMM models, as well as the first solution to decoding the optimal state transition sequence and the corresponding state dwelling time.
New formulation of the Logistic-Normal process to analyze trajectory tracking data
TLDR
This work proposes a new model based on the Logistic-Normal process that is invariant with respect to the choice of the reference element and the ordering of the probability vectors components, and estimates the model under a Bayesian framework.
Rating transitions forecasting: a filtering approach
TLDR
This paper considers that the dynamics of rating migrations is governed by an unobserved latent factor, and proposes a filtering formula which can be used for predicting future transition probabilities according to economic regimes without using any external covariates.
Learning Temporal Rules from Noisy Timeseries Data
TLDR
Neural Temporal Logic Programming (Neural TLP) is proposed which first learns implicit temporal relations between atomic events and then lifts logic rules for composite events, given only the composite events labels for supervision.
A Spatiotemporal Approach to Predicting Glaucoma Progression Using a CT-HMM
TLDR
This work model and predict longitudinal glaucoma measurements using an interpretable, discrete state space model and jointly model the change in RNFL with VFI using a CT-HMM and predict future measurements.
A survey of cyber-physical system implementations of real-time personalized interventions
TLDR
The state-of-the-art of the systems that have been built to-date of CPSs for real-time personalized interventions are reviewed to summarize current technical challenges and future opportunities for both future CPS implementers and behavioral scientists designing CPS for personalized interventions.
Mobile Health
TLDR
Six chapters that demonstrate the novel utility of mHealth, present design lessons in developing mHealth applications, and describe tools for managing mHealth data collection studies are described.
Integrated Continuous-time Hidden Markov Models
TLDR
A new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the previous observation, not only on its current state is proposed.

References

SHOWING 1-10 OF 144 REFERENCES
Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks
TLDR
The EM algorithm is used to extend the representation of CTBNs to allow a much richer class of transition durations distributions, known as phase distributions, which are a highly expressive semi-parametric representation, which can approximate any duration distribution arbitrarily closely.
Activity recognition and abnormality detection with the switching hidden semi-Markov model
TLDR
The switching hidden semi-markov model (S-HSMM) is introduced, a two-layered extension of thehidden semi-Markov model for the modeling task and an effective scheme to detect abnormality without the need for training on abnormal data is proposed.
Efficient maximum likelihood parameterization of continuous-time Markov processes.
TLDR
A maximum likelihood estimator is introduced for constructing continuous-time Markov processes over finite state-spaces from data observed at a finite time interval that is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models.
Generator estimation of Markov jump processes
Generator estimation of Markov jump processes based on incomplete observations nonequidistant in time.
TLDR
This paper considers the case of a given time series of the discretely observed jump process and shows how to compute efficiently the maximum likelihood estimator of its infinitesimal generator and demonstrates in detail that the method allows us to handle observations nonequidistant in time.
Summary Statistics for Endpoint-Conditioned Continuous-Time Markov Chains
Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behaviour, and mathematical finance. We consider the problem of
Statistical inference for discretely observed Markov jump processes
Summary.  Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity
Multi-State Models for Panel Data: The msm Package for R
TLDR
The range of Markov models and their extensions which can be fitted to panel-observed data, and their implementation in the msm package for R are reviewed, intended to be straightforward to use, flexible and comprehensively documented.
Unsupervised learning of disease progression models
TLDR
A probabilistic disease progression model that learns a continuous-time progression model from discrete-time observations with non-equal intervals and learns a compact set of medical concepts as the bridge between the hidden progression process and the observed medical evidence, which are usually extremely sparse and noisy.
Longitudinal Modeling of Glaucoma Progression Using 2-Dimensional Continuous-Time Hidden Markov Model
TLDR
The learned model not only corroborates the clinical findings that structural degeneration is more evident than functional degeneration in early glaucoma and the opposite is observed in more advanced stages, but also reveals the exact stages where the trend reverses.
...
...