  Analysis of multivariate healthcare time series data is inherently
challenging: irregular sampling, noisy and missing values, and heterogeneous
patient groups with different dynamics violating exchangeability. In addition,
interpretability and quantification of uncertainty are critically important.
Here, we propose a novel class of models, a mixture of coupled hidden Markov
models (M-CHMM), and demonstrate how it elegantly overcomes these challenges.
To make the model learning feasible, we derive two algorithms to sample the
sequences of the latent variables in the CHMM: samplers based on (i) particle
filtering and (ii) factorized approximation. Compared to existing inference
methods, our algorithms are computationally tractable, improve mixing, and
allow for likelihood estimation, which is necessary to learn the mixture model.
Experiments on challenging real-world epidemiological and semi-synthetic data
demonstrate the advantages of the M-CHMM: improved data fit, capacity to
efficiently handle missing and noisy measurements, improved prediction
accuracy, and ability to identify interpretable subsets in the data.
