Hidden Markov models as recurrent neural networks: An application to Alzheimer's disease.

Hidden Markov models (HMMs) are commonly used for disease progression modeling when the true patient health state is not fully known. Since HMMs may have multiple local optima, performance can be improved by incorporating additional patient covariates to inform estimation. To allow for this, we develop hidden Markov recurrent neural networks (HMRNNs), a special case of recurrent neural networks with the same likelihood function as a corresponding discrete-observation HMM. The HMRNN can be combined with any other predictive neural networks that take patient information as input, with all parameters estimated simultaneously via gradient descent. Using a dataset of Alzheimer's disease patients, we demonstrate how combining the HMRNN with other predictive neural networks improves disease forecasting performance and offers a novel clinical interpretation compared with a standard HMM trained via expectation-maximization.