DifferentiableHMM: Neural Differentiable Hidden Markov Model

Abstract

Modeling clinical time series demands interpretable patient states alongside the ability to capture long-range dependencies. Classical HMMs provide discrete, clinically meaningful states but ignore distant history; RNNs capture rich temporal patterns but act as black boxes. We introduce DifferentiableHMM, a unified, end-to-end differentiable probabilistic model, not a simple stacking of an HMM and a neural net. An LSTM encoder produces history-aware representations that condition both transition probabilities and GMM emission mixture weights via a small MixtureSelector network; transitions, emissions and the selector are optimized jointly by backpropagating through EM-like inference, producing a single coherent model in which inference and learning reinforce one another. On a MIMIC-III ICU benchmark, DifferentiableHMM reduces sequence negative log-likelihood by 40%, increases one-step R² by 5%, and lowers calibration error by 24% versus HMM and LSTM baselines. Discrete latent states retain clinical interpretability (mutual information = 0.824) and ablations show the performance gains disappear if components are trained separately. DifferentiableHMM therefore reconciles interpretability, calibrated uncertainty, and neural expressivity in a principled framework for healthcare sequence modeling.