Switching State Space Modeling via Constrained Inference for Clinical Outcome Prediction

In clinical settings, timely and accurate prediction of adverse patient outcomes can help guide treatment decisions. While deep learning models have demonstrated strong predictive performance, they often lack interpretability. To address this gap, we propose a framework that combines the predictive strength of a black-box discriminative model, such as a deep neural network, with the interpretability of a latent variable model. Specifically, we develop a constrained inference approach to train a switching state-space model-an autoregressive hidden Markov model (AR-HMM)-that learns interpretable discrete latent states from multivariate clinical time series, enabling the modeling of patient trajectories as transitions among these states while also achieving high predictive accuracy in downstream outcomes. Our method leverages knowledge distillation: a high-capacity LSTM "teacher" model is first trained to predict a target clinical outcome of interest, and its predictive behavior is then transferred to an interpretable AR-HMM "student" model through a similarity constraint during training. We use a constrained variational inference approach to estimate the parameters of the AR-HMM with a similarity preserving constraint, ensuring that input pairs with similar representation in the teacher model also have similar representation in the student model. We evaluated our approach using two real-world clinical datasets. Our approach demonstrates predictive performance comparable to state-of-the-art deep learning models, while producing interpretable latent trajectories that reflect clinically meaningful patient states.