Danny Eitan

Ron Teichner, Ron Meir, Danny Eitan

Consider a situation where a new patient arrives in the Intensive Care Unit (ICU) and is monitored by multiple sensors. We wish to assess relevant unmeasured physiological variables (e.g., cardiac contractility and output and vascular resistance) that have a strong effect on the patients diagnosis and treatment. We do not have any information about this specific patient, but, extensive offline information is available about previous patients, that may only be partially related to the present patient (a case of dataset shift). This information constitutes our prior knowledge, and is both partial and approximate. The basic question is how to best use this prior knowledge, combined with online patient data, to assist in diagnosing the current patient most effectively. Our proposed approach consists of three stages: (i) Use the abundant offline data in order to create both a non-causal and a causal estimator for the relevant unmeasured physiological variables. (ii) Based on the non-causal estimator constructed, and a set of measurements from a new group of patients, we construct a causal filter that provides higher accuracy in the prediction of the hidden physiological variables for this new set of patients. (iii) For any new patient arriving in the ICU, we use the constructed filter in order to predict relevant internal variables. Overall, this strategy allows us to make use of the abundantly available offline data in order to enhance causal estimation for newly arriving patients. We demonstrate the effectiveness of this methodology on a (non-medical) real-world task, in situations where the offline data is only partially related to the new observations. We provide a mathematical analysis of the merits of the approach in a linear setting of Kalman filtering and smoothing, demonstrating its utility.

Stav Belogolovsky, Ido Greenberg, Danny Eitan et al.

Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In addition, current methods model measurements and control together, limiting generalization to different control policies. These properties severely limit applicability to medical treatment problems, which require reliable forecasting given high noise, limited data and changing treatment policies. We introduce the Neural Eigen-SDE algorithm (NESDE), which relies on piecewise linear dynamics modeling with spectral representation. NESDE provides control over the expressiveness level; decoupling of control from measurements; and closed-form continuous prediction in inference. NESDE is demonstrated to provide robust forecasting in both synthetic and real high-noise medical problems. Finally, we use the learned dynamics models to publish simulated medical gym environments.