  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.
