LEARNING TEMPORAL PROBABILISTIC CAUSAL-MODELS FROM LONGITUDINAL DATA

Medical problems often require the analysis and interpretation of larg e collections of longitudinal data in terms of a structural model of t he underlying physiological behavior. A suitable way to deal with this problem is to identify a temporal causal model that may effectively e xplain the patterns observed in the data. Here we will concentrate on probabilistic models, that provide a convenient framework to represent and manage underspecified information; in particular, we will conside r the class of Causal Probabilistic Networks (CPN). We propose a metho d to perform structural learning of CPNs representing time-series thro ugh model selection. Starting from a set of plausible causal structure s and a collection of possibly incomplete longitudinal data, we apply a learning algorithm to extract from the data the conditional probabil ities describing each model. The models are then ranked according to t heir performance in reconstructing the original time-series, using sev eral scoring functions, based on one-step ahead predictions, In this p aper we describe the proposed methodology through an example taken fro m the diabetes monitoring domain. The selection process is applied to a set of input-output models that generalize the class of ARX models, where the inputs are the insulin and meal intakes and the outputs are the blood glucose levels. Although the physiological process underlyin g this particular application is characterized by strong non-lineariti es and low data reliability, we show that it is possible to obtain mea ningful results, in terms of conditional probability learning and mode l ranking power.