Probabilistic independence of causal influences

Authors:

Adam Zagorecki and Marek J. Druzdzel
Decision Systems Laboratory
School of Information Sciences
and Intelligent Systems Program
University of Pittsburgh
135 North Bellefield Avenue
Pittsburgh, PA 15260, U.S.A.
e-mail: adamz@sis.pitt.edu, marek@sis.pitt.edu

Abstract:

One practical problem with building large scale Bayesian network models is an exponential growth of the number of numerical parameters in conditional probability tables. Obtaining large number of probabilities from domain experts is too expensive and too time demanding in practice. A widely accepted solution to this problem is the assumption of independence of causal influences (ICI) which allows for parametric models that define conditional probability distributions using only a number of parameters that is linear in the number of causes. ICI models, such as the noisy-OR and the noisy-AND gates, have been widely used by practitioners. In this paper we propose PICI, probabilistic ICI, an extension of the ICI assumption that leads to more expressive parametric models. We provide examples of three PICI models and demonstrate how they can cope with a combination of positive and negative influences, something that is hard for noisy-OR and noisy-AND gates.