Interval-based reasoning over continuous variables using independent component analysis and Bayesian networks

Abstract

Bayesian networks (BNs) can be used for probabilistic reasoning over discrete variables. Their extension to the continuous domain, however, remains an open research issue. In this work, we address the Bayesian inference problem for continuous variables when negative evidence is available. This situation is faced when, because of unreliable or imperfect sensors, some variables are observed to be at specific intervals. We propose two solutions to this issue. The first one, dubbed dynamic discrete BN (DD-BN), is simply an adaptation of the dynamic discretization method; the second, referred to as SICA, is based on spline functions and the independent component analysis (ICA) method. SICA can represent a wide range of general multivariate distributions and possesses some integration characteristics that facilitate the inference process. Empirical trials on public datasets and simulated data yielded promising results regarding inference time and accuracy. Indeed, SICA achieved the highest accuracy at the expense of increased inference time with increasing dimensions.