Weak Dependencies in Approximation Spaces

The article reviews the basics of the variable precision rough set and the Bayesian approaches to data dependencies detection and analysis. The variable precision rough set and the Bayesian rough set theories are extensions of the rough set theory. They are focused on the recognition and modelling of set overlap-based, also referred to as probabilistic, relationships between sets. The set-overlap relationships are used to construct approximations of undefinable sets. The primary application of the approach is to analysis of weak data co-occurrence-based dependencies in probabilistic decision tables learned from data. The probabilistic decision tables are derived from data to represent the inter-data item connections, typically for the purposes of their analysis or data value prediction. The theory is illustrated with a comprehensive application example illustrating utilization of probabilistic decision tables to face image classification.