New Approach to Learning Noisy Boolean Functions

We give a new formulation of noise removal from data being Boolean functions used in Conceptual Inductive Learning. The algorithm is used as a part of a functional decomposition program. Paper gives an eecient heuristic algorithm for the minimization of multi-output Exclusive DNF (EDNF) expressions that generalize the Disjunctive Normal Forms (DNF) expressions popularly used in Machine Learning (ML). The algorithm can be used for preprocessing, after any stage of decomposition, and for postprocessing. In EDNF, the ANDs of DNF are AND-ed with NANDs, providing Exclusion cases. The EDNF is thus a disjunctive sum of AND/NAND gates, called Conditional Decoder (CDEC) functors. A pruning technique is based on analysis of sizes of AND and NAND parts in CDEC functors, and the numbers of true and false minterms covered by them. Experiments on ML benchmarks prove that our approach generates high-quality solutions, is especially eecient on strongly unspeciied functions, and reduces the recognition errors.