Conference paper

Proceedings of the 8th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty.

Oeconomica

Praha

2005

159-166

Ing. Jiří Vomlel, Ph.D. (ÚTIA - Oddělení matematické teorie rozhodování)

Decomposition of Probability Tables Representing Boolean Functions [file]

We apply tensor rank-one decomposition (Savicky and Vomlel, 2005) to conditional probability tables representing Boolean functions. We present a numerical algorithm that can be used to find a minimal tensor rank-one decomposition together with the results of the experiments performed using the proposed algorithm.
We will pay special attention to a family of Boolean functions that are common in probabilistic models from practice - monotone and symmetric Boolean functions. We will show that these functions can be better decomposed than general Boolean functions, specifically, rank of their corresponding tensor is lower than average rank of a general Boolean function.