Bounds for Bayesian network classifiers with reduced precision parameters

Sebastian Tschiatschek, Carlos Eduardo Cancino Chacón, Franz Pernkopf

Abstract: Bayesian network classifiers are probabilistic classifiers achieving good classification rates in various applications. These classifiers consist of a directed acyclic graph and a set of conditional probability densities, which in case of discrete-valued nodes can be represented by conditional probability tables. In this paper, we investigate the effect of quantizing these conditional probabilities. We derive worst-case and best-case bounds on the classification rate using interval arithmetic. Furthermore, we determine performance bounds that hold with a user specified confidence using quantization theory. Our results emphasize that only small bit-widths are necessary to achieve good classification rates.