Empirical System Learning for Statistical Pattern Recognition With Non-Uniform Error Criteria

Most pattern recognition systems attempt to maximize the rate of correct recognition, regardless of the varying and often subjective significance of individual patterns. There are situations in which such uniform treatment of the recognition results may not be appropriate or sufficient, giving rise to the consideration of the non-uniform error cost issue and, in the context of machine learning, the cost-sensitive learning. Although a number of proposals to address the issue have been considered, the problem of system design or training that achieves minimum expected error cost remains an open one. This paper introduces a decision-theoretic framework based on the Bayes decision theory for applications with non-uniform error criteria. It addresses the two fundamental aspects in Bayes' decision theory, the optimal decision policy and the acquisition of system knowledge (i.e., training) for implementing the decision policy. The framework includes, among other components of the recognizer, a minimum risk decision rule, a smooth system objective function that serves as a surrogate for optimization involving non-uniform error costs, and a parameter optimization procedure to obtain the recognizer's parameters. To demonstrate and confirm the effectiveness of the proposed framework, Gaussian mixture classifiers are designed and implemented in experiments on multi-class datasets generated from Monte Carlo simulations as well as various prevalent machine learning datasets.