Frugal hypothesis testing and classification

Abstract

The design and analysis of decision rules using detection theory and statistical learning theory is important because decision making under uncertainty is pervasive. Three perspectives on limiting the complexity of decision rules are considered in this thesis: geometric regularization, dimensionality reduction, and quantization or clustering. Controlling complexity often reduces resource usage in decision making and improves generalization when learning decision rules from noisy samples. A new margin-based classifier with decision boundary surface area regularization and optimization via variational level set methods is developed. This novel classifier is termed the geometric level set (GLS) classifier. A method for joint dimensionality reduction and margin-based classification with optimization on the Stiefel manifold is developed. This dimensionality reduction approach is extended for information fusion in sensor networks. A new distortion is proposed for the quantization or clustering of prior probabilities appearing in the thresholds of likelihood ratio tests. This distortion is given the name mean Bayes risk error (MBRE). The quantization framework is extended to model human decision making and discrimination in segregated populations.