Optimal classifiers with minimum expected error within a Bayesian framework - Part II: Properties and performance analysis

Authors:
Lori A. Dalton;Edward R. Dougherty
Affiliations:
The Ohio State University, Department of Electrical and Computer Engineering, 205 Dreese Laboratory, 2015 Neil Avenue, Columbus, OH 43210, USA;Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA and Computational Biology Division, Translational Genomics Research Institute, Phoenix, AZ, USA
Venue:
Pattern Recognition
Year:
2013

Citing 9
Cited 1

Design and Analysis of Robust Binary Filters in the Context of a Prior Distribution for the States of Nature

Journal of Mathematical Imaging and Vision
Robust optimal granulometric bandpass filters

Signal Processing
Bayesian robust optimal linear filters

Signal Processing
Bayesian robustness in the control of gene regulatory networks

IEEE Transactions on Signal Processing
Optimal robust classifiers

Pattern Recognition
Bayesian Minimum Mean-Square Error Estimation for Classification Error—Part I: Definition and the Bayesian MMSE Error Estimator for Discrete Classification

IEEE Transactions on Signal Processing
Bayesian Minimum Mean-Square Error Estimation for Classification Error—Part II: Linear Classification of Gaussian Models

IEEE Transactions on Signal Processing
Robust Wiener- Kolmogorov theory

IEEE Transactions on Information Theory
Optimal classifiers with minimum expected error within a Bayesian framework-Part I: Discrete and Gaussian models

Pattern Recognition

Classifier design given an uncertainty class of feature distributions via regularized maximum likelihood and the incorporation of biological pathway knowledge in steady-state phenotype classification

Pattern Recognition

Quantified Score

Hi-index	0.01

Visualization

Abstract

In part I of this two-part study, we introduced a new optimal Bayesian classification methodology that utilizes the same modeling framework proposed in Bayesian minimum-mean-square error (MMSE) error estimation. Optimal Bayesian classification thus completes a Bayesian theory of classification, where both the classifier error and our estimate of the error may be simultaneously optimized and studied probabilistically within the assumed model. Having developed optimal Bayesian classifiers in discrete and Gaussian models in part I, here we explore properties of optimal Bayesian classifiers, in particular, invariance to invertible transformations, convergence to the Bayes classifier, and a connection to Bayesian robust classifiers. We also explicitly derive optimal Bayesian classifiers with non-informative priors, and explore relationships to linear and quadratic discriminant analysis (LDA and QDA), which may be viewed as plug-in rules under Gaussian modeling assumptions. Finally, we present several simulations addressing the robustness of optimal Bayesian classifiers to false modeling assumptions. Companion website: http://gsp.tamu.edu/Publications/supplementary/dalton12a.