Quadratic discriminant analysis is a method for classification where each class posterior is modeled by a Gaussian distribution. Our work establishes new theory for Bayesian estimation for the Gaussian distributions. We take a distribution-based approach instead of the standard parameter-based approach. We show that Bayesian QDA is linked to Friedman's regularized QDA. Also, we show that the class that minimizes the misclassification cost is also found by comparing the class posteriors estimated by minimizing an expected risk, where the risk can be any Bregman divergence. Extensive simulations establish that Bayesian QDA with data-dependent priors is an effective classification method.

Personnel:

Maya R. Gupta (EE Associate Professor)

Santosh Srivastava (PhD, UW Applied Math 2007)

Bela Frigyik (Post-doc, Dept. of Math., Purdue Univ.)

Publications:

"Bayesian Quadratic Discriminant Analysis," Santosh Srivastava, Maya R. Gupta, and Bela Frigyik, Journal of Machine Learning Research, vol. 8, pp. 1277-1305, 2007. Complete Simulation Code

"Thesis: Bayesian Minimum Expected Risk Estimation of Distributions for Statistical Learning," Santosh Srivastava, Univ. of Washington PhD Thesis, 2007.

"Distribution-based Bayesian minimum expected risk parametric classification," Santosh Srivastava and Maya R. Gupta, Proc of the IEEE Intl. Symposium on Information Theory, 2006.

Related Work:

Principles of Estimation