Bayesian Reduced Rank Regression for Classification
Many classical multivariate analysis methods are special cases of reduced rank regression, including canonical correlation analysis, redundancy analysis, and R. A. Fisher’s linear discriminant analysis. The latter classifies an object based on a few linear combinations of its multivariate measurements. Classical inference for linear discriminant analysis may be based on asymptotic theory or resampling methods. A Bayesian linear discriminant analysis is proposed using Bayesian reduced rank regression as a starting point. The model can be implemented in Bayesian software with Markov chain Monte Carlo approaches and is easily extendable.
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