Journal Article

Classification and Categorical Inputs with Treed Gaussian Process Models

Gramacy, Robert B., Broderick, Tamara

2011

Overview

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have, separately, enjoyed great success in application to classification problems. An example of the former is Bayesian CART. In the latter, real-valued GP output may be utilized for classification via latent variables, which provide classification rules by means of a softmax function. We formulate a Bayesian model averaging scheme to combine these two models and describe a Monte Carlo method for sampling from the full posterior distribution with joint proposals for the tree topology and the GP parameters corresponding to latent variables at the leaves. We concentrate on efficient sampling of the latent variables, which is important to obtain good mixing in the expanded parameter space. The tree structure is particularly helpful for this task and also for developing an efficient scheme for handling categorical predictors, which commonly arise in classification problems. Our proposed classification TGP (CTGP) methodology is illustrated on a collection of synthetic and real data sets. We assess performance relative to existing methods and thereby show how CTGP is highly flexible, offers tractable inference, produces rules that are easy to interpret, and performs well out of sample.

• Publisher: Springer-Verlag,Springer,Springer Nature B.V
• Subject: Algorithmics. Computability. Computer arithmetics / Applied sciences / Automatic classification / Bayesian analysis / Bioinformatics / Classification / Computer science; control theory; systems / Exact sciences and technology / Family physicians / Inference / Marketing / Mathematical models / Mathematics / Mathematics and Statistics / Methods / Methods of scientific computing (including symbolic computation, algebraic computation) / Monte Carlo simulation / Multivariate analysis / Normal distribution / Numerical analysis. Scientific computation / Pattern Recognition / Probability and statistics / Probability theory and stochastic processes / Psychometrics / Rules / Sampling / Sciences and techniques of general use / Signal,Image and Speech Processing / Statistical Theory and Methods / Statistics / Stochastic processes / Theoretical computing / Tree structures / Variables