Bayesian model based classification and its applications

 

Bayesian classification models are useful for flexible prediction and proper quantification of uncertainties. We consider two specific classification problems: (i) classification when the sample size is much smaller than number of parameters (large `p' small `n' problems) and (ii) curve classification.

In problem (i), we develop several Bayesian multiclass classification methods based on reproducing kernel Hilbert spaces. We consider the multinomial-logit models as well as models related to the Support Vector Machines (SVM). Precise classification of tumors is critical for cancer diagnosis and treatment. Using gene expression data to classify tumor types is a very promising tool in cancer diagnosis and we use our methods for this analysis.

Next, in (ii), we propose classification models where the predictor is a random function. We develop an unified hierarchical model which accommodate both the adaptive function estimation model as well as the logistic classification model. These two models are coupled to borrow strengths from each other in this unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible.