  Relevance Vector Machine (RVM) is a supervised learning algorithm extended
from Support Vector Machine (SVM) based on the Bayesian sparsity model.
Compared with the regression problem, RVM classification is difficult to be
conducted because there is no closed-form solution for the weight parameter
posterior. Original RVM classification algorithm used Newton's method in
optimization to obtain the mode of weight parameter posterior then approximated
it by a Gaussian distribution in Laplace's method. It would work but just
applied the frequency methods in a Bayesian framework. This paper proposes a
Generic Bayesian approach for the RVM classification. We conjecture that our
algorithm achieves convergent estimates of the quantities of interest compared
with the nonconvergent estimates of the original RVM classification algorithm.
Furthermore, a Fully Bayesian approach with the hierarchical hyperprior
structure for RVM classification is proposed, which improves the classification
performance, especially in the imbalanced data problem. By the numeric studies,
our proposed algorithms obtain high classification accuracy rates. The Fully
Bayesian hierarchical hyperprior method outperforms the Generic one for the
imbalanced data classification.
