Investigation on the construction of the Relevance Vector Machine based on cross entropy minimization

As a machine learning method under sparse Bayesian framework, classical Relevance Vector Machine (RVM) applies kernel methods to construct Radial Basis Function(RBF) networks using a least number of relevant basis functions. Compared to the well-known Support Vector Machine (SVM), the RVM provides a better sparsity, and an automatic estimation of hyperparameters. However, the performance of the original RVM purely depends on the smoothness of the presumed prior of the connection weights and parameters. Consequently, the sparsity is actually still controlled by the selection of kernel functions or kernel parameters. This may lead to severe underfitting or overfitting in some cases. In the research presented in this paper, we explicitly involve the number of basis functions into the objective of the optimization procedure, and construct the RVM by the minimization of the cross entropy between the 'hypothetical' probability distribution in the forward training pathway and the 'true' probability distribution in the backward testing pathway. The experimental results have shown that our proposed methodology can achieve both the least complexity of structure and goodness of appropriate fit to data.