Probabilistic feature selection and classification vector machine

Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data with irrelevant features, traditional sparse Bayesian classifiers suffer from performance degradation and low efficiency due to the incapability of eliminating irrelevant features. To tackle this problem, we propose a novel sparse Bayesian embedded feature selection algorithm that adopts truncated Gaussian distributions as both sample and feature priors. The proposed algorithm, called probabilistic feature selection and classification vector machine (PFCVM_LP) is able to simultaneously select relevant features and samples for classification tasks. In order to derive the analytical solutions, Laplace approximation is applied to compute approximate posteriors and marginal likelihoods. Finally, parameters and hyperparameters are optimized by the type-II maximum likelihood method. Experiments on three datasets validate the performance of PFCVM_LP along two dimensions: classification performance and effectiveness for feature selection. Finally, we analyze the generalization performance and derive a generalization error bound for PFCVM_LP. By tightening the bound, the importance of feature selection is demonstrated.