A Bayesian approach to joint feature selection and classifier design

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 26; no. 9; pp. 1105 - 1111
• Main Authors: Krishnapuram, B., Harternink, A.J., Carin, L., Figueiredo, M.A.T.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2004; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Artificial Intelligence; automatic relevance determination; Bayes Theorem; Bayesian methods; Biomarkers, Tumor - genetics; Cluster Analysis; Colonic Neoplasms - diagnosis; Colonic Neoplasms - genetics; Computer Simulation; Diagnosis, Computer-Assisted - methods; Distribution functions; EM algorithm; feature selection; Gene Expression Profiling - methods; Humans; Index Terms- Pattern recognition; Information Storage and Retrieval - methods; Kernel; Leukemia - diagnosis; Leukemia - genetics; Models, Biological; Models, Statistical; Pattern Recognition, Automated - methods; Polynomials; relevance vector machines; Reproducibility of Results; Sensitivity and Specificity; sparse probit regression; sparsity; Statistical learning; Supervised learning; Support vector machine classification; Support vector machines; Testing; Training data
• ISSN: 0162-8828; 1939-3539
• DOI: 10.1109/TPAMI.2004.55

This paper adopts a Bayesian approach to simultaneously learn both an optimal nonlinear classifier and a subset of predictor variables (or features) that are most relevant to the classification task. The approach uses heavy-tailed priors to promote sparsity in the utilization of both basis functions and features; these priors act as regularizers for the likelihood function that rewards good classification on the training data. We derive an expectation- maximization (EM) algorithm to efficiently compute a maximum a posteriori (MAP) point estimate of the various parameters. The algorithm is an extension of recent state-of-the-art sparse Bayesian classifiers, which in turn can be seen as Bayesian counterparts of support vector machines. Experimental comparisons using kernel classifiers demonstrate both parsimonious feature selection and excellent classification accuracy on a range of synthetic and benchmark data sets.