Sparse Multinomial Logistic Regression via Bayesian L1 Regularisation

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Gavin Cawley, Nicola Talbot, Mark Girolami


Multinomial logistic regression provides the standard penalised maximum- likelihood solution to multi-class pattern recognition problems. More recently, the development of sparse multinomial logistic regression models has found ap- plication in text processing and microarray classification, where explicit identifi- cation of the most informative features is of value. In this paper, we propose a sparse multinomial logistic regression method, in which the sparsity arises from the use of a Laplace prior, but where the usual regularisation parameter is inte- grated out analytically. Evaluation over a range of benchmark datasets reveals this approach results in similar generalisation performance to that obtained using cross-validation, but at greatly reduced computational expense.