288 pp. per issue
6 x 9, illustrated
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Neural Computation

November 1, 2000, Vol. 12, No. 11, Pages 2655-2684
(doi: 10.1162/089976600300014881)
© 2000 Massachusetts Institute of Technology
Gaussian Processes for Classification: Mean-Field Algorithms
Article PDF (165 KB)

We derive a mean-field algorithm for binary classification with gaussian processes that is based on the TAP approach originally proposed in statistical physics of disordered systems. The theory also yields an approximate leave-one-out estimator for the generalization error, which is computed with no extra computational cost. We show that from the TAP approach, it is possible to derive both a simpler “naive” mean-field theory and support vector machines (SVMs) as limiting cases. For both mean-field algorithms and support vector machines, simulation results for three small benchmark data sets are presented. They show that one may get state-of-the-art performance by using the leave-one-out estimator for model selection and the built-in leave-one-out estimators are extremely precise when compared to the exact leave-one-out estimate. The second result is taken as strong support for the internal consistency of the mean-field approach.