Choice of Basis for Laplace Approximation

Authors:
David J. C. MacKay
Affiliations:
Cavendish Laboratory, Cambridge, CB3 0HE, United Kingdom. E-mail: Email: mackay@mrao.cam.ac.uk
Venue:
Machine Learning
Year:
1998

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Abstract

Maximum a posteriori optimization of parameters and the Laplace approximation for the marginal likelihood are both basis-dependent methods. This note compares two choices of basis for models parameterized by probabilities, showing that it is possible to improve on the traditional choice, the probability simplex, by transforming to the ‘softmax’ basis.