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(Neural Computation. 2002;14:1169-1182.)
© 2002 The MIT Press

Letter

Products of Gaussians and Probabilistic Minor Component Analysis

C. K. I. Williams

c.k.i.williams{at}ed.ac.uk, Division of Informatics, University of Edinburgh, Edinburgh EH1 2QL, U.K.

F. V. Agakov

F.Agakov{at}lft.uni-erlangen.de, System Engineering Research Group, Chair of Manufacturing Technology Friedrich-Alexander-University Erlangen-Nuremberg, 91058 Erlangen, Germany

Recently, Hinton introduced the products of experts architecture for density estimation, where individual expert probabilities are multiplied and renormalized. We consider products of gaussian "pancakes" equally elongated in all directions except one and prove that the maximum likelihood solution for the model gives rise to a minor component analysis solution. We also discuss the covariance structure of sums and products of gaussian pancakes or one-factor probabilistic principal component analysis models.






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