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Products of Gaussians and Probabilistic Minor Component C.K.I. Williams
 

Summary: Products of Gaussians and Probabilistic Minor Component
Analysis
C.K.I. Williams
Division of Informatics, University of Edinburgh, Edinburgh EH1 2QL, UK
c.k.i.williams@ed.ac.uk http://anc.ed.ac.uk
F.V. Agakov
System Engineering Research Group, Chair of Manufacturing Technology
Friedrich-Alexander-University Erlangen-Nuremberg, 91058 Erlangen, Germany
F.Agakov@lft.uni-erlangen.de
July 2, 2001
Abstract
Recently Hinton introduced the Products of Experts (PoE) architecture for density estimation,
where individual expert probabilities are multiplied and re-normalized. 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 1-factor probabilistic principal
component analysis (PPCA) models.
1 Introduction
Recently Hinton (1999) introduced a new Product of Experts (PoE) model for combining expert proba-
bilities, where probability p(xj) is computed as a normalized multiplication of probabilities p i (xj i ) of

  

Source: Agakov, Felix - Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh
Edinburgh, University of - Division of Informatics, Institute for Adaptive and Neural Computation
Williams, Chris - Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh

 

Collections: Computer Technologies and Information Sciences