Product Analysis: Explaining Observations as Products of Hidden Variables

Anitha Kannan, M.Math. thesis, University of Waterloo, 2001

Supervisor: Brendan J. Frey

Committee members: Nick Cercone and Richard Mann

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Thesis Abstract: [Download the thesis]

Many types of observations are functions of hidden variables. In methods such as factor analysis and principal component analysis, we model observations as a linear combination of hidden variables. However, observations often are not a linear function of hidden variables. For example, images of an object under varying ambient lighting conditions are produced by the product of light intensity and the pixel intensities of a light-normalized image.

In this thesis, we introduce a technique called product analysis for learning product models. This model formulates observations as a linear function of products of hidden variables. Exact inference in this model is intractable, so we use a variational inference technique. We show how a generalized expectation maximization algorithm can be used to learn the model. We also explore a number of applications that can be formulated using product analysis models.