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Abstract:
The technique of principal component analysis (PCA) has
recently been expressed as the maximum likelihood solution for a
generative latent variable model. In this paper we use this
probabilistic reformulation as the basis for a Bayesian treatment
of PCA. Our key result is that effective dimensionality of the
latent space (equivalent to the number of retained principal
components) can be determined automatically as part of the Bayesian
inference procedure. An important application of this framework is
to mixtures of probabilistic PCA models, in which each component
can determine its own effective complexity.
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