Abstract
One of the central issues in the use of principal component
analysis (PCA) for data modelling is that of choosing the appropriate
number of retained components. This problem was recently addressed
through the formulation of a Bayesian treatment of PCA in terms of a
probabilistic latent variable model. A central feature of this approach
is that the effective dimensionality of the latent space is determined
automatically as part of the Bayesian inference procedure. In common
with most non-trivial Bayesian models, however, the required
marginalizations are analytically intractable, and so an approximation
scheme based on a local Gaussian representation of the posterior
distribution was employed. In this paper we develop an alternative,
variational formulation of Bayesian PCA, based on a factorial
representation of the posterior distribution. This approach is
computationally efficient, and unlike other approximation schemes, it
maximizes a rigorous lower bound on the marginal log probability of the
observed data
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