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Improved Variational Approximation for Bayesian PCA Shivani Agarwal and Christopher M. Bishop
 

Summary: Improved Variational Approximation for Bayesian PCA
Shivani Agarwal and Christopher M. Bishop
August 7, 2003
Abstract
As with most non-trivial models, an exact Bayesian treatment of the probabilistic PCA model (under
a meaningful prior) is analytically intractable. Various approximations have therefore been proposed in
the literature; these include approximations based on type-II maximum likelihood as well as variational
approximations. In this document, we describe an improved variational approximation for Bayesian PCA.
This is achieved by defining a more general prior over the model parameters that has stronger conjugacy
properties, thereby allowing for a more accurate variational approximation to the true posterior.
1 Introduction
The probabilistic PCA model is defined by1
p(t|x, , W, ) = N(t|Wx + , -1
Id), (1)
where t Rd
is the observed variable, x Rq
(q < d) is a latent variable with prior distribution
p(x) = N(x|0, Iq), (2)
and Rd
, W Rdq

  

Source: Agarwal, Shivani - Department of Computer Science and Automation, Indian Institute of Science, Bangalore

 

Collections: Computer Technologies and Information Sciences