Matthias Seeger, Guillaume Bouchard
AISTATS 2012 : Fifteenth International Conference on Artificial Intelligence and Statistics 2012, La Palma, Canary Islands, Spain, April 21-23, 2012.
Probabilistic matrix factorization methods aim to
extract meaningful correlation structure from an
incomplete data matrix by postulating low rank
constraints. Recently, variational Bayesian (VB)
inference techniques have successfully been applied
to such large scale bilinear models. However,
current algorithms are of the alternate updating
or stochastic gradient descent type, slow
to converge and prone to getting stuck in shallow
local minima. While for MAP or maximum
margin estimation, singular value shrinkage algorithms
have been proposed which can far outperform
alternate updating, this methodological
avenue remains unexplored for Bayesian techniques.
In this paper, we show how to combine a
recent singular value shrinkage characterization
of fully observed spherical Gaussian VB matrix
factorization with local variational bounding in
order to obtain efficient VB inference for general
MF models with non-conjugate likelihood potentials.
In particular, we show how to handle Poisson
and Bernoulli potentials, far more suited for
most MF applications than Gaussian likelihoods.
Our algorithm can be run even for very large
models and is easily implemented in Matlab. It
exhibits better prediction performance than MAP
estimation on several real-world datasets.
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