Automatic Relevance Determination for Multiway Models

Morten Mørup, Lars Kai Hansen

AbstractEstimating the adequate number of components is an important yet difficult
problem in multi-way modelling. We demonstrate how a Bayesian framework
for model selection based on Automatic Relevance Determination (ARD) can be
adapted to the Tucker and CP models. By assigning priors for the model parameters
and learning the hyperparameters of these priors the method is able to turn
off excess components and simplify the core structure at a computational cost of
fitting the conventional Tucker/CP model. To investigate the impact of the choice
of priors we based the ARD on both Laplace and Gaussian priors corresponding
to regularization by the sparsity promoting l1-norm and the conventional l2-norm,
respectively. While the form of the priors had limited effect on the results obtained
the ARD approach turned out to form a useful, simple, and efficient tool for
selecting the adequate number of components of data within the Tucker and CP
structure. For the Tucker and CP model the approach performs better than heuristics
such as the Bayesian Information Criterion, Akaikes Information Criterion,
DIFFIT and the numerical convex hull (NumConvHull) while operating only at
the cost of estimating an ordinary CP/Tucker model. For the CP model the ARD
approach performs almost as well as the core consistency diagnostic. Thus, the
ARD framework is a simple yet efficient tool for the estimation of the adequate
number of components in multi-way models. A Matlab implementation of the
proposed algorithm is available for download at
TypeJournal paper [With referee]
JournalJournal of Chemometrics, Special Issue: In Honor of Professor Richard A. Harshman
Year2009    Vol. 23    No. 7-8    pp. 352 - 363
PublisherJohn Wiley & Sons, Ltd
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing

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