  Infinite Tucker Decomposition (InfTucker) and random function prior models,
as nonparametric Bayesian models on infinite exchangeable arrays, are more
powerful models than widely-used multilinear factorization methods including
Tucker and PARAFAC decomposition, (partly) due to their capability of modeling
nonlinear relationships between array elements. Despite their great predictive
performance and sound theoretical foundations, they cannot handle massive data
due to a prohibitively high training time. To overcome this limitation, we
present Distributed Infinite Tucker (DINTUCKER), a large-scale nonlinear tensor
decomposition algorithm on MAPREDUCE. While maintaining the predictive accuracy
of InfTucker, it is scalable on massive data. DINTUCKER is based on a new
hierarchical Bayesian model that enables local training of InfTucker on
subarrays and information integration from all local training results. We use
distributed stochastic gradient descent, coupled with variational inference, to
train this model. We apply DINTUCKER to multidimensional arrays with billions
of elements from applications in the "Read the Web" project (Carlson et al.,
2010) and in information security and compare it with the state-of-the-art
large-scale tensor decomposition method, GigaTensor. On both datasets,
DINTUCKER achieves significantly higher prediction accuracy with less
computational time.
