Bayesian Nonparametric Models for Multiway Data Analysis

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches-such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)-amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entiti...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 37; no. 2; pp. 475 - 487
Main Authors: Xu, Zenglin, Yan, Feng, Qi, Yuan
Format: Journal Article
Language:English
Published: United States IEEE 01.02.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms for data and knowledge management
Bayes methods
Computational modeling
Data analysis
Data models
Decomposition
Gaussian processes
Machine learning
Matrix decomposition
Noise
Tensile stress
Gaussian process
tensor/matrix factorization
network modeling
stochastic blockmodel
nonparametric Bayes
Multiway analysis
random graphs and exchangeable arrays
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:Get full text
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Summary:Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches-such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)-amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g., missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models for multiway data analysis. We name these models InfTucker. These new models essentially conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula> processes with nonlinear covariance functions. Moreover, on network data, our models reduce to nonparametric stochastic blockmodels and can be used to discover latent groups and predict missing interactions. To learn the models efficiently from data, we develop a variational inference technique and explore properties of the Kronecker product for computational efficiency. Compared with a classical variational implementation, this technique reduces both time and space complexities by several orders of magnitude. On real multiway and network data, our new models achieved significantly higher prediction accuracy than state-of-art tensor decomposition methods and blockmodels.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2013.201