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Bayesian Latent Factor Model for Higher-order Data: an Extended Abstract
Zerui Tao · Xuyang ZHAO · Toshihisa Tanaka · Qibin Zhao

Latent factor models are canonical tools to learn low-dimensional and linear embedding of original data. Traditional latent factor models are based on low-rank matrix factorization of covariance matrices. However, for higher-order data with multiple modes, i.e., tensors, this simple treatment fails to take into account the mode-specific relations. This ignorance leads to inefficiency in analysis of complex structures as well as poor data compression ability. In this paper, unlike covariance matrices, we investigate high-order covariance tensor directly by exploiting tensor ring (TR) format and propose the Bayesian TR latent factor model, which can represent complex multi-linear correlations and achieves efficient data compression. To overcome the difficulty of finding the optimal TR-ranks and simultaneously imposing sparsity on loading coefficients, a multiplicative Gamma process (MGP) prior is adopted to automatically infer the ranks and obtain sparsity. Then, we establish efficient parameter-expanded EM algorithm to learn the maximum a posteriori (MAP) estimate of model parameters.

Author Information

Zerui Tao (Tokyo University of Agriculture and Technology)
Xuyang ZHAO (Tokyo University of Agriculture and Technology)
Toshihisa Tanaka (Tokyo University of Agriculture and Technology)
Qibin Zhao (RIKEN AIP)

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