CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerfultechnique for tensor completion through explicitly capturing the multilinearlatent factors. The existing CP algorithms require the tensor rank to bemanually specified, however, the determination of tensor rank remains achallenging problem especially for CP rank. In addition, existing approaches donot take into account uncertainty information of latent factors, as well asmissing entries. To address these issues, we formulate CP factorization using ahierarchical probabilistic model and employ a fully Bayesian treatment byincorporating a sparsity-inducing prior over multiple latent factors and theappropriate hyperpriors over all hyperparameters, resulting in automatic rankdetermination. To learn the model, we develop an efficient deterministicBayesian inference algorithm, which scales linearly with data size. Our methodis characterized as a tuning parameter-free approach, which can effectivelyinfer underlying multilinear factors with a low-rank constraint, while alsoproviding predictive distributions over missing entries. Extensive simulationson synthetic data illustrate the intrinsic capability of our method to recoverthe ground-truth of CP rank and prevent the overfitting problem, even when alarge amount of entries are missing. Moreover, the results from real-worldapplications, including image inpainting and facial image synthesis,demonstrate that our method outperforms state-of-the-art approaches for bothtensor factorization and tensor completion in terms of predictive performance.
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