  Robust tensor completion (RTC) aims to recover a low-rank tensor from its
incomplete observation with outlier corruption. The recently proposed tensor
ring (TR) model has demonstrated superiority in solving the RTC problem.
However, the existing methods either require a pre-assigned TR rank or
aggressively pursue the minimum TR rank, thereby often leading to biased
solutions in the presence of noise. In this paper, a Bayesian robust tensor
ring decomposition (BRTR) method is proposed to give more accurate solutions to
the RTC problem, which can avoid exquisite selection of the TR rank and penalty
parameters. A variational Bayesian (VB) algorithm is developed to infer the
probability distribution of posteriors. During the learning process, BRTR can
prune off slices of core tensor with marginal components, resulting in
automatic TR rank detection. Extensive experiments show that BRTR can achieve
significantly improved performance than other state-of-the-art methods.
