论文标题
贝叶斯强大的张量环模型不完整的多路数据
Bayesian Robust Tensor Ring Model for Incomplete Multiway Data
论文作者
论文摘要
强大的张量完成（RTC）旨在从其不完整的观察结果中恢复低排名的张量。最近提出的张量环（TR）模型在解决RTC问题方面表现出了优越性。但是，现有方法要么需要预先分配的TR等级，要么积极地追求最小TR等级，从而在存在噪声的情况下通常会导致有偏见的解决方案。在本文中，提出了一种贝叶斯强张量子环分解（BRTR）方法，以提供更准确的RTC问题解决方案，该解决方案可以避免对TR等级和惩罚参数的精美选择。开发了一种差异贝叶斯（VB）算法，以推断后期的概率分布。在学习过程中，BRTR可以将核心张量的切片与边缘组件切成薄片，从而导致自动TR秩检测。广泛的实验表明，与其他最先进的方法相比，BRTR可以取得明显提高的性能。
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.
