标题： 贝叶斯框架下用于低秩张量逼近的交替线性方案 显示英文标题

标题： Alternating linear scheme in a Bayesian framework for low-rank tensor approximation

摘要： 多方式数据通常以张量形式自然出现，可以通过低秩张量分解近似表示。 这很有用，因为可以显著降低复杂性，并促进大规模数据集的处理。 在本文中，我们通过解决一个贝叶斯推理问题，为给定的张量找到一个低秩表示。 这是通过将整体推理问题分成子问题来实现的，在这些子问题中，我们依次推断一个张量分解成分的后验分布。 这导致了对众所周知的迭代算法交替线性方案（ALS）的概率解释。 这样就可以考虑测量噪声，同时结合特定应用的先验知识，并量化低秩张量估计的不确定性。 为了从张量分解成分的后验分布中计算低秩张量估计，我们提出了一种在张量列车格式中执行无迹变换的算法。 显示英文摘要

摘要： Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets can be facilitated. In this paper, we find a low-rank representation for a given tensor by solving a Bayesian inference problem. This is achieved by dividing the overall inference problem into sub-problems where we sequentially infer the posterior distribution of one tensor decomposition component at a time. This leads to a probabilistic interpretation of the well-known iterative algorithm alternating linear scheme (ALS). In this way, the consideration of measurement noise is enabled, as well as the incorporation of application-specific prior knowledge and the uncertainty quantification of the low-rank tensor estimate. To compute the low-rank tensor estimate from the posterior distributions of the tensor decomposition components, we present an algorithm that performs the unscented transform in tensor train format.