论文标题
贝叶斯框架中的线性方案用于低级张量近似
Alternating linear scheme in a Bayesian framework for low-rank tensor approximation
论文作者
论文摘要
多路数据通常以张力格式出现，该格式可以通过低级张量分解大致表示。这很有用，因为复杂性可以显着降低，并且可以促进大规模数据集的处理。在本文中，我们通过解决贝叶斯推理问题来发现给定张量的低级别表示。这是通过将整个推断问题分为子问题来实现的，在该问题中，我们依次推断一个张量分解成分的后验分布。这导致对众所周知的迭代算法交替线性方案（ALS）的概率解释。通过这种方式，启用了测量噪声的考虑，以及对应用特定的先验知识的结合以及低级张量估计值的不确定性量化。为了根据张量分解组件的后验分布来计算低级张量估计值，我们提出了一种算法，该算法在张量列车格式中执行无气味变换。
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.
