Regularized high dimension low tubal-rank tensor regression
Regularized high dimension low tubal-rank tensor regression
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DOI：
10.1214/22-ejs2004
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发表时间：
2022-01
影响因子：
1.1
通讯作者：
S. Roy;G. Michailidis
中科院分区：
文献类型：
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作者：
S. Roy;G. Michailidis
张量回归模型在神经影像分析、神经网络、图像处理等社会科学和行为科学领域都有着广泛的应用，张量分解理论的最新进展促进了各种张量回归模型的发展。大多数现有文献的焦点都集中在回归系数张量的正则多矢（CP）分解及其变体上。CP分解的系数张量能够以相对较小的样本大小进行估计，但它可能并不总是捕获数据中的潜在复杂结构。在这项工作中，我们利用最近开发的概念的管秩和发展的张量回归模型，其中系数张量被分解成两个组成部分：一个低管秩张量和一个结构稀疏的。我们首先解决了构成系数张量的两个分量的可识别性问题，随后开发了一个快速且可扩展的交替最小化算法来求解凸正则化程序。此外，我们提供了有限的样本误差界下的高维标度的模型参数。该模型的性能进行评估的合成数据，也被用于一个应用程序，涉及数据从智能辅导平台。
: Tensor regression models are of emerging interest in diverse fields of social and behavioral sciences, including neuroimaging analysis, neural networks, image processing and so on. Recent theoretical advance- ments of tensor decomposition have facilitated significant development of various tensor regression models. The focus of most of the available lit- erature has been on the Canonical Polyadic (CP) decomposition and its variants for the regression coefficient tensor. A CP decomposed coefficient tensor enables estimation with relatively small sample size, but it may not always capture the underlying complex structure in the data. In this work, we leverage the recently developed concept of tubal rank and develop a tensor regression model, wherein the coefficient tensor is decomposed into two components: a low tubal rank tensor and a structured sparse one. We first address the issue of identifiability of the two components comprising the coefficient tensor and subsequently develop a fast and scalable Alternating Minimization algorithm to solve the convex regularized program. Further, we provide finite sample error bounds under high dimensional scaling for the model parameters. The performance of the model is assessed on synthetic data and is also used in an application involving data from an intelligent tutoring platform.