基于凸优化的低秩张量估计
Estimation of low-rank tensors via convex optimization
AI总结：
针对部分观测下多路数组（张量）的Tucker分解估计问题，提出三种基于凸优化的方法，通过迹范数正则化自动估计秩，并在预测性能、速度和恢复已知多线性结构方面优于传统方法。
摘要：
在本文中，我们提出了三种从部分观测中估计多路数组（张量）的Tucker分解的方法。所有方法都表述为凸最小化问题，因此最小值保证唯一。所提出的方法可以通过优化自动估计因子数量（秩），因此无需事先指定秩。我们采用的关键技术是迹范数正则化，这是低秩矩阵估计的常用方法。此外，我们提出了一种简单的启发式方法来提高所得分解的可解释性。通过对合成和真实世界数据集的数值实验，展示了三种方法的优缺点。我们表明，所提出的基于凸优化的方法在预测性能上更准确、速度更快，并且在恢复已知多线性结构方面比传统方法更可靠。
英文摘要：
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is guaranteed to be unique. The proposed approaches can automatically estimate the number of factors (rank) through the optimization. Thus, there is no need to specify the rank beforehand. The key technique we employ is the trace norm regularization, which is a popular approach for the estimation of low-rank matrices. In addition, we propose a simple heuristic to improve the interpretability of the obtained factorization. The advantages and disadvantages of three proposed approaches are demonstrated through numerical experiments on both synthetic and real world datasets. We show that the proposed convex optimization based approaches are more accurate in predictive performance, faster, and more reliable in recovering a known multilinear structure than conventional approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
