.png){kind=icon}
返回
AN OPTIMAL STATISTICAL AND COMPUTATIONAL FRAMEWORK FOR GENERALIZED TENSOR ESTIMATION
.png){kind=icon}
OA
AI
DOI：10.1214/21-AOS2061.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator consists of finding a low-rank tensor fit to the data under generalized parametric models. To overcome the difficulty of nonconvexity in these problems, we introduce a unified approach of projected gradient descent that adapts to the underlying low-rank structure. Under mild conditions on the loss function, we establish both an upper bound on statistical error and the linear rate of computational convergence through a general deterministic analysis. Then we further consider a suite of generalized tensor estimation problems, including sub-Gaussian tensor PCA, tensor regression, and Poisson and binomial tensor PCA. We prove that the proposed algorithm achieves the minimax optimal rate of convergence in estimation error. Finally, we demonstrate the superiority of the proposed framework via extensive experiments on both simulated and real data.
Keyword:
Generalize tensor estimation
gradient descent
image denoising
low-rank tensor
minimax optimality
nonconvex optimization
期刊
IF:
3.7
论文数:
2.8K
被引数:
2.9W
机构
引用论文
DC Offset Error Compensation Algorithm for PR Current Control of a Single-Phase Grid-Tied Inverter.png)
EnergiesOAAI
EnergiesIF0
OAAI分享收藏分享收藏分享收藏MULTILAYER TENSOR FACTORIZATION WITH APPLICATIONS TO RECOMMENDER SYSTEMSANNALS OF STATISTICS
OAAI
ANNALS OF STATISTICSIF3.7
OAAI分享收藏
查看更多内容