Improving Tensor Regression by Optimal Model Averaging

• 成果类型: Article
• 署名作者: Bu, Qiushi; Liang, Hua; Zhang, Xinyu; Zou, Jiahui
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; George Washington University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Capital University of Economics & Business
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2398164
• 发表日期: 2025
• 页码: 1115-1126
• 关键词: selection

摘要

Tensors have broad applications in neuroimaging, data mining, digital marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively reduce the number of parameters to gain dimensionality-reduction and thus plays a key role in tensor regression. However, in CP decomposition, there is uncertainty about which rank to use. In this article, we develop a model averaging method to handle this uncertainty by weighting the estimators from candidate tensor regression models with different ranks. When all candidate models are misspecified, we prove that the model averaging estimator is asymptotically optimal. When correct models are included in the set of candidate models, we prove the consistency of parameters and the convergence of the model averaging weight. Simulations and empirical studies illustrate that the proposed method has superiority over the competition methods and has promising applications. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.