Improving Tensor Regression by Optimal Model Averaging
针对CP张量分解中秩选择的不确定性，提出一种模型平均方法，通过加权不同秩的候选模型来提升张量回归的预测性能，并证明了渐近最优性和参数一致性。
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.