Sufficient dimension folding via tensor inverse regression

Sufficient dimension reduction (SDR) techniques have proven to be very useful data analysis tools in various applications. Conventional SDR methods mainly tackle simple vector-valued predictors, but they are inappropriate for data with array (tensor)-valued predictors. In this paper, we propose a tensor dimension reduction approach based on inverse regression, and we refer to it as T-IRE, which reduces the dimension of original array-valued predictors while simultaneously retaining the structural information within predictors and the proposed method also provides an efficient estimation algorithm. Empirical performance and two dataset analysis demonstrate the advantages of our proposed method.