Generalized multilinear models for sufficient dimension reduction on tensor-valued predictors
张量预测变量充分降维的广义多线性模型
We consider supervised learning problems with tensor-valued input. We derive multilinear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the predictors given the response as a member of the quadratic exponential family. We develop estimation procedures of sufficient reductions for both continuous and binary tensor-valued predictors. We prove the consistency and asymptotic normality of the estimated sufficient…