A1307
Title: Generalized multilinear models for sufficient dimension reduction on tensor-valued predictors
Authors: Efstathia Bura - Vienna University of Technology (Austria) [presenting]
Daniel Kapla - TU Wien (Austria)
Abstract: Supervised learning problems with tensor-valued input are considered. Multilinear sufficient reductions for regression or classification problems are derived by modeling the conditional distribution of the predictors given the response as a member of the quadratic exponential family. Estimation procedures of sufficient reductions for both continuous and binary tensor-valued predictors are developed. Consistency and asymptotic normality of the estimated sufficient reduction are proven using manifold theory. For multilinear normal predictors, the estimation algorithm is highly computationally efficient and is applicable to situations where the dimension of the reduction exceeds the sample size. The method outperforms competing techniques in both simulated settings and real-world datasets involving continuous and binary tensor-valued predictors.
