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Title: Robust multilinear rank estimation for tensor regression Authors:  Namgil Lee - Kangwon National University (Korea, South) [presenting]
Abstract: Tensor regression refers to a regression analysis whose coefficients and input covariates are in form of multiway arrays, i.e., tensors. The multilinear ranks of a tensor is a generalization of the rank of a matrix in linear algebra into a tensor. We propose a statistical method for robust estimation of multilinear ranks of regression coefficients in tensor regressions assuming tensor-variate generalized linear models (GLMs). A multilinear structure underlying the regression coefficients is shown to cause severe bias in the estimation of the multilinear ranks of higher-order tensors. The proposed method analyzes the multilinear structure in the core tensor obtained from the higher-order singular value decomposition of regression coefficients. Through simulated experiments, it is shown that the proposed method is especially efficient and robust for noisy data and low-rank models, and insensitive to choices of hyperparameters.