Higher-Order Low-Rank Regression
This addresses regression tasks for domains with tensor outputs, offering a faster and more accurate solution compared to prior tensor methods.
The paper tackles regression with tensor-structured outputs by proposing HOLRR, an efficient algorithm that solves a non-convex multilinear rank-constrained problem, showing it outperforms existing methods in accuracy and speed.
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension is also presented. Experiments on synthetic and real data show that HOLRR outperforms multivariate and multilinear regression methods and is considerably faster than existing tensor methods.