  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.
