Low-Rank Regression with Tensor Responses

Guillaume Rabusseau 1 Hachem Kadri 1
1 QARMA - éQuipe AppRentissage et MultimediA [Marseille]
LIF - Laboratoire d'informatique Fondamentale de Marseille
Abstract : 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 computes accurate solutions while being computationally very competitive.
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Guillaume Rabusseau, Hachem Kadri. Low-Rank Regression with Tensor Responses. NIPS, Dec 2016, Barcelone, Spain. ⟨hal-01471279⟩

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