Minimax Optimal Alternating Minimization for Kernel Nonparametric Tensor Learning

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Taiji Suzuki, Heishiro Kanagawa, Hayato Kobayashi, Nobuyuki Shimizu, Yukihiro Tagami


We investigate the statistical performance and computational efficiency of the alternating minimization procedure for nonparametric tensor learning. Tensor modeling has been widely used for capturing the higher order relations between multimodal data sources. In addition to a linear model, a nonlinear tensor model has been received much attention recently because of its high flexibility. We consider an alternating minimization procedure for a general nonlinear model where the true function consists of components in a reproducing kernel Hilbert space (RKHS). In this paper, we show that the alternating minimization method achieves linear convergence as an optimization algorithm and that the generalization error of the resultant estimator yields the minimax optimality. We apply our algorithm to some multitask learning problems and show that the method actually shows favorable performances.