Gaussian process nonparametric tensor estimator and its minimax optimality

Heishiro Kanagawa (Tokyo Tech), Taiji Suzuki (Tokyo Tech), Hayato Kobayashi, Nobuyuki Shimizu, Yukihiro Tagami

ICML 2016 (The 33rd International Conference on Machine Learning), 2016/6


Machine Learning Data Science

We investigate the statistical efficiency of a nonparametric Gaussian process method for a nonlinear tensor estimation problem. Low-rank tensor estimation has been used as a method to learn higher order relations among several data sources in a wide range of applications, such as multi-task learning, recommendation systems, and spatiotemporal analysis. We consider a general setting where a common linear tensor learning is extended to a nonlinear learning problem in reproducing kernel Hilbert space and propose a nonparametric Bayesian method based on the Gaussian process method. We prove its statistical convergence rate without assuming any strong convexity, such as restricted strong convexity. Remarkably, it is shown that our convergence rate achieves the minimax optimal rate. We apply our proposed method to multi-task learning and show that our method significantly outperforms existing methods through numerical experiments on real-world data sets.

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