  Nonparametric extension of tensor regression is proposed. Nonlinearity in a
high-dimensional tensor space is broken into simple local functions by
incorporating low-rank tensor decomposition. Compared to naive nonparametric
approaches, our formulation considerably improves the convergence rate of
estimation while maintaining consistency with the same function class under
specific conditions. To estimate local functions, we develop a Bayesian
estimator with the Gaussian process prior. Experimental results show its
theoretical properties and high performance in terms of predicting a summary
statistic of a real complex network.
