Doubly Decomposing Nonparametric Tensor Regression

TL;DR

This paper introduces a nonparametric tensor regression method that decomposes high-dimensional nonlinear functions into local components using low-rank tensor decomposition, improving estimation convergence and prediction accuracy.

Contribution

It presents a novel nonparametric tensor regression framework with a Bayesian estimator using Gaussian process priors, enhancing convergence rates and predictive performance.

Findings

The proposed method outperforms naive approaches in convergence rate.

Bayesian estimator demonstrates strong theoretical properties.

High accuracy in predicting complex network statistics.

Abstract

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.