Doubly Decomposing Nonparametric Tensor Regression
This work addresses high-dimensional tensor regression for applications like network analysis, but it appears incremental as it builds on existing tensor decomposition and nonparametric methods.
The authors tackled the problem of nonparametric tensor regression in high-dimensional spaces by decomposing nonlinearity into simple local functions using low-rank tensor decomposition, which improved convergence rates while maintaining consistency under specific conditions. They developed a Bayesian estimator with Gaussian process priors and demonstrated high performance in predicting summary statistics of a real complex network.
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.