Doubly Decomposing Nonparametric Tensor Regression


Masaaki Imaizumi, Kohei Hayashi ;
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:727-736, 2016.


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.

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