Doubly Decomposing Nonparametric Tensor Regression
Doubly Decomposing Nonparametric Tensor Regression
复制标题
DOI：
--
复制
发表时间：
2015-06
期刊：
影响因子：
--
通讯作者：
M. Imaizumi;K. Hayashi
中科院分区：
文献类型：
--
作者：
M. Imaizumi;K. Hayashi
提出了张量回归的非参数扩张。高维张量空间中的非线性通过结合低秩张量分解被分解成简单的局部函数。与朴素的非参数方法相比，我们的公式大大提高了估计的收敛速度，同时在特定条件下保持与同一函数类的一致性。为了估计局部函数，我们开发了高斯过程先验的贝叶斯估计器。实验结果表明，它的理论性能和高性能的预测方面的一个真实的复杂网络的汇总统计。
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.