变分贝叶斯张量分位数回归

IF 0.8 3区 数学 Q2 MATHEMATICS
Yunzhi Jin, Yanqing Zhang
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引用次数: 0

摘要

分位数回归被广泛应用于统计学习的变量关系研究中。传统的分位数回归模型是基于向量值协变量的,可以通过传统的估计方法进行有效的估计。然而,许多现代应用涉及具有本征张量结构的张量数据。传统的分位数回归不能很好地处理张量回归问题。为此,我们考虑了张量值协变量的张量分位数回归,并基于非对称拉普拉斯模型和张量系数的CANDECOMP/PARAFAC分解,开发了一种新的变分贝叶斯估计方法来进行估计和预测。为了结合张量系数的稀疏性,我们考虑了张量系数边际因子向量的多向收缩先验。该方法的核心思想是有效地结合张量的先验结构信息,并利用张量分解的矩阵化来简化张量系数估计的复杂度。采用坐标上升算法对变分下界进行优化。仿真研究和实例验证了该方法的数值性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Variational Bayesian Tensor Quantile Regression

Quantile regression is widely used in variable relationship research for statistical learning. Traditional quantile regression model is based on vector-valued covariates and can be efficiently estimated via traditional estimation methods. However, many modern applications involve tensor data with the intrinsic tensor structure. Traditional quantile regression can not deal with tensor regression issues well. To this end, we consider a tensor quantile regression with tensor-valued covariates and develop a novel variational Bayesian estimation approach to make estimation and prediction based on the asymmetric Laplace model and the CANDECOMP/PARAFAC decomposition of tensor coefficients. To incorporate the sparsity of tensor coefficients, we consider the multiway shrinkage priors for marginal factor vectors of tensor coefficients. The key idea of the proposed method is to efficiently combine the prior structural information of tensor and utilize the matricization of tensor decomposition to simplify the complexity of tensor coefficient estimation. The coordinate ascent algorithm is employed to optimize variational lower bound. Simulation studies and a real example show the numerical performances of the proposed method.

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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
138
审稿时长
14.5 months
期刊介绍: Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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