High Dimensional Bayesian Regularization in Regressions Involving Symmetric Tensors
High Dimensional Bayesian Regularization in Regressions Involving Symmetric Tensors
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DOI：
10.1007/978-3-030-50153-2_26
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发表时间：
2020-05-16
期刊：
影响因子：
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通讯作者：
Guhaniyogi R
中科院分区：
文献类型：
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作者：
Guhaniyogi R
本文开发了一个具有对称张量响应和向量预测器的回归框架。现有的文献涉及对称张量响应和向量预测通过将张量响应向量化为多变量向量来进行，从而忽略了张量中的结构信息。最近的一些方法提出了新的回归框架，利用对称张量的结构，并假设对应于标量预测的对称张量系数是低秩的。虽然系数张量的低秩约束在计算上是有效的，但在某些真实的数据应用中，它们可能会出现限制。受此启发，我们提出了一类新型的对称张量系数的正则化或收缩先验。我们的建模框架先验地将对称张量系数表示为低秩和稀疏结构的总和，使用贝叶斯正则化技术对这两种结构进行适当的正则化。所提出的框架允许识别的张量节点显着影响每个标量预测。我们的框架是使用一个有效的马尔可夫链蒙特卡罗算法实现的。仿真研究的实证结果表明，所提出的方法比其竞争对手具有竞争力的性能。
This article develops a regression framework with a symmetric tensor response and vector predictors. The existing literature involving symmetric tensor response and vector predictors proceeds by vectorizing the tensor response to a multivariate vector, thus ignoring the structural information in the tensor. A few recent approaches have proposed novel regression frameworks exploiting the structure of the symmetric tensor and assume symmetric tensor coefficients corresponding to scalar predictors to be low-rank. Although low-rank constraint on coefficient tensors are computationally efficient, they might appear to be restrictive in some real data applications. Motivated by this, we propose a novel class of regularization or shrinkage priors for the symmetric tensor coefficients. Our modeling framework a-priori expresses a symmetric tensor coefficient as sum of low rank and sparse structures, with both these structures being suitably regularized using Bayesian regularization techniques. The proposed framework allows identification of tensor nodes significantly influenced by each scalar predictor. Our framework is implemented using an efficient Markov Chain Monte Carlo algorithm. Empirical results in simulation studies show competitive performance of the proposed approach over its competitors.