A note on rank reduction in sparse multivariate regression.
A note on rank reduction in sparse multivariate regression.
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DOI：
10.1080/15598608.2015.1081573
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发表时间：
2016
影响因子：
0.6
通讯作者：
Chan KS
中科院分区：
文献类型：
--
作者：
Chen K;Chan KS
Chen等人提出了一种稀疏奇异值分解的降秩回归（RSSVD）方法，用于降秩模型的变量选择。为了对多变量响应进行联合建模，该方法有效地构建了预定数量的潜在变量作为预测因子的一些稀疏线性组合。在这里，我们推广的方法也进行降秩，并使其在降秩向量自回归（VAR）建模中的使用，以执行自动秩确定和顺序选择。我们表明，在平稳的时间序列数据的背景下，广义方法正确地识别模型秩和稀疏依赖结构之间的多变量响应和预测，概率渐近。我们证明了所提出的方法的有效性，通过模拟和分析一个宏观经济的多元时间序列，使用降秩VAR模型。
A reduced-rank regression with sparse singular value decomposition (RSSVD) approach was proposed by Chen et al. for conducting variable selection in a reduced-rank model. To jointly model the multivariate response, the method efficiently constructs a prespecified number of latent variables as some sparse linear combinations of the predictors. Here, we generalize the method to also perform rank reduction, and enable its usage in reduced-rank vector autoregressive (VAR) modeling to perform automatic rank determination and order selection. We show that in the context of stationary time-series data, the generalized approach correctly identifies both the model rank and the sparse dependence structure between the multivariate response and the predictors, with probability one asymptotically. We demonstrate the efficacy of the proposed method by simulations and analyzing a macro-economical multivariate time series using a reduced-rank VAR model.