Stability Approach to Regularization Selection for Reduced-Rank Regression
降秩回归的正则化选择：稳定性方法AI 解读 ↓
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降秩回归的正则化选择：稳定性方法
- 研究问题
- 在多响应、多预测变量的降秩回归中，如何选择正则化参数，使估计的系数矩阵秩可靠反映有效潜在因子数量？
- 方法与思路
- 作者提出 StARS-RRR，以稳定性选择调节参数并估计系数矩阵秩，分析其一致性，并开展模拟与乳腺癌数据应用。
- 材料陈述的贡献
- 摘要称该方法具有秩估计一致性，在所考察模拟中比 AIC、BIC 和交叉验证更准确，应用中也获得较小预测误差。
- 阅读关注点
- 应核对稳定性的定义、抽样方案和参数选择规则，以及秩一致性的适用条件、模拟设置与应用中随机划分的评价方式。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未说明一致性的具体条件，所述比较不能推出普遍优势。
原文摘要
The reduced-rank regression model is a popular model to deal with multivariate response and multiple predictors, and is widely used in biology, chemometrics, econometrics, engineering, and other fields. In the reduced-rank regression modelling, a central objective is to estimate the rank of the coefficient matrix that represents the number of effective latent factors in predicting the multivariate response. Although theoretical results such as rank estimation consistency have been established for various methods, in practice rank determination still relies on information criterion based methods such as AIC and BIC or subsampling based methods such as cross validation. Unfortunately, the theoretical properties of these practical methods are largely unknown. In this paper, we present a novel method called StARS-RRR that selects the tuning parameter and then estimates the rank of the coefficient matrix for reduced-rank regression based on the stability approach. We prove that StARS-RRR achieves rank estimation consistency, i.e., the rank estimated with the tuning parameter selected by StARS-RRR is consistent to the true rank. Through a simulation study, we show that StARS-RRR outperforms other tuning parameter selection methods including AIC, BIC, and cross validation as it provides the most accurate estimated rank. In addition, when applied to a breast cancer dataset, StARS-RRR discovers a reasonable number of genetic pathways that affect the DNA copy number variations and results in a smaller prediction error than the other methods with a random-splitting process.