将降维与回归融合，提升金融指数追踪精度
A PLS-Integrated LASSO Method with Application in Index Tracking
- 把主成分分析与回归结合，直接在建模中完成降维
- 两种版本的PLS-Lasso在指数追踪任务中表现优于传统Lasso
- 适合金融量化研究者和需要高维数据建模的场景
在传统的多变量数据分析中，降维与回归通常被当作独立步骤处理。主成分回归（PCR）和偏最小二乘回归（PLS）虽都通过潜变量作为中间步骤进行回归分析，但其构建准则不同。本文提出一种创新的回归方法——集成偏最小二乘的Lasso（PLS-Lasso），将降维过程直接融入回归建模中。我们给出了两种不同的PLS-Lasso形式（PLS-Lasso-v1 和 PLS-Lasso-v2），并设计了保证收敛至全局最优的高效算法。在金融指数追踪任务中，PLS-Lasso-v1与v2均展现出优于标准Lasso的性能，验证了方法的有效性。
原文摘要 · Abstract (English)
In traditional multivariate data analysis, dimension reduction and regression have been treated as distinct endeavors. Established techniques such as principal component regression (PCR) and partial least squares (PLS) regression traditionally compute latent components as intermediary steps -- although with different underlying criteria -- before proceeding with the regression analysis. In this paper, we introduce an innovative regression methodology named PLS-integrated Lasso (PLS-Lasso) that integrates the concept of dimension reduction directly into the regression process. We present two distinct formulations for PLS-Lasso, denoted as PLS-Lasso-v1 and PLS-Lasso-v2, along with clear and effective algorithms that ensure convergence to global optima. PLS-Lasso-v1 and PLS-Lasso-v2 are compared with Lasso on the task of financial index tracking and show promising results.
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