A PLS-Integrated LASSO Method with Application in Index Tracking

2025-11-28

AI Summary

In traditional multivariate analysis, dimensionality reduction and regression are typically treated separately, leading to information loss and suboptimal modeling efficiency. To address this, we propose the PLS-Lasso framework, which—uniquely—integrates the latent variable construction of Partial Least Squares (PLS) directly into Lasso regression, enabling joint optimization of dimensionality reduction, variable selection, and sparse regression. We design two algorithmic variants, both rigorously proven to converge to the global optimum by synergistically leveraging PLS’s directionality, ℓ₁ regularization, and convex optimization theory—ensuring statistical interpretability and computational reliability. Empirical evaluation on financial index tracking demonstrates that PLS-Lasso significantly outperforms standard Lasso, achieving a superior trade-off between tracking error and model sparsity. This validates the effectiveness and practicality of the unified modeling paradigm.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Integrates dimension reduction directly into regression modeling process
• Develops two formulations for financial index tracking applications
• Compares performance with traditional Lasso on multivariate data analysis

Innovation

• PLS-Lasso integrates dimension reduction into regression
• Two formulations with algorithms ensure global convergence
• Method applied to financial index tracking outperforms Lasso