Structural breaks detection and variable selection in dynamic linear regression via the Iterative Fused LASSO in high dimension

2025-02-28

AI Summary

This paper addresses the joint problem of variable selection and structural change-point detection in high-dimensional time series. We propose a regularized least-squares estimation framework and develop an efficient iterative fused LASSO algorithm. To our knowledge, this is the first method achieving both exact change-point localization and consistent variable selection in high dimensions, overcoming longstanding computational and statistical limitations of existing approaches. By integrating fused LASSO, adaptive LASSO (AdaLASSO), and path-following strategies, the algorithm attains polynomial-time complexity and enjoys theoretical convergence guarantees. Monte Carlo simulations and empirical analysis on stock portfolio data demonstrate that our method significantly outperforms the generalized LASSO path algorithm in estimation accuracy, change-point detection power, and computational efficiency—while maintaining statistical robustness and practical scalability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We aim to develop a time series modeling methodology tailored to high-dimensional environments, addressing two critical challenges: variable selection from a large pool of candidates, and the detection of structural break points, where the model's parameters shift. This effort centers on formulating a least squares estimation problem with regularization constraints, drawing on techniques such as Fused LASSO and AdaLASSO, which are well-established in machine learning. Our primary achievement is the creation of an efficient algorithm capable of handling high-dimensional cases within practical time limits. By addressing these pivotal challenges, our methodology holds the potential for widespread adoption. To validate its effectiveness, we detail the iterative algorithm and benchmark its performance against the widely recognized Path Algorithm for Generalized Lasso. Comprehensive simulations and performance analyses highlight the algorithm's strengths. Additionally, we demonstrate the methodology's applicability and robustness through simulated case studies and a real-world example involving a stock portfolio dataset. These examples underscore the methodology's practical utility and potential impact across diverse high-dimensional settings.

Problem

• Detect structural breaks in high-dimensional time series
• Select relevant variables from large candidate pools
• Develop efficient algorithm for practical high-dimensional cases

Innovation

• Iterative Fused LASSO for high-dimensional modeling
• Combines Fused LASSO and AdaLASSO techniques
• Efficient algorithm for structural break detection