A method for sparse and robust independent component analysis

2025-02-06

AI Summary

To address the challenges of sparse and robust independent component identification and interpretable causal graph modeling in high-dimensional data, this paper proposes Sparse Invariant Coordinate Selection (SICS). SICS is the first method to integrate LASSO-type sparsity regularization into the Invariant Coordinate Selection (ICS) framework, while incorporating robust scatter matrices to enhance outlier resistance. Theoretically, we establish asymptotic consistency of the estimator. Methodologically, SICS simultaneously ensures loading sparsity and statistical robustness, enabling direct construction of sparse causal graphs from estimated independent component loadings. Simulation studies demonstrate that SICS significantly improves accuracy in recovering sparse loadings compared to existing approaches. In real-data applications, SICS successfully yields well-structured, interpretable sparse causal networks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Computational social science

Abstract

This work presents sparse invariant coordinate analysis, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate analysis, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes a consistency result for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with simulations. The method is also illustrated with example in constructing sparse causal graphs.

Problem

• Develops sparse robust independent component analysis method
• Uses LASSO-type penalty to promote sparsity
• Applies robust scatter matrices for robustness

Innovation

• Sparse invariant coordinate selection method
• LASSO-type penalty for sparsity
• Robust scatter matrices for robustness