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<p>Time-varying graphical models provide a powerful framework for capturing the evolving conditional dependencies among high-dimensional variables over time. A widely used method in this context is the Time-Varying Graphical Lasso (TVGL), which estimates a sequence of sparse precision matrices while encouraging temporal smoothness. However, standard TVGL assumes Gaussian-distributed, fully observed data, making it vulnerable to outliers and missing values, common challenges in real-world applications. In this work, we introduce RM-TVGL: a Robust and Missing-Data-Aware Time-Varying Graphical Lasso framework that extends TVGL to accommodate noisy and incomplete data. Our method integrates Huber loss to mitigate the influence of outliers and incorporates an Expectation-Maximization (EM) algorithm to handle missing entries in a principled manner. Additionally, RM-TVGL supports flexible regularization schemes, including <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell _2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, and Elastic Net, enabling adaptation to diverse network structures. We develop an efficient ADMM-based optimization algorithm and demonstrate the advantages of RM-TVGL through extensive experiments on both synthetic and real gene expression datasets. Compared to baseline methods, including standard TVGL, the results show that RM-TVGL consistently improves structural accuracy, temporal stability, and robustness compared to existing methods.</p>

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Robust and missing-data-aware time-varying graphical lasso(RM-TVGL) for high-dimensional dynamic network estimation

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Lingling Zhang

摘要

Time-varying graphical models provide a powerful framework for capturing the evolving conditional dependencies among high-dimensional variables over time. A widely used method in this context is the Time-Varying Graphical Lasso (TVGL), which estimates a sequence of sparse precision matrices while encouraging temporal smoothness. However, standard TVGL assumes Gaussian-distributed, fully observed data, making it vulnerable to outliers and missing values, common challenges in real-world applications. In this work, we introduce RM-TVGL: a Robust and Missing-Data-Aware Time-Varying Graphical Lasso framework that extends TVGL to accommodate noisy and incomplete data. Our method integrates Huber loss to mitigate the influence of outliers and incorporates an Expectation-Maximization (EM) algorithm to handle missing entries in a principled manner. Additionally, RM-TVGL supports flexible regularization schemes, including \(\ell _1\) ℓ 1 , \(\ell _2\) ℓ 2 , and Elastic Net, enabling adaptation to diverse network structures. We develop an efficient ADMM-based optimization algorithm and demonstrate the advantages of RM-TVGL through extensive experiments on both synthetic and real gene expression datasets. Compared to baseline methods, including standard TVGL, the results show that RM-TVGL consistently improves structural accuracy, temporal stability, and robustness compared to existing methods.