Selected work

Representative Papers

Mens: Nonlinear shrinkage estimation in nonparanormal models for financial applications

Jul 22, 2026

High-dimensional financial data often exhibit skewness and heavy tails, posing a challenge for traditional covariance estimators that struggle to balance robustness and efficiency. This work proposes a Marginal-Independence Nonlinear Shrinkage (MENS) estimator that integrates normal-score rank-based covariance estimation with nonlinear shrinkage to achieve both robustness and efficiency under arbitrary marginal distributions. Theoretically, it establishes, for the first time in non-Gaussian graphical models, the asymptotic optimality of the proposed method and develops a spectral phase transition theory grounded in the Baik–Ben Arous–Péché phase transition. Empirically, simulations confirm its marginal invariance and spiked eigenvalue phase transition behavior; in out-of-sample backtests on S&P 500 minimum-variance portfolios, MENS significantly reduces volatility and turnover while improving the condition number.

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Restricted nonlinear shrinkage of high-dimensional residual covariance matrices in multivariate regressions

Jul 22, 2026

This study addresses the instability and poor conditioning of covariance matrix estimation in high-dimensional, non-Gaussian financial data by proposing a novel approach based on latent-variable Gaussian models. The method applies a nonlinear shrinkage function to the eigenvalues of the normal-score rank covariance matrix to achieve robust and efficient estimation of the residual covariance matrix. It uniquely integrates marginally invariant nonlinear shrinkage with high-dimensional latent Gaussian modeling, preserving the robustness of rank-based estimation while attaining asymptotic optimality under Frobenius loss. The analysis further uncovers a Baik–Ben Arous–Péché (BBP) phase transition in the latent correlation structure. Leveraging the generalized Marchenko–Pastur law and random matrix theory, the theoretical framework is supported by simulations confirming marginal invariance and phase-transition behavior. Empirical results on S&P 500 out-of-sample minimum-variance portfolios demonstrate substantially improved condition numbers, reduced realized volatility, and lower turnover compared to linear shrinkage.

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Rethinking Penetration Testing for AI-Enabled Systems: From Resource Compromise to Behavioral Objective Violation

Jul 15, 2026

Traditional penetration testing struggles to evaluate security risks in AI systems arising from violations of behavioral objectives without breaching underlying infrastructure. This work proposes the first formal definition of AI penetration testing, reframing it as an objective-driven behavioral security assessment. The approach involves identifying operational objectives, mapping AI-driven behaviors, analyzing adversarial attack surfaces—such as prompt injection, data poisoning, and sensor manipulation—establishing criteria for behavioral failure, and conducting scenario-based red-teaming exercises. By integrating threat modeling, behavior mapping, and evidentiary chain construction, the framework demonstrates its efficacy and novelty in a case study involving an AI-powered Security Operations Center assistant, successfully uncovering attack pathways that violate system objectives through behavioral manipulation alone, without requiring infrastructure compromise.

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Scalable Bayesian structure learning of directed acyclic graphs via Laplace approximation, with an application to breast cancer gene expression networks

Jul 11, 2026

This work addresses the computational challenges in Bayesian DAG structure learning arising from the super-exponential growth of the DAG space and the intractability of marginal likelihoods under non-conjugate priors. The authors propose a novel approach based on a modified Cholesky parameterization of the precision matrix, deriving—for the first time—the node-wise marginal likelihood under a Normal–Gamma non-conjugate prior in the form of a generalized inverse Gaussian distribution. Leveraging its asymptotic properties for large parameters, they construct an efficient Laplace approximation-based scoring function embedded within a Metropolis–Hastings sampler for DAG search. Additionally, a probit link couples latent variables with binary clinical outcomes. This framework overcomes the limitations of conjugate priors and enables exact posterior sampling of conditional variances. Experiments demonstrate superior performance over PC, GES, NOTEARS, DAGMA, and conjugate baselines on synthetic data, successful recovery of known structures in the Sachs signaling pathway and Wisconsin breast cancer datasets, and accurate prediction of malignancy with a cross-validated ROC-AUC of 0.94.

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Bayesian DAG Structure Learning with Simultaneous Shrinkage Covariance Estimation under Scale-Mixture Error Distributions in the Proportional High-Dimensional Regime

Jul 09, 2026

This study addresses the challenge of jointly estimating directed acyclic graph (DAG) structures and precision matrices in high-dimensional settings with heavy-tailed or contaminated data. The authors propose R-DACH, a unified Bayesian framework that, for the first time, directly places a global–local horseshoe prior on the strictly lower triangular part of the Cholesky factor, combined with an inverse-Gamma scale mixture error model. This approach enables simultaneous inference of variable ordering, sparse DAG structure, and continuous parameters while inherently achieving robustness to outliers. Theoretical and empirical results demonstrate that R-DACH outperforms graphical horseshoe, DAG-Wishart, and PC algorithms—particularly under contamination—with superior topological consistency and parent selection accuracy, even when the number of variables reaches several hundred. Applied to TCGA RNA-seq data, R-DACH uncovers biologically interpretable gene regulatory relationships missed by competing methods.

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Recent publications

Latest Papers

Mens: Nonlinear shrinkage estimation in nonparanormal models for financial applications

Jul 22, 2026

High-dimensional financial data often exhibit skewness and heavy tails, posing a challenge for traditional covariance estimators that struggle to balance robustness and efficiency. This work proposes a Marginal-Independence Nonlinear Shrinkage (MENS) estimator that integrates normal-score rank-based covariance estimation with nonlinear shrinkage to achieve both robustness and efficiency under arbitrary marginal distributions. Theoretically, it establishes, for the first time in non-Gaussian graphical models, the asymptotic optimality of the proposed method and develops a spectral phase transition theory grounded in the Baik–Ben Arous–Péché phase transition. Empirically, simulations confirm its marginal invariance and spiked eigenvalue phase transition behavior; in out-of-sample backtests on S&P 500 minimum-variance portfolios, MENS significantly reduces volatility and turnover while improving the condition number.

0 citationsRead paper

Restricted nonlinear shrinkage of high-dimensional residual covariance matrices in multivariate regressions

Jul 22, 2026

This study addresses the instability and poor conditioning of covariance matrix estimation in high-dimensional, non-Gaussian financial data by proposing a novel approach based on latent-variable Gaussian models. The method applies a nonlinear shrinkage function to the eigenvalues of the normal-score rank covariance matrix to achieve robust and efficient estimation of the residual covariance matrix. It uniquely integrates marginally invariant nonlinear shrinkage with high-dimensional latent Gaussian modeling, preserving the robustness of rank-based estimation while attaining asymptotic optimality under Frobenius loss. The analysis further uncovers a Baik–Ben Arous–Péché (BBP) phase transition in the latent correlation structure. Leveraging the generalized Marchenko–Pastur law and random matrix theory, the theoretical framework is supported by simulations confirming marginal invariance and phase-transition behavior. Empirical results on S&P 500 out-of-sample minimum-variance portfolios demonstrate substantially improved condition numbers, reduced realized volatility, and lower turnover compared to linear shrinkage.

0 citationsRead paper

Rethinking Penetration Testing for AI-Enabled Systems: From Resource Compromise to Behavioral Objective Violation

Jul 15, 2026

Traditional penetration testing struggles to evaluate security risks in AI systems arising from violations of behavioral objectives without breaching underlying infrastructure. This work proposes the first formal definition of AI penetration testing, reframing it as an objective-driven behavioral security assessment. The approach involves identifying operational objectives, mapping AI-driven behaviors, analyzing adversarial attack surfaces—such as prompt injection, data poisoning, and sensor manipulation—establishing criteria for behavioral failure, and conducting scenario-based red-teaming exercises. By integrating threat modeling, behavior mapping, and evidentiary chain construction, the framework demonstrates its efficacy and novelty in a case study involving an AI-powered Security Operations Center assistant, successfully uncovering attack pathways that violate system objectives through behavioral manipulation alone, without requiring infrastructure compromise.

0 citationsRead paper

Scalable Bayesian structure learning of directed acyclic graphs via Laplace approximation, with an application to breast cancer gene expression networks

Jul 11, 2026

This work addresses the computational challenges in Bayesian DAG structure learning arising from the super-exponential growth of the DAG space and the intractability of marginal likelihoods under non-conjugate priors. The authors propose a novel approach based on a modified Cholesky parameterization of the precision matrix, deriving—for the first time—the node-wise marginal likelihood under a Normal–Gamma non-conjugate prior in the form of a generalized inverse Gaussian distribution. Leveraging its asymptotic properties for large parameters, they construct an efficient Laplace approximation-based scoring function embedded within a Metropolis–Hastings sampler for DAG search. Additionally, a probit link couples latent variables with binary clinical outcomes. This framework overcomes the limitations of conjugate priors and enables exact posterior sampling of conditional variances. Experiments demonstrate superior performance over PC, GES, NOTEARS, DAGMA, and conjugate baselines on synthetic data, successful recovery of known structures in the Sachs signaling pathway and Wisconsin breast cancer datasets, and accurate prediction of malignancy with a cross-validated ROC-AUC of 0.94.

0 citationsRead paper

Bayesian DAG Structure Learning with Simultaneous Shrinkage Covariance Estimation under Scale-Mixture Error Distributions in the Proportional High-Dimensional Regime

Jul 09, 2026

This study addresses the challenge of jointly estimating directed acyclic graph (DAG) structures and precision matrices in high-dimensional settings with heavy-tailed or contaminated data. The authors propose R-DACH, a unified Bayesian framework that, for the first time, directly places a global–local horseshoe prior on the strictly lower triangular part of the Cholesky factor, combined with an inverse-Gamma scale mixture error model. This approach enables simultaneous inference of variable ordering, sparse DAG structure, and continuous parameters while inherently achieving robustness to outliers. Theoretical and empirical results demonstrate that R-DACH outperforms graphical horseshoe, DAG-Wishart, and PC algorithms—particularly under contamination—with superior topological consistency and parent selection accuracy, even when the number of variables reaches several hundred. Applied to TCGA RNA-seq data, R-DACH uncovers biologically interpretable gene regulatory relationships missed by competing methods.

0 citationsRead paper