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1. Simultaneous Change Point Inference and Structure Recovery for High Dimensional Gaussian Graphical Models

   Liu, B.; Zhang, X.; Liu, Y. (October 2021, Journal of machine learning research)

   In this article, we investigate the problem of simultaneous change point inference and structure recovery in the context of high dimensional Gaussian graphical models with possible abrupt changes. In particular, motivated by neighborhood selection, we incorporate a threshold variable and an unknown threshold parameter into a joint sparse regression model which combines p l1-regularized node-wise regression problems together. The change point estimator and the corresponding estimated coefficients of precision matrices are obtained together. Based on that, a classifier is introduced to distinguish whether a change point exists. To recover the graphical structure correctly, a data-driven thresholding procedure is proposed. In theory, under some sparsity conditions and regularity assumptions, our method can correctly choose a homogeneous or heterogeneous model with high accuracy. Furthermore, in the latter case with a change point, we establish estimation consistency of the change point estimator, by allowing the number of nodes being much larger than the sample size. Moreover, it is shown that, in terms of structure recovery of Gaussian graphical models, the proposed thresholding procedure achieves model selection consistency and controls the number of false positives. The validity of our proposed method is justified via extensive numerical studies. Finally, we apply our proposed method to the S&P 500 dataset to show its empirical usefulness. 

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2. Robust Model Selection of Gaussian Graphical Models

   Zahin, Abrar; Anguluri, Rajasekhar; Sankar, Lalitha; Kosut, Oliver; Dasarathy, Gautam (April 2025, Transactions on Machine Learning Research)

   In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this “robust model selection” problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed that are known to provably recover the underlying tree-structure up to an (unavoidable) equivalence class. In this paper, we extend these results beyond tree-structured graphs. We first characterize the equivalence class up to which general graphs can be recovered in the presence of noise. Despite the inherent ambiguity (which we prove is unavoidable), the structure that can be recovered reveals local clustering information and global connectivity patterns in the underlying model. Such information is useful in a range of real-world problems, including power grids, social networks, protein-protein interactions, and neural structures. We then propose an algorithm which provably recovers the underlying graph up to the identified ambiguity. We further provide finite sample guarantees in the high-dimensional regime for our algorithm and validate our results through numerical simulations. 

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3. Network cross-validation by edge sampling

   https://doi.org/10.1093/biomet/asaa006  

   Li, Tianxi; Levina, Elizaveta; Zhu, Ji (April 2020, Biometrika)

   null (Ed.)

   Summary While many statistical models and methods are now available for network analysis, resampling of network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but it is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. In this paper we propose a new network resampling strategy, based on splitting node pairs rather than nodes, that is applicable to cross-validation for a wide range of network model selection tasks. We provide theoretical justification for our method in a general setting and examples of how the method can be used in specific network model selection and parameter tuning tasks. Numerical results on simulated networks and on a statisticians’ citation network show that the proposed cross-validation approach works well for model selection. 

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4. Integration of nested cross-validation, automated hyperparameter optimization, high-performance computing to reduce and quantify the variance of test performance estimation of deep learning models

   Calle, Paul; Bates, Averi; Reynolds, Justin; Liu, Yunlong; Cui, Haoyang; Ly, Sinaro; Wang, Chen; Zhang, Qinghao; Armendi, Alberto; Shettar, Shashank; et al (March 2025, arXivorg)

   The variability and biases in the real-world performance benchmarking of deep learning models for medical imaging compromise their trustworthiness for real-world deployment. The common approach of holding out a single fixed test set fails to quantify the variance in the estimation of test performance metrics. This study introduces NACHOS (Nested and Automated Cross-validation and Hyperparameter Optimization using Supercomputing) to reduce and quantify the variance of test performance metrics of deep learning models. NACHOS integrates Nested Cross-Validation (NCV) and Automated Hyperparameter Optimization (AHPO) within a parallelized high-performance computing (HPC) framework. NACHOS was demonstrated on a chest X-ray repository and an Optical Coherence Tomography (OCT) dataset under multiple data partitioning schemes. Beyond performance estimation, DACHOS (Deployment with Automated Cross-validation and Hyperparameter Optimization using Supercomputing) is introduced to leverage AHPO and cross-validation to build the final model on the full dataset, improving expected deployment performance. The findings underscore the importance of NCV in quantifying and reducing estimation variance, AHPO in optimizing hyperparameters consistently across test folds, and HPC in ensuring computational feasibility. By integrating these methodologies, NACHOS and DACHOS provide a scalable, reproducible, and trustworthy framework for DL model evaluation and deployment in medical imaging. 

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5. Testability of Instrumental Variables in Linear Non-Gaussian Acyclic Causal Models

   https://doi.org/10.3390/e24040512  

   Xie, Feng; He, Yangbo; Geng, Zhi; Chen, Zhengming; Hou, Ru; Zhang, Kun (April 2022, Entropy)

   This paper investigates the problem of selecting instrumental variables relative to a target causal influence X→Y from observational data generated by linear non-Gaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear non-Gaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method. 

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