Article
Computer Science, Artificial Intelligence
Hang Yu, Songwei Wu, Justin Dauwels
Summary: Estimating a sequence of dynamic undirected graphical models is crucial in various systems to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. We propose a low-complexity tuning-free Bayesian approach, called BASS, for automatic structure learning from data.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2023)
Article
Mathematics
Claudia Angelini, Daniela De Canditiis, Anna Plaksienko
Summary: In this paper, we propose a joint data estimation method called jewel, using group Lasso penalty and establishing the consistency property of the estimator.
Article
Biochemical Research Methods
Victor Bernal, Venustiano Soancatl-Aguilar, Jonas Bulthuis, Victor Guryev, Peter Horvatovich, Marco Grzegorczyk
Summary: This paper investigates the statistical properties of partial correlations obtained using shrinkage methods and proposes a new (parametric) approach to address bias in network analysis. These methods account for the number of variables, sample size, and shrinkage values, and perform better than alternative methods in balancing true positives and false positives. The effectiveness of these methods is demonstrated through simulations and gene expression datasets.
Article
Mathematics, Interdisciplinary Applications
Kevin H. Lee, Qian Chen, Wayne S. DeSarbo, Lingzhou Xue
Summary: Researchers introduced finite mixture of ordinal graphical models to study the heterogeneous conditional dependence relationships of ordinal data in psychological science. By developing a penalized likelihood approach and designing a generalized EM algorithm, the significant computational challenges were effectively addressed, demonstrating good performance in simulation studies and real applications.
Article
Mathematical & Computational Biology
Katherine H. Shutta, Roberta De Vito, Denise M. Scholtens, Raji Balasubramanian
Summary: This tutorial provides an overview of Gaussian graphical models and demonstrates various tools for GGM analysis in R. It introduces the mathematical foundations of GGMs and emphasizes their applications in high-dimensional datasets. The methods are illustrated using a publicly available gene expression dataset from ovarian cancer patients.
STATISTICS IN MEDICINE
(2022)
Article
Health Care Sciences & Services
Jiali Lin, Inyoung Kim
Summary: This paper proposes a method for learning multiple connected graphs with multilevel variables. It incorporates a hierarchical Bayesian approach to estimate the classes of observations and learn about the network structures. The unique advantages of the method are demonstrated through simulations and a breast cancer application.
STATISTICAL METHODS IN MEDICAL RESEARCH
(2022)
Article
Statistics & Probability
Tianhong Sheng, Bing Li, Eftychia Solea
Summary: We introduce a skewed Gaussian graphical model which is a more flexible extension of the Gaussian graphical model. The conditional independence in the skewed Gaussian distribution is still characterized by the sparseness in the parameters, but with the addition of a shape parameter. We develop an algorithm to efficiently estimate the model and show its superiority in cases where the distributional assumptions are not satisfied.
JOURNAL OF MULTIVARIATE ANALYSIS
(2023)
Article
Computer Science, Theory & Methods
Chunshan Liu, Daniel R. Kowal, Marina Vannucci
Summary: Gaussian graphical models are useful for studying conditional dependence among random variables, but time series data pose additional challenges with their dynamic nature and heavy-tailed characteristics. To address these challenges, dynamic and robust Bayesian graphical models are proposed, utilizing hidden Markov models and heavy-tailed multivariate t-distributions.
STATISTICS AND COMPUTING
(2022)
Article
Biology
S. Na, M. Kolar, O. Koyejo
Summary: Differential graphical models seek to represent differences in conditional dependence structures between two groups, with an extended setting considered in this manuscript involving latent variable Gaussian graphical models. The proposed two-stage estimation method decomposes the differential network into sparse and low-rank components, demonstrating superior performance in experiments compared to existing methods.
Article
Statistics & Probability
Jingfei Zhang, Yi Li
Summary: This article proposes a Gaussian graphical regression model to link graph structures to external covariates. In co-expression QTL studies, the method can determine how genetic variants and clinical conditions modulate network structures, and recover gene networks. The utility and efficacy of the method is demonstrated through simulation studies and an application example.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Computer Science, Information Systems
Saurabh Sihag, Ali Tajer
Summary: This paper discusses the problem of estimating the structure of similar graphical models in high dimensions. The focus is on Gaussian and Ising models, and the sample complexity of estimating their structures is characterized. Necessary and sufficient conditions for a bounded probability of error are determined. Additionally, a low complexity, online structure estimation algorithm for Ising models is proposed.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Engineering, Electrical & Electronic
Cody Mazza-Anthony, Bogdan Mazoure, Mark Coates
Summary: This paper introduces two novel estimators based on the OWL norm for estimating sparse structured precision matrices, which can simultaneously identify groups of related edges and control sparsity. The ccGOWL estimator shows good computational efficiency and accuracy in both synthetic data and real-world applications, demonstrating its efficacy in gene network analysis and econometrics.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Statistics & Probability
Qingyang Liu, Yuping Zhang, Zhengqing Ouyang
Summary: This paper focuses on joint structural estimation of time-varying mixed graphical models based on multivariate data over a series of time points. Various techniques, such as flexible local estimator, group lasso penalty, and an accelerated ADMM-based algorithm, are employed to handle the changing network structure, demonstrating practical merits through synthetic and real data applications.
Article
Automation & Control Systems
Gabor Lugosi, Jakub Truszkowski, Vasiliki Velona, Piotr Zwiernik
Summary: The study introduces a new input model for querying single entries of the covariance matrix to recover the support of the inverse covariance matrix with low query and computational complexities. The algorithms are suitable for recovering the structure of tree-like graphs and graphs of small treewidth more efficiently than computing the empirical covariance matrix for large classes of graphs.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Biochemical Research Methods
Victor Bernal, Rainer Bischoff, Peter Horvatovich, Victor Guryev, Marco Grzegorczyk
Summary: Gaussian graphical models (GGMs) are commonly used in systems biology to reconstruct regulatory networks by overcoming the 'high-dimensional problem' through shrinkage methods. However, the shrinkage introduces a non-linear bias in the partial correlations, impacting their interpretation and hindering network comparability. A proposed method, 'un-shrinking', aims to correct this bias and provide partial correlations closer to actual values for easier interpretation.
BMC BIOINFORMATICS
(2021)
