We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…
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48 results for “Gaussian graphical model”
This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a threshold-based algorithm for walk summable Gaussian graphical models. Both alg…
Graphical lasso may fail to fit models when data points are insufficient.
problem When does graphical lasso fail to select and fit a graphical model?
method Computational experiments with graphical lasso.
result Graphical lasso may fail when the number of data points is less than the maximum likelihood threshold.
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lassostat.ME
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to model the output network influenced by conditioning input variables. While highly …
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statist…
Paper adapts multiplicative weights method to Gaussian graphical models.
problem Graphical model selection in Gaussian random fields.
method Adapted multiplicative weights method from Ising model to Gaussian model.
result Achieves sample complexity bound similar to existing methods.
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally…
The paper shows cross-validation fails in learning Gaussian graphical model structures.
problem Cross-validation's failure in learning Gaussian graphical model structures.
method Finite-sample bounds on misidentification probability of Lasso estimator.
result Cross-validation is inconsistent for learning Gaussian graphical model structures.
Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.
problem Modeling statistical relationships between variables with sparsity and clustering.
method Two-phase algorithm using sGS-ADMM for initial point and pALM for solution.
result Demonstrates good performance and efficiency of the proposed model and algorithm on synthetic and real data.
Paper compares two methods for inferring network structures in presence of latent confounders.
problem Inferring network structures in presence of latent confounders.
method Gaussian graphical models with latent variables (LVGGM) and PCA-based removal of confounding (PCA+GGM).
result Proposes a new method combining strengths of LVGGM and PCA+GGM, proving consistency and convergence rate.
In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estima…
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories.
problem Learning Gaussian graphical models from dependent data.
method Two complementary approaches: local edge-testing and burn-in/thinning reduction.
result Both approaches provide finite-sample recovery guarantees and empirical comparisons.
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.
Novel method for learning Gaussian graphical models from paired data.
problem Learning Gaussian graphical models for dependent groups.
method Introducing twin order to explore the search space more efficiently.
result The twin order makes the model space a distributive lattice, leading to more efficient model exploration.
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting challenging. For example, Gaussian graphical models have recently been extended to the…
We consider the task of estimating a Gaussian graphical model in the high-dimensional setting. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to an l1 penalty, is a well-studied approach for this task. We begin by introducing a surprising connection between the graphical lasso and hi…
Surveying joint Gaussian graphical models to identify shared structures across domains.
problem Estimating shared structures across different data sources.
method Statistical inference of joint Gaussian graphical models.
result Improved estimation power for high-dimensional data.
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical mode…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional…
Clusterpath estimator simplifies graphical model interpretation for large datasets.
problem Difficulty in interpreting graphical models with many variables.
method Clusterpath estimator that groups variables for block-structured precision matrix.
result CGGM outperforms other methods in variable clustering and practical applications.
A new method combines Gaussian graphical models for better distributed Gaussian process predictions.
problem Poor results from traditional DGP due to violated conditional independence assumption.
method Proposes using Gaussian graphical models to aggregate local predictions from subsets of data.
result Our method outperforms other state-of-the-art DGP approaches on both synthetic and real datasets.
New neural network approach for optimizing latent variable models.
problem Stability issues in marginalizing Gaussian Bayesian networks.
method Developed a new graphical structure and a neural network algorithm.
result Established a duality between parameter optimization and neural network training.
New method controls false edge detections in Gaussian graphical models.
problem High false edge detections in well-established estimators.
method Nodewise variable selection approach to control false discovery rate.
result Significant gain in performance compared to competing methods.
Spectral sparsification improves Gaussian graphical models under MTP2 constraints.
problem Learning accurate, sparse graphs from data under MTP2 constraints.
method Spectral graph sparsification applied to Gaussian graphical models.
result Spectral-MTP2 preserves MTP2 and approximates the original model well.
We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal m…
In this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the equations between the resulting steady-state covariance matrix and the Laplacia…
In many applications, multivariate samples may harbor previously unrecognized heterogeneity at the level of conditional independence or network structure. For example, in cancer biology, disease subtypes may differ with respect to subtype-specific interplay between molecular components. Then, both subtype discovery and…
Fair GLASSO estimates fair GGMs by balancing statistical dependencies across groups.
problem Fairness in graphical models with biased data.
method Regularized graphical lasso with bias metrics, proximal gradient algorithm.
result Preserves statistical accuracy while promoting fairness across groups.
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority…
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally. Unfortunately, real-world data often does not fit well to sparse graphical models. I…
Algorithm learns non-Gaussian graphical models via Hessian scores and triangular transport.
problem Learning graph structure from non-Gaussian data.
method Score based on integrated Hessian information, coupled with triangular transport map.
result Algorithm successfully recovers graph structure for non-Gaussian data.
We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an -regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove -sparsisten…
A new copula model for multi-attribute data using optimal transport.
problem Relaxing the Gaussian assumption for multi-attribute graphical models.
method Introducing a new copula (Cyclically Monotone Copula) and using optimal transport theory.
result The model allows arbitrary continuous distributions and is more flexible than classical methods.
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Tri…
PACE-GGM uses Gaussian mechanism for private covariance estimation.
problem Private estimation of covariance matrices in high dimensions.
method Data-adaptive selection of entries, Gaussian mechanism, maximum-entropy reconstruction.
result Consistent improvements in estimation error compared to Gaussian mechanism and baselines.
A new multi-task learning estimator improves Gaussian graphical regression model fitting.
problem High error rate in fitting Gaussian graphical regression models due to separate node-wise lasso regressions.
method Proposes a multi-task learning estimator with cross-task group sparsity and within-task element-wise sparsity penalties, solved via an efficient augmented Lagrangian algorithm.
result Error rate improvement over separate node-wise lasso estimates, demonstrated through simulations and application to gene co-expression network study.
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from different resources and have heterogeneous hidden commonality in real-world applicati…
New method for mixed data types in graphical models.
problem Challenges in analyzing data with mixed variable types.
method Latent Gaussian copula models with leveraged polychoric and polyserial correlations.
result Flexible and scalable methodology for mixed data types.
A new Bayesian modeling method is proposed by combining the maximization of the marginal likelihood with a momentum-space renormalization group transformation for Gaussian graphical models. Moreover, we present a scheme for computint the statistical averages of hyperparameters and mean square errors in our proposed met…
Paper proposes a transfer learning framework for tensor Gaussian graphical models.
problem Pooling heterogeneous tensor data for improved estimation and variable selection.
method Transfer learning framework that uses data-adaptive weights from auxiliary domains.
result Significant improvement in estimation errors and variable selection consistency.
We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al.…
Optimal sample complexity for learning Gaussian DAG models established.
problem Learning the structure of Gaussian DAG models from observational data.
method Established minimax optimal sample complexity for two settings: equal variances without ordering knowledge and general linear models with ordering knowledge.
result Optimal sample complexity for both settings, matching undirected graphical models under equal variances.
The Nonparanormal SKEPTICstat.ME
We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators includin…