Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical models provide the following several useful properties: - Graphi…
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48 results for “graphical structure”
We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We intr…
In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin methods---have their own distinct strengths but also possess significant drawbacks. Conditio…
Graphical models for covariance matrices improve structure learning.
problem Learning structure in graphical models for covariance matrices.
method Structural learning via -penalized loss minimization.
result Method outperforms alternatives in simulations and real-world applications.
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of…
Graphical notation simplifies complex polynomial constraints in linear models.
problem Complex polynomial constraints in linear structural equation models are impractical.
method Developed a graphical notation to represent these constraints.
result The graphical notation simplifies the representation of many polynomial constraints.
Simultaneous Identification of Sparse Structures and Communities in Heterogeneous Graphical Modelsstat.ML
Paper identifies sparse structures and communities in heterogeneous graphical models.
problem Detecting community structures in graphical models.
method Novel decomposition into sparse and low-rank parts, three-stage estimation procedure.
result Consistent model selection for adaptive penalized estimator.
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.
Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithmmath.OC
Efficiently estimates hub graphical models with structured sparsity.
problem Computational difficulty in fitting graphical models with hub nodes, especially in high-dimensional data.
method Two-phase algorithm: ADMM for initial point generation and SSN-ALM for accurate solution.
result Significantly improves estimation accuracy and efficiency compared to existing methods.
Nonparametric undirected graphical model selection using diffusion models
problem Undirected graphical model selection
method Diffusion models
result Model selection consistency
VFG model embeds flow-based models with hierarchical structures using variational inference.
problem Flow-based models struggle with high-dimensional latent spaces and lack of tractable inference for graphical structures.
method Integrates flow-based functions through variational inference with aggregation nodes for hierarchical information integration.
result VFG models achieve improved ELBO and likelihood values on multiple datasets.
Bayesian method for estimating functional graphical models from neuroimaging data.
problem Estimating dependence structures from functional data in neuroscience.
method Fully Bayesian regularization scheme, including direct Bayesian analog of functional graphical lasso and graphical horseshoe.
result Insight into brain compensation after traumatic brain injury.
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
Composing graphical models with neural networks for structured representations and fast inferencestat.ML
We propose a general modeling and inference framework that composes probabilistic graphical models with deep learning methods and combines their respective strengths. Our model family augments graphical structure in latent variables with neural network observation models. For inference, we extend variational autoencode…
Profile Graphical Modelsstat.ME
Profile graphical models represent multivariate dependence under varying risk factors.
problem Capturing varying conditional independence structures across different levels of a risk factor.
method Introducing a novel class of graphical models (profile graphical models) that represent multivariate dependence under varying risk factors, and developing a Bayesian approach for learning shared sparsity structures.
result Demonstrated enhanced ability to capture subject-specific differences in protein network data from acute myeloid leukemia.
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.
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for t…
High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approachstat.ML
Proposes a method to estimate functional graphical models from multivariate random functions.
problem Estimating conditional independence structure of multivariate random functions.
method Neighborhood selection approach combining function-on-function regression and graph recovery.
result Statistical consistency of the method in high-dimensional settings.
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.
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…
New method learns dependencies in high-dimensional data without graph assumptions.
problem Learning dependencies in nonparametric and high-dimensional settings.
method Neighbourhood lattice decomposition for nonparametric CI learning.
result Compact, non-graphical representation of CI exists in any graphical model.
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data is drawn identically from a generating distribution. Introducing sparsity a…
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…
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.
Graphical models improve portfolio optimization for financial time series.
problem Optimizing portfolios with time-varying covariance patterns.
method Various graphical models (PCA-KMeans, autoencoders, dynamic clustering, structural learning) to capture covariance matrix patterns.
result Graphical models outperform baseline methods in generating steady returns with low risk.
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…
Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter the conditional dependence between the random variables, and potentially produce s…
This paper develops a nonparametric model for complex network data.
problem Capturing conditional independence structure in multivariate data with heterogeneous graph structures.
method Integrates network embedding with nonparametric graphical model estimation, solving a linear equation system.
result The proposed method effectively recovers heterogeneous graph structures without distributional assumptions.
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.
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…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model…
The report evaluates heuristics for learning timescale graphical event models.
problem Lack of heuristics for determining hyper-parameters in timescale graphical event models.
method Proposed and evaluated different heuristics for hyper-parameter determination and refined an existing distance measure.
result Conclusions about the applicability of different heuristics on synthetic data.
Paper proposes a method to detect fair communities in graphs considering demographic attributes.
problem Inconsistent community detection violates fairness constraints for nodes with demographic attributes.
method Develops an -regularized pseudo-likelihood approach for fair graphical model selection.
result The method ensures demographic groups are fairly represented within detected communities.
New algorithm reduces regret in graphical bilinear bandits.
problem Optimizing decisions in a network of agents playing bilinear games.
method Optimism in the face of uncertainty principle applied to combinatorial NP-hard problem.
result Upper bound of on -regret demonstrated.
New method learns graphical models with latent variables for extreme events.
problem Learning graphical models with latent variables for multivariate extremes.
method Tractable convex program exttt{eglatent} for Hüsler-Reiss models.
result Consistently recovers conditional graph and latent variables.
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when p>>n. However, analogous approaches for learning the structure of graphical mod…
Computes Lie algebra structure constants using a graphical calculus.
problem Computing Lie algebra structure constants efficiently.
method Graphical calculus for classical invariant theory.
result Generalizes known methods for to other Lie algebras.
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhoo…
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…
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.
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…
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…
While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models linking both continuous and discrete variables (mixed data), which are common in many scientific applications. We propose a novel graphical mode…
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.
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by the lasso. We present the Condition-on-Selection method that allows for valid s…
This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests and decomposable models minimizing information criteria such as AIC or BIC, and for displaying the independence graphs of the models. It has also some…
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.