The Sylvester Graphical Lasso (SyGlasso)

• URL: http://arxiv.org/abs/2002.00288v1
• Date: Sat, 1 Feb 2020 22:57:45 GMT
• Title: The Sylvester Graphical Lasso (SyGlasso)
• Authors: Yu Wang, Byoungwook Jang, Alfred Hero
• Abstract summary: The model is based on the Sylvester equation that defines a generative model. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.
• Score: 4.322234105727178
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.

Related papers

• Likelihood Based Inference in Fully and Partially Observed Exponential Family Graphical Models with Intractable Normalizing Constants [4.532043501030714]
  Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling. This paper is to demonstrate that full likelihood based analysis of these models is feasible in a computationally efficient manner.
  arXiv  Detail & Related papers  (2024-04-27T02:58:22Z)
• Cyclic Directed Probabilistic Graphical Model: A Proposal Based on Structured Outcomes [0.0]
  We describe a probabilistic graphical model - probabilistic relation network - that allows the direct capture of directional cyclic dependencies. This model does not violate the probability axioms, and it supports learning from observed data. Notably, it supports probabilistic inference, making it a prospective tool in data analysis and in expert and design-making applications.
  arXiv  Detail & Related papers  (2023-10-25T10:19:03Z)
• Provable Tensor Completion with Graph Information [49.08648842312456]
  We introduce a novel model, theory, and algorithm for solving the dynamic graph regularized tensor completion problem. We develop a comprehensive model simultaneously capturing the low-rank and similarity structure of the tensor. In terms of theory, we showcase the alignment between the proposed graph smoothness regularization and a weighted tensor nuclear norm.
  arXiv  Detail & Related papers  (2023-10-04T02:55:10Z)
• Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes [3.469001874498102]
  thesis focuses on data that has complex-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and interpretable manner. practical applications of the methodology are considered using real datasets. This includes brain-connectivity analysis using data, space weather forecasting using solar imaging data, longitudinal analysis of public opinions using Twitter data, and mining of mental health related issues using TalkLife data.
  arXiv  Detail & Related papers  (2023-01-15T05:39:30Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Graph Polynomial Convolution Models for Node Classification of Non-Homophilous Graphs [52.52570805621925]
  We investigate efficient learning from higher-order graph convolution and learning directly from adjacency matrix for node classification. We show that the resulting model lead to new graphs and residual scaling parameter. We demonstrate that the proposed methods obtain improved accuracy for node-classification of non-homophilous parameters.
  arXiv  Detail & Related papers  (2022-09-12T04:46:55Z)
• On the Strong Correlation Between Model Invariance and Generalization [54.812786542023325]
  Generalization captures a model's ability to classify unseen data. Invariance measures consistency of model predictions on transformations of the data. From a dataset-centric view, we find a certain model's accuracy and invariance linearly correlated on different test sets.
  arXiv  Detail & Related papers  (2022-07-14T17:08:25Z)
• Bivariate vine copula based regression, bivariate level and quantile curves [0.0]
  We introduce a novel graph structure model specifically designed for a symmetric treatment of two responses in a predictive regression setting. We use vine copulas the typical shortfalls of regression, as the need for transformations or interactions of predictors, collinearity or quantile crossings are avoided. We apply our approach to weather measurements from Seoul, Korea.
  arXiv  Detail & Related papers  (2022-05-05T10:41:01Z)
• Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations [57.15855198512551]
  We propose a novel score-based generative model for graphs with a continuous-time framework. We show that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule.
  arXiv  Detail & Related papers  (2022-02-05T08:21:04Z)
• An additive graphical model for discrete data [6.821476515155997]
  We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. We exploit the properties of discrete random variables to uncover a deeper relation between additive conditional independence and conditional independence than previously known.
  arXiv  Detail & Related papers  (2021-12-29T17:48:12Z)
• Hyperbolic Graph Embedding with Enhanced Semi-Implicit Variational Inference [48.63194907060615]
  We build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure.
  arXiv  Detail & Related papers  (2020-10-31T05:48:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.