Related papers: Graph-constrained Analysis for Multivariate Functi…
We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain…
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…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
Modern recording techniques enable neuroscientists to simultaneously study neural activity across large populations of neurons, with capturing predictor-dependent correlations being a fundamental challenge in neuroscience. Moreover, the…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
Estimation of brain functional connectivity from EEG data is of great importance both for medical research and diagnosis. It involves quantifying the conditional dependencies among the activity of different brain areas from the time-varying…
Functional covariates arise in many scientific and engineering applications when model inputs take the form of time-dependent or spatially distributed profiles, such as varying boundary conditions or changing material behaviours. In…
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.…
This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a…
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…
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…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
This paper addresses graph learning in Gaussian Graphical Models (GGMs). In this context, data matrices often come with auxiliary metadata (e.g., textual descriptions associated with each node) that is usually ignored in traditional graph…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…