Related papers: The Functional Graphical Lasso
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…
Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
The dimension of random simplicial complexes (defined as the maximal dimension among all faces) is a natural extreme value associated with the complex, and is closely related to other functionals defined by a maximum, such as the clique…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
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…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…
In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped…
This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This…
Graphical LASSO (GLASSO) is a widely used method for estimating sparse precision matrices and learning undirected graphical models in high-dimensional settings. Because GLASSO penalizes entries of the precision matrix directly, however, it…
High-dimensional multivariate time series are common in many scientific and industrial applications, where the interest lies in identifying key dependence structure within the data for subsequent analysis tasks, such as forecasting. An…
Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…
Penalized regression models such as the Lasso have proved useful for variable selection in many fields - especially for situations with high-dimensional data where the numbers of predictors far exceeds the number of observations. These…
We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…
High dimensional Gaussian graphical models provide a rigorous framework to describe a network of statistical dependencies between entities, such as genes in genomic regulation studies or species in ecology. Penalized methods, including the…
This article investigates uncertainty quantification of the generalized linear lasso~(GLL), a popular variable selection method in high-dimensional regression settings. In many fields of study, researchers use data-driven methods to select…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…