Related papers: Regression graphs and sparsity-inducing reparametr…

In this work, we present a new approach for constructing models for correlation matrices with a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

The standard way to parameterize the distributions represented by a directed acyclic graph is to insert a parametric family for the conditional distribution of each random variable given its parents. We show that when one's goal is to test…

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…

In this paper, we study the implicit bias of gradient descent for sparse regression. We extend results on regression with quadratic parametrization, which amounts to depth-2 diagonal linear networks, to more general depth-N networks, under…

Although sparse neural networks have been studied extensively, the focus has been primarily on accuracy. In this work, we focus instead on network structure, and analyze three popular algorithms. We first measure performance when structure…

In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…

Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the…

Deep learning models have been shown to be vulnerable to adversarial attacks. This perception led to analyzing deep learning models not only from the perspective of their performance measures but also their robustness to certain types of…

Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…

While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…

Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed…

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…

Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…