Related papers: The Distance Precision Matrix: computing networks …

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…

In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

Sparse networks can be found in a wide range of applications, such as biological and communication networks. Inference of such networks from data has been receiving considerable attention lately, mainly driven by the need to understand and…

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…

Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

Differences between biological networks corresponding to disease conditions can help delineate the underlying disease mechanisms. Existing methods for differential network analysis do not account for dependence of networks on covariates. As…

Network data arises through observation of relational information between a collection of entities. Recent work in the literature has independently considered when (i) one observes a sample of networks, connectome data in neuroscience being…

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…

A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…

Gene covariation networks are commonly used to study biological processes. The inference of gene covariation networks from observational data can be challenging, especially considering the large number of players involved and the small…

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical…