Related papers: High-dimensional robust precision matrix estimatio…

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…

We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…

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…

The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical…

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…

Cellwise outliers are widespread in data and traditional robust methods may fail when applied to datasets under such contamination. We propose a variable selection procedure, that uses a pairwise robust estimator to obtain an initial…

Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…

This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes…

We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…

The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…

We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr-Muller-Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux-Ollerer's…

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…

A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…

In data analysis, contamination caused by outliers is inevitable, and robust statistical methods are strongly demanded. In this paper, our concern is to develop a new approach for robust data analysis based on scoring rules. The scoring…