Related papers: Robust Online Covariance and Sparse Precision Esti…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
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…
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…
We introduce collapsed compilation, a novel approximate inference algorithm for discrete probabilistic graphical models. It is a collapsed sampling algorithm that incrementally selects which variable to sample next based on the partial…
We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…
Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…
We introduce a methodology to construct parsimonious probabilistic models. This method makes use of Information Filtering Networks to produce a robust estimate of the global sparse inverse covariance from a simple sum of local inverse…
The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially for huge data sets and online learning. While this recursive algorithm is popular for computation and memory efficiency, quantifying…
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…
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…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula yields an online signal recovery algorithm that can be…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…