Related papers: Covariance estimation with nonnegative partial cor…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Coarse data arise when learners observe only partial information about samples; namely, a set containing the sample rather than its exact value. This occurs naturally through measurement rounding, sensor limitations, and lag in economic…
This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…
Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…
In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In…
We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…
We present a weighted estimator of the covariance and correlation in bipartite complex systems with a double layer of heterogeneity. The advantage provided by the weighted estimators lies in the fact that the unweighted sample covariance…
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…
Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
Assume that $X_{1}, \ldots, X_{N}$ is an $\varepsilon$-contaminated sample of $N$ independent Gaussian vectors in $\mathbb{R}^d$ with mean $\mu$ and covariance $\Sigma$. In the strong $\varepsilon$-contamination model we assume that the…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
Stochastic gradients for deep neural networks exhibit strong correlations along the optimization trajectory, and are often aligned with a small set of Hessian eigenvectors associated with outlier eigenvalues. Recent work shows that…