Related papers: Simultaneous penalized M-estimation of covariance …
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
In the context of undirected Gaussian graphical models, we introduce three estimators based on elastic net penalty for the underlying dependence graph. Our goal is to estimate the sparse precision matrix, from which to retrieve both the…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
This paper provides a comprehensive estimation framework for large covariance matrices via a log-det heuristics augmented by a nuclear norm plus $\ell_{1}$-norm penalty. We develop the model framework, which includes high-dimensional…
The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events…
We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted…
We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…
Given $n$ i.i.d. observations of a random vector $(X,Z)$, where $X$ is a high-dimensional vector and $Z$ is a low-dimensional index variable, we study the problem of estimating the conditional inverse covariance matrix $\Omega(z) =…
Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…
Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…
Nonlinear Mixed effects models are hidden variables models that are widely used in many fields such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to…
A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear…
We study the asymptotic properties of geodesically convex $M$-estimation on non-linear spaces. Namely, we prove that under very minimal assumptions besides geodesic convexity of the cost function, one can obtain consistency and asymptotic…