We study the estimation error of constrained M-estimators, and derive explicit upper bounds
on the expected estimation error determined by the Gaussian width of the constraint set …

We provide novel theoretical results regarding local optima of regularized M-estimators,
allowing for nonconvexity in both loss and penalty functions. Under restricted strong …

We study the estimation capacity of the generalized Lasso, ie, least squares minimization
combined with a (convex) structural constraint. While Lasso-type estimators were originally …

Regularized m-estimators are widely used due to their ability of recovering a low-
dimensional model in high-dimensional scenarios. Some recent efforts on this subject …

Major progress has been made in the previous decade to characterize the asymptotic
behavior of regularized M-estimators in high-dimensional regression problems in the …

The problem of optimizing a nonconvex function is known to be computationally intractable
in general [19, 24]. Unlike convex functions, nonconvex functions may possess local optima …

We consider unregularized robust M-estimators for linear models under Gaussian design
and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and …

Suppose that we observe y∈R^n and X∈R^n*m in the following errors-in-variables model:
y&= &X_ 0 β^*+ ϵ\X&= &X_ 0+ W where X_0 is an n*m design matrix with independent …

In the context of linear regression, we construct a data-driven convex loss function with
respect to which empirical risk minimisation yields optimal asymptotic variance in the …

Given a dictionary of Mn predictors, in a random design regression setting with n
observations, we construct estimators that target the best performance among all the linear …