Related papers: Estimating the minimizer and the minimum value of …

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…

Instrumental variables (IVs) provide a powerful strategy for identifying causal effects in the presence of unobservable confounders. Within the nonparametric setting (NPIV), recent methods have been based on nonlinear generalizations of…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

We study the problem of minimizing a relatively-smooth convex function using stochastic Bregman gradient methods. We first prove the convergence of Bregman Stochastic Gradient Descent (BSGD) to a region that depends on the noise (magnitude…

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the…

We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on…

The nonparametric regression with a random design model is considered. We want to recover the regression function at a point x where the design density is vanishing or exploding. Depending on assumptions on the regression function local…

We study the minimization of a convex function $f(X)$ over the set of $n\times n$ positive semi-definite matrices, but when the problem is recast as $\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq n$. We study…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

A rank estimator in robust regression is a minimizer of a function which depends (in addition to other factors) on the ordering of residuals but not on their values. Here we focus on the optimization aspects of rank estimators. We…

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…

A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional…