Related papers: Robust oracle estimation and uncertainty quantific…
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…
We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We consider the nonparametric regression and the classification problems for $\psi$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. A penalized estimation…
The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…
Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in…
This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample…
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is…
Noisy pairwise comparison feedback has been incorporated to improve the overall query complexity of interactively learning binary classifiers. The \textit{positivity comparison oracle} is used to provide feedback on which is more likely to…
We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our…
Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…
An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (oracle inequality) is obtained
Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges, such as personalized medicine and optimal resource allocation. In this paper, we develop a general class of two-step algorithms for…
In this work, we consider a class of linear ill-posed problems with operators that map from the sequence space $ \ell_r $ ($r \ge 1$) into a Banach space and in addition satisfy a conditional stability estimate in the scale of sequence…
We study the problem of estimating the one-point specification probabilities in non-necessary finite discrete random fields from partially observed independent samples. Our procedures are based on model selection by minimization of a…
Penalized least squares estimation is a popular technique in high-dimensional statistics. It includes such methods as the LASSO, the group LASSO, and the nuclear norm penalized least squares. The existing theory of these methods is not…
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…
While variable selection has received extensive attention in the literature, its exploration in the presence of response measurement error remains underexplored. In this paper, we investigate this important problem within the context of…