Related papers: Robust Nonparametric Regression under Poisoning At…
We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…
Adversarially robust machine learning has received much recent attention. However, prior attacks and defenses for non-parametric classifiers have been developed in an ad-hoc or classifier-specific basis. In this work, we take a holistic…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…
In many learning problems, the training and testing data follow different distributions and a particularly common situation is the \textit{covariate shift}. To correct for sampling biases, most approaches, including the popular kernel mean…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…
This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of…
Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…
Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
This paper studies density estimation under pointwise loss in the setting of contamination model. The goal is to estimate $f(x_0)$ at some $x_0\in\mathbb{R}$ with i.i.d. observations, $$ X_1,\dots,X_n\sim (1-\epsilon)f+\epsilon g, $$ where…
We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…