相关论文: An Upper Bound of the Bias of Nadaraya-Watson Kern…

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients…

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework…

In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…

The most direct way to express arbitrary dependencies in datasets is to estimate the joint distribution and to apply afterwards the argmax-function to obtain the mode of the corresponding conditional distribution. This method is in practice…

Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made…

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…

Adversarial training and data augmentation with noise are widely adopted techniques to enhance the performance of neural networks. This paper investigates adversarial training and data augmentation with noise in the context of regularized…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a…

Nonparametric density estimation for compositional data supported on the simplex is examined under a missing at random mechanism. Rather than imputing missing values and estimating the density from a completed data set, we adopt a strategy…

Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows…

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known…

Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for…

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on…

The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theory. Since the generalization ability of the 'lazy trained'…