Related papers: Bandwidth selection in kernel empirical risk minim…
We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the…
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…
We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…
This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
Existing multi-view learning methods based on kernel function either require the user to select and tune a single predefined kernel or have to compute and store many Gram matrices to perform multiple kernel learning. Apart from the huge…
This paper is concerned with adaptive nonparametric estimation using the Goldenshluger-Lepski selection method. This estimator selection method is based on pairwise comparisons between estimators with respect to some loss function. The…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the…
Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data. However, for complex data that are increasingly available in many scientific fields, the specification of their underlying…
Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…
We study an adaptive estimation procedure called the Goldenshluger-Lepski method in the context of reproducing kernel Hilbert space (RKHS) regression. Adaptive estimation provides a way of selecting tuning parameters for statistical…
We consider the overfitting behavior of minimum norm interpolating solutions of Gaussian kernel ridge regression (i.e. kernel ridgeless regression), when the bandwidth or input dimension varies with the sample size. For fixed dimensions, we…
We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the…
We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms…
This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…