Related papers: Adaptive Kernel Regression for Constrained Route A…
Precise asymptotics have revealed many surprises in high-dimensional regression. These advances, however, have not extended to perhaps the simplest estimator: direct Nadaraya-Watson (NW) kernel smoothing. Here, we describe how one can use…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
In this paper, we consider contextual stochastic optimization using Nadaraya-Watson kernel regression, which is one of the most common approaches in nonparametric regression. Recent studies have explored the asymptotic convergence behavior…
Generative models are often conditioned on a small set of examples via cross-attention. Under the Gaussian optimal-transport path, we show that the exact velocity field induced by a finite support set is a Nadaraya--Watson kernel smoother…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…
This paper presents an end-to-end differentiable algorithm for robust and detail-preserving surface normal estimation on unstructured point-clouds. We utilize graph neural networks to iteratively parameterize an adaptive anisotropic kernel…
In regression problems where covariates are naturally organized in a hierarchical tree structure, a central challenge is to select the resolution at which covariates enter the model. Determining this level of feature aggregation is of…
Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the…
We propose a new method for construction of the absolute permeability map consistent with the interpreted results of well logging and well test measurements in oil reservoirs. Nadaraya-Watson kernel regression is used to approximate…
In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya--Watson smooth backfitting but at the same time achieves the oracle property of local linear…
Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to…
In the autoencoder based anomaly detection paradigm, implementing the autoencoder in edge devices capable of learning in real-time is exceedingly challenging due to limited hardware, energy, and computational resources. We show that these…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition…
Despite remarkable improvements in speed and accuracy, convolutional neural networks (CNNs) still typically operate as monolithic entities at inference time. This poses a challenge for resource-constrained practical applications, where both…
While quantum annealing (QA) has been developed for combinatorial optimization, practical QA devices operate at finite temperature and under noise, and their outputs can be regarded as stochastic samples close to a Gibbs--Boltzmann…
This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…