Related papers: Automatic and location-adaptive estimation in func…

Recent medical image reconstruction techniques focus on generating high-quality medical images suitable for clinical use at the lowest possible cost and with the fewest possible adverse effects on patients. Recent works have shown…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…

We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic…

In this paper we propose a semiparametric spatial autoregressive model that combines a linear covariate component with a nonparametrically estimated spatial term, allowing flexible dependence modeling without restrictive covariance…

This research focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. In such a context, we study the Trend Filtering, a nonparametric estimator introduced by…

We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…

In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in…

Nonparametric learning is a fundamental concept in machine learning that aims to capture complex patterns and relationships in data without making strong assumptions about the underlying data distribution. Owing to simplicity and…

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…

We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…

Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point.…

We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive…

This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into…

Illuminant estimation plays a key role in digital camera pipeline system, it aims at reducing color casting effect due to the influence of non-white illuminant. Recent researches handle this task by using Convolution Neural Network (CNN) as…

Local regression is widely used to explore spatial heterogeneity, but anisotropic or effectively low-dimensional neighborhoods can produce ill-conditioned local solves, causing coefficient variation driven by numerical artifacts rather than…

We propose a simple methodology to approximate functions with given asymptotic behavior by specifically constructed terms and an unconstrained deep neural network (DNN). The methodology we describe extends to various asymptotic behaviors…

Making an adaptive prediction based on one's input is an important ability for general artificial intelligence. In this work, we step forward in this direction and propose a semi-parametric method, Meta-Neighborhoods, where predictions are…

Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving…

K-Nearest Neighbors (KNN) search is a fundamental algorithm in artificial intelligence software with applications in robotics, and autonomous vehicles. These wide-ranging applications utilize KNN either directly for simple classification or…

The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…