English
Related papers

Related papers: Rates of Convergence for Nearest Neighbor Classifi…

200 papers

We develop a general framework for margin-based multicategory classification in metric spaces. The basic work-horse is a margin-regularized version of the nearest-neighbor classifier. We prove generalization bounds that match the state of…

Machine Learning · Computer Science 2014-01-31 Aryeh Kontorovich , Roi Weiss

We design a data-dependent metric in $\mathbb R^d$ and use it to define the $k$-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard $k$-nearest neighbor…

Statistics Theory · Mathematics 2012-05-23 Gérard Biau , Luc Devroye , Vida Dujmovic , Adam Krzyzak

Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature…

Computer Vision and Pattern Recognition · Computer Science 2018-03-19 Hossein Rajabzadeh , Mansoor Zolghadri Jahromi , Mohammad Sadegh Zare , Mostafa Fakhrahmad

Expectations of multivariate functions with missing labels occur in various fields such as transfer learning and average treatment effects. Although non-parametric estimators based on nearest-neighbour matching are frequently used in this…

Statistics Theory · Mathematics 2026-05-18 Simon Viel

Neural networks are not learning optimal decision boundaries. We show that decision boundaries are situated in areas of low training data density. They are impacted by few training samples which can easily lead to overfitting. We provide a…

Machine Learning · Computer Science 2023-10-09 Johannes Schneider

We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective…

Statistics Theory · Mathematics 2021-06-16 Steffen Betsch , Bruno Ebner , Bernhard Klar

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…

Statistics Theory · Mathematics 2015-03-20 Adam D. Bull

The problem of nearest-neighbor (NN) condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds…

Computational Geometry · Computer Science 2019-04-30 Alejandro Flores-Velazco , David Mount

Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…

Data Structures and Algorithms · Computer Science 2019-02-18 Abhinav Mishra

In this paper, we establish explicit convergence rates for the stochastic smooth approximations of infimal convolutions introduced and developed in \cite{MR4581306,MR4923371}. In particular, we quantify the convergence of the associated…

Optimization and Control · Mathematics 2026-02-23 Diego Morales , Pedro Pérez-Aros , Emilio Vilches

Despite the wide use of $k$-Nearest Neighbors as classification models, their explainability properties remain poorly understood from a theoretical perspective. While nearest neighbors classifiers offer interpretability from a ``data…

Machine Learning · Computer Science 2026-01-23 Pablo Barceló , Alexander Kozachinskiy , Miguel Romero Orth , Bernardo Subercaseaux , José Verschae

Providing various machine learning (ML) applications in the real world, concerns about discrimination hidden in ML models are growing, particularly in high-stakes domains. Existing techniques for assessing the discrimination level of ML…

Machine Learning · Computer Science 2024-05-16 Yijun Bian , Yujie Luo

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is…

Statistics Theory · Mathematics 2011-06-24 Guillermo Henry , Andrés Muñoz , Daniela Rodriguez

Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…

Machine Learning · Computer Science 2026-03-12 Eng-Jon Ong , Omer Bobrowski , Gesine Reinert , Primoz Skraba

kNN is a very effective Instance based learning method, and it is easy to implement. Due to heterogeneous nature of data, noises from different possible sources are also widespread in nature especially in case of large-scale databases. For…

Machine Learning · Computer Science 2020-05-19 Joydip Dhar , Ashaya Shukla , Mukul Kumar , Prashant Gupta

We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…

Statistics Theory · Mathematics 2012-11-12 Yehua Li , Tailen Hsing

Neural Networks have high accuracy in solving problems where it is difficult to detect patterns or create a logical model. However, these algorithms sometimes return wrong solutions, which become problematic in high-risk domains like…

Machine Learning · Computer Science 2025-06-26 Miguel N. Font , José L. Jorro-Aragoneses , Carlos M. Alaíz

A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities…

Statistics Theory · Mathematics 2022-03-14 J. Jon Ryu , Shouvik Ganguly , Young-Han Kim , Yung-Kyun Noh , Daniel D. Lee

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

Machine Learning · Statistics 2020-07-01 Yuhao Zhou , Jiaxin Shi , Jun Zhu

We present Local Naive Bayes Nearest Neighbor, an improvement to the NBNN image classification algorithm that increases classification accuracy and improves its ability to scale to large numbers of object classes. The key observation is…

Computer Vision and Pattern Recognition · Computer Science 2011-12-02 Sancho McCann , David G. Lowe