相关论文: Classification with the nearest neighbor rule in g…

Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor…

In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the…

The nearest neighbor rule is a classic yet essential classification model, particularly in problems where the supervising information is given by pairwise dissimilarities and the embedding function are not easily obtained. Prototype…

Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…

We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution…

Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…

In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…

We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly…

We consider a problem of multiclass classification, where the training sample $S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb P(Y = m | X = x) = \eta_m(x)$, $1 \leq m \leq M$, and $\eta_1(x), \dots, \eta_M(x)$ are…

This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule…

When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…

Nearest neighbor has always been one of the most appealing non-parametric approaches in machine learning, pattern recognition, computer vision, etc. Previous empirical studies partly shows that nearest neighbor is resistant to noise, yet…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…

In the realizable online setting, a learner is tasked with making predictions for a stream of instances, where the correct answer is revealed after each prediction. A learning rule is online consistent if its mistake rate eventually…

Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and…

Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this…

When data is of an extraordinarily large size or physically stored in different locations, the distributed nearest neighbor (NN) classifier is an attractive tool for classification. We propose a novel distributed adaptive NN classifier for…

A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…