相关论文: Rates of Convergence for Nearest Neighbor Classifi…

Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…

In regression analysis one wants to estimate the regression function from a data. In this paper we consider the rate of convergence for the nearest neighbor estimator in case that the regression function is $(p,C)$-smooth. It is an open…

Given an $n$-sample of random vectors $(X_i,Y_i)_{1 \leq i \leq n}$ whose joint law is unknown, the long-standing problem of supervised classification aims to \textit{optimally} predict the label $Y$ of a given a new observation $X$. In…

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…

Nearest neighbor classifier is arguably the most simple and popular nonparametric classifier available in the literature. However, due to the concentration of pairwise distances and the violation of the neighborhood structure, this…

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…

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…

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…

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…

Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius $r$ that applies to all…

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…

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has…

We study statistical properties of the k-nearest neighbors algorithm for multiclass classification, with a focus on settings where the number of classes may be large and/or classes may be highly imbalanced. In particular, we consider a…

Nearest neighbor imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the nearest neighbor imputation estimator for general population parameters, including…

We introduce a class of depth-based classification procedures that are of a nearest-neighbor nature. Depth, after symmetrization, indeed provides the center-outward ordering that is necessary and sufficient to define nearest neighbors. Like…

The $k$-nearest neighbor ($k$-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the number of neighbors $k$. This parameter exerts a direct impact on…

$k$-nearest neighbor classification is a popular non-parametric method because of desirable properties like automatic adaption to distributional scale changes. Unfortunately, it has thus far proved difficult to design active learning…

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours…

Matching methods are widely used for causal inference in observational studies. Among them, nearest neighbor matching is arguably the most popular. However, nearest neighbor matching does not generally yield an average treatment effect…