Related papers: Local nearest neighbour classification with applic…

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…

``Localization'' has proven to be a valuable tool in the Statistical Learning literature as it allows sharp risk bounds in terms of the problem geometry. Localized bounds seem to be much less exploited in the Stochastic Optimization…

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…

The k-nearest-neighbour procedure is a well-known deterministic method used in supervised classification. This paper proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in…

It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than…

We study the problem of lossless feature selection for a $d$-dimensional feature vector $X=(X^{(1)},\dots ,X^{(d)})$ and label $Y$ for binary classification as well as nonparametric regression. For an index set $S\subset \{1,\dots ,d\}$,…

Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…

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…

We study community detection in the \emph{symmetric $k$-stochastic block model}, where $n$ nodes are evenly partitioned into $k$ clusters with intra- and inter-cluster connection probabilities $p$ and $q$, respectively. Our main result is a…

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…

We study the scaling of classification error rates with respect to the size of the training dataset. In contrast to classical results where rates are minimax optimal for a problem class, this work starts with the empirical observation that,…

This paper investigates the phenomenon of benign overfitting in binary classification problems with heavy-tailed input distributions, extending the analysis of maximum margin classifiers to $\alpha$ sub-exponential distributions ($\alpha…

Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster…

Demands for minimum parameter setup in machine learning models are desirable to avoid time-consuming optimization processes. The $k$-Nearest Neighbors is one of the most effective and straightforward models employed in numerous problems.…

The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has…

We establish optimal convergence rates up to a log-factor for a class of deep neural networks in a classification setting under a restraint sometimes referred to as the Tsybakov noise condition. We construct classifiers in a general setting…

$K$-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of $K$-NN, learning an appropriate distance metric…

We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…