Related papers: Coresets for the Nearest-Neighbor Rule
The nearest-neighbor rule is a well-known classification technique that, given a training set P of labeled points, classifies any unlabeled query point with the label of its closest point in P. The nearest-neighbor condensation problem aims…
In nearest-neighbor classification, a training set $P$ of points in $\mathbb{R}^d$ with given classification is used to classify every point in $\mathbb{R}^d$: Every point gets the same classification as its nearest neighbor in $P$.…
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…
Let $\mathcal{P}$ be a simple polygon with $m$ vertices and let $P$ be a set of $n$ points inside $\mathcal{P}$. We prove that there exists, for any $\varepsilon>0$, a set $\mathcal{C} \subset P$ of size $O(1/\varepsilon^2)$ such that the…
Coreset selection is powerful in reducing computational costs and accelerating data processing for deep learning algorithms. It strives to identify a small subset from large-scale data, so that training only on the subset practically…
A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to…
The problem of nearest neighbor condensing has enjoyed a long history of study, both in its theoretical and practical aspects. In this paper, we introduce the problem of weighted distance nearest neighbor condensing, where one assigns…
A furthest neighbor data structure on a metric space $(V,\mathrm{dist})$ and a set $P \subseteq V$ answers the following query: given $v \in V$, output $p \in P$ maximizing $\mathrm{dist}(v,p)$; in the approximate version, it is allowed to…
Given a training set $P \subset \mathbb{R}^d$, the nearest-neighbor classifier assigns any query point $q \in \mathbb{R}^d$ to the class of its closest point in $P$. To answer these classification queries, some training points are more…
A critical piece of the modern information retrieval puzzle is approximate nearest neighbor search. Its objective is to return a set of $k$ data points that are closest to a query point, with its accuracy measured by the proportion of exact…
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…
The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X,D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).…
A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems…
A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a…
In nearest-neighbor classification problems, a set of $d$-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the same classification as the nearest…
Developing increasingly efficient and accurate algorithms for approximate nearest neighbor search is a paramount goal in modern information retrieval. A primary approach to addressing this question is clustering, which involves partitioning…
In this study, we present a novel ranking model based on learning neighborhood relationships embedded in the index space. Given a query point, conventional approximate nearest neighbor search calculates the distances to the cluster…
A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as…
$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…
Safe deployment of deep neural networks in high-stake real-world applications requires theoretically sound uncertainty quantification. Conformal prediction (CP) is a principled framework for uncertainty quantification of deep models in the…