Related papers: An adaptive nearest neighbor rule for classificati…
The Lopsided Lov\'{a}sz Local Lemma (LLLL) is a powerful probabilistic principle which has been used in a variety of combinatorial constructions. While originally a general statement about probability spaces, it has recently been…
The problem of relevance ranking consists of sorting a set of objects with respect to a given criterion. Since users may prefer different relevance criteria, the ranking algorithms should be adaptable to the user needs. Two main approaches…
We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable…
We study sequential decision-making in batched nonparametric contextual bandits, where actions are selected over a finite horizon divided into a small number of batches. Motivated by constraints in domains such as medicine and marketing --…
Interpretability techniques in NLP have mainly focused on understanding individual predictions using attention visualization or gradient-based saliency maps over tokens. We propose using k nearest neighbor (kNN) representations to identify…
Suppose that we wish to estimate a vector $\mathbf{x}$ from a set of binary paired comparisons of the form "$\mathbf{x}$ is closer to $\mathbf{p}$ than to $\mathbf{q}$" for various choices of vectors $\mathbf{p}$ and $\mathbf{q}$. The…
We study universal consistency and convergence rates of simple nearest-neighbor prototype rules for the problem of multiclass classification in metric paces. We first show that a novel data-dependent partitioning rule, named Proto-NN, is…
One of the simplest and most effective classical machine learning algorithms is the $k$-nearest neighbors algorithm ($k$NN) which classifies an unknown test state by finding the $k$ nearest neighbors from a set of $M$ train states. Here we…
Using prototype methods to reduce the size of training datasets can drastically reduce the computational cost of classification with instance-based learning algorithms like the k-Nearest Neighbour classifier. The number and distribution of…
Information-theoretic quantities, such as conditional entropy and mutual information, are critical data summaries for quantifying uncertainty. Current widely used approaches for computing such quantities rely on nearest neighbor methods and…
We show that for every $k\in\mathbb{N}$ and $\varepsilon>0$, for large enough alphabet $R$, given a $k$-CSP with alphabet size $R$, it is NP-hard to distinguish between the case that there is an assignment satisfying at least…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph…
Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…
Abstract We present PAC-Bayesian bounds for the generalisation error of the K-nearest-neighbour classifier (K-NN). This is achieved by casting the K-NN classifier into a kernel space framework in the limit of vanishing kernel bandwidth. We…
We examine the Bayes-consistency of a recently proposed 1-nearest-neighbor-based multiclass learning algorithm. This algorithm is derived from sample compression bounds and enjoys the statistical advantages of tight, fully empirical…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
We construct a hybrid quantum-classical approach for the $K$-Nearest Neighbour algorithm, where the information is embedded in a phase-distributed multimode coherent state with the assistance of a single photon. The task of finding the…
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One…
Ensembles based on k nearest neighbours (kNN) combine a large number of base learners, each constructed on a sample taken from a given training data. Typical kNN based ensembles determine the k closest observations in the training data…