Related papers: Query Complexity of k-NN based Mode Estimation
We consider the problem of finding stationary points in Bilevel optimization when the lower-level problem is unconstrained and strongly convex. The problem has been extensively studied in recent years; the main technical challenge is to…
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…
Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has…
Traditional route planning and k nearest neighbors queries only consider distance or travel time and ignore road safety altogether. However, many travellers prefer to avoid risky or unpleasant road conditions such as roads with high crime…
We consider a rank regression setting, in which a dataset of $N$ samples with features in $\mathbb{R}^d$ is ranked by an oracle via $M$ pairwise comparisons. Specifically, there exists a latent total ordering of the samples; when presented…
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…
Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
We consider the problem of estimating the mean of a distribution supported by the $k$-dimensional probability simplex in the setting where an $\varepsilon$ fraction of observations are subject to adversarial corruption. A simple particular…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
This paper studies the sample complexity (aka number of comparisons) bounds for the active best-$k$ items selection from pairwise comparisons. From a given set of items, the learner can make pairwise comparisons on every pair of items, and…
We connect the problem of properly PAC learning decision trees to the parameterized Nearest Codeword Problem ($k$-NCP). Despite significant effort by the respective communities, algorithmic progress on both problems has been stuck: the…
We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural…
Despite their unprecedented performance in various domains, utilization of Deep Neural Networks (DNNs) in safety-critical environments is severely limited in the presence of even small adversarial perturbations. The present work develops a…
Nearest neighbor (NN) problem is an important scientific problem. The NN query, to find the closest one to a given query point among a set of points, is widely used in applications such as density estimation, pattern classification,…
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…
As from time to time it is impractical to ask agents to provide linear orders over all alternatives, for these partial rankings it is necessary to conduct preference completion. Specifically, the personalized preference of each agent over…
This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…
Machine learning models deployed in the wild can be challenged by out-of-distribution (OOD) data from unknown classes. Recent advances in OOD detection rely on distance measures to distinguish samples that are relatively far away from the…
In this paper, we propose an ensemble learning algorithm named \textit{bagged $k$-distance for mode-based clustering} (\textit{BDMBC}) by putting forward a new measurement called the \textit{probability of localized level sets}…