Related papers: Improvements on the k-center problem for uncertain…
In this work, we study a range of constrained versions of the $k$-supplier and $k$-center problems such as: capacitated, fault-tolerant, fair, etc. These problems fall under a broad framework of constrained clustering. A unified framework…
In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…
For a set $Q$ of points in the plane and a real number $\delta \ge 0$, let $\mathbb{G}_\delta(Q)$ be the graph defined on $Q$ by connecting each pair of points at distance at most $\delta$. We consider the connectivity of…
Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…
Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…
While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to the same degree. Uncertainty methods are designed to provide…
We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as…
Given a simple polygon $P$ and a set $Q$ of points contained in $P$, we consider the geodesic $k$-center problem where we want to find $k$ points, called \emph{centers}, in $P$ to minimize the maximum geodesic distance of any point of $Q$…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Let $P$ be a set of points in some metric space. The approximate furthest neighbor problem is, given a second point set $C,$ to find a point $p \in P$ that is a $(1+\epsilon)$ approximate furthest neighbor from $C.$ The dynamic version is…
The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…
Over the last few years Explainable Clustering has gathered a lot of attention. Dasgupta et al. [ICML'20] initiated the study of explainable $k$-means and $k$-median clustering problems where the explanation is captured by a threshold…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems. Instead of allowing all possible second-stage decisions, the k-adaptability…
We study the minimum weight basis problem on matroid when elements' weights are uncertain. For each element we only know a set of possible values (an uncertainty area) that contains its real weight. In some cases there exist bases that are…
This paper introduces a scalable approach for probabilistic top-k similarity ranking on uncertain vector data. Each uncertain object is represented by a set of vector instances that are assumed to be mutually-exclusive. The objective is to…