相关论文: A Lottery Model for Center-type Problems With Outl…

Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…

We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound…

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…

Real-world datasets often contain outliers, and the presence of outliers can make the clustering problems to be much more challenging. In this paper, we propose a simple uniform sampling framework for solving three representative…

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

We study the probability distribution of the area and the number of vertices of random polygons in a convex set $K\subset\mathbb{R}^2$. The novel aspect of our approach is that it yields uniform estimates for all convex sets…

We study the problem of fairness in k-centers clustering on data with disjoint demographic groups. Specifically, this work proposes a variant of fairness which restricts each group's number of centers with both a lower bound…

We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the "random assignment" model where the weights are assigned randomly to…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

We consider online convex optimization when a number k of data points are outliers that may be corrupted. We model this by introducing the notion of robust regret, which measures the regret only on rounds that are not outliers. The aim for…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

We study the problem of fair $k$-median where each cluster is required to have a fair representation of individuals from different groups. In the fair representation $k$-median problem, we are given a set of points $X$ in a metric space.…

The Josephus problem is a well--studied elimination problem consisting in determining the position of the survivor after repeated applications of a deterministic rule removing one person at a time from a given group. A natural probabilistic…

The neighbor-based method has become a powerful tool to handle the outlier detection problem, which aims to infer the abnormal degree of the sample based on the compactness of the sample and its neighbors. However, the existing methods…

In this paper we consider two metric covering/clustering problems - \textit{Minimum Cost Covering Problem} (MCC) and $k$-clustering. In the MCC problem, we are given two point sets $X$ (clients) and $Y$ (servers), and a metric on $X \cup…

Outlier detection is a core task in data mining with a plethora of algorithms that have enjoyed wide scale usage. Existing algorithms are primarily focused on detection, that is the identification of outliers in a given dataset. In this…

At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific…

We consider clustering in the perturbation resilience model that has been studied since the work of Bilu and Linial [ICS, 2010] and Awasthi, Blum and Sheffet [Inf. Proc. Lett., 2012]. A clustering instance $I$ is said to be…

In this paper, we present a framework to design approximation algorithms for capacitated facility location problems with penalties/outliers using LP-rounding. Primal-dual technique, which has been particularly successful in dealing with…