相关论文: Multiclass MinMax Rank Aggregation

We propose an adaptive proximal gradient method for minimizing the sum of two functions, where one is a simple convex function, and the other belongs to one of the three classes: nonconvex smooth, convex nonsmooth, or convex smooth. The key…

Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified value. This generalizes the problem of finding a nearest…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…

We introduce a lower bounding technique for the min max correlation clustering problem and, based on this technique, a combinatorial 4-approximation algorithm for complete graphs. This improves upon the previous best known approximation…

We consider the rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the…

We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases.…

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Fine-tuning large language models requires high computational and memory resources, and is therefore associated with significant costs. When training on federated datasets, an increased communication effort is also needed. For this reason,…

We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…

This paper considers the optimization problem in the form of $\min_{X \in \mathcal{F}_v} f(x) + \lambda \|X\|_1,$ where $f$ is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X^T X = I_q, v \in \mathrm{span}(X)\}$, and $v$ is a…

An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…

We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…

We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

This paper addresses the problem of rank aggregation, which aims to find a consensus ranking among multiple ranking inputs. Traditional rank aggregation methods are deterministic, and can be categorized into explicit and implicit methods…

MSmix is a recently developed R package implementing maximum likelihood estimation of finite mixtures of Mallows models with Spearman distance for full and partial rankings. The package is designed to implement computationally tractable…

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…

In this paper, we consider the problem of finding a minimum common partition of two strings. The problem has its application in genome comparison. As it is an NP-hard, discrete combinatorial optimization problem, we employ a metaheuristic…

In this paper, we address the top-$K$ ranking problem with a monotone adversary. We consider the scenario where a comparison graph is randomly generated and the adversary is allowed to add arbitrary edges. The statistician's goal is then to…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…