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This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…

Machine Learning · Statistics 2018-07-17 Arnaud Dessein , Nicolas Papadakis , Jean-Luc Rouas

Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using…

Machine Learning · Statistics 2022-05-27 Aldo Glielmo , Claudio Zeni , Bingqing Cheng , Gabor Csanyi , Alessandro Laio

Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…

Statistics Theory · Mathematics 2025-10-06 Jiaping Yang , Yunxin Zhang

While autonomous agents often surpass humans in their ability to handle vast and complex data, their potential misalignment (i.e., lack of transparency regarding their true objective) has thus far hindered their use in critical applications…

Artificial Intelligence · Computer Science 2024-12-03 Frédéric Berdoz , Roger Wattenhofer

A major challenge to deploying robots widely is navigation in human-populated environments, commonly referred to as social robot navigation. While the field of social navigation has advanced tremendously in recent years, the fair evaluation…

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social…

Physics and Society · Physics 2009-09-10 Petter Holme , Gourab Ghoshal

Deploying robots in human environments requires effective social robot navigation. This article focuses on proxemics, proposing a new taxonomy and suggesting future directions through an analysis of state-of-the-art studies and the…

Robotics · Computer Science 2025-03-20 Ehud Nahum , Yael Edan , Tal Oron-Gilad

We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…

Computer Science and Game Theory · Computer Science 2023-05-18 Piotr Faliszewski , Andrzej Kaczmarczyk , Krzysztof Sornat , Stanisław Szufa , Tomasz Wąs

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…

Logic in Computer Science · Computer Science 2011-07-07 Uli Fahrenberg , Claus Thrane , Kim G. Larsen

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…

Discrete Mathematics · Computer Science 2021-02-18 Ramon Ferrer-i-Cancho , Carlos Gómez-Rodríguez , Juan Luis Esteban

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…

Machine Learning · Computer Science 2020-02-10 David Alvarez-Melis , Nicolò Fusi

We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss…

Optimization and Control · Mathematics 2025-01-30 Man Yiu Tsang , Karmel S. Shehadeh

We present a comprehensive study on discrete morphological symmetries of dynamical systems, which are commonly observed in biological and artificial locomoting systems, such as legged, swimming, and flying animals/robots/virtual characters.…

Robotics · Computer Science 2023-07-27 Daniel Ordonez-Apraez , Mario Martin , Antonio Agudo , Francesc Moreno-Noguer

A crucial privacy-driven issue nowadays is re-identifying anonymized social networks by mapping them to correlated cross-domain auxiliary networks. Prior works are typically based on modeling social networks as random graphs representing…

Social and Information Networks · Computer Science 2017-07-28 Luoyi Fu , Xinzhe Fu , Zhongzhao Hu , Zhiying Xu , Xinbing Wang

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

Optimization and Control · Mathematics 2020-10-23 Luca De Gennaro Aquino , Stephan Eckstein

In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…

Algebraic Geometry · Mathematics 2012-03-13 Lucio Guerra , Gian Pietro Pirola

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an…

Theoretical Economics · Economics 2026-01-14 Arthur Charpentier

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

Social and Information Networks · Computer Science 2014-06-23 Matthieu Roy , Stefan Schmid , Gilles Trédan

Machine learning is increasingly used to inform decision-making in sensitive situations where decisions have consequential effects on individuals' lives. In these settings, in addition to requiring models to be accurate and robust, socially…

Machine Learning · Computer Science 2021-03-02 Amir-Hossein Karimi , Gilles Barthe , Bernhard Schölkopf , Isabel Valera

We investigate the fundamental principles that drive the development of scalable algorithms for network optimization. Despite the significant amount of work on parallel and decentralized algorithms in the optimization community, the methods…

Machine Learning · Statistics 2017-08-15 Patrick Rebeschini , Sekhar Tatikonda
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