Department of Computer Science（计算机科学系）；George Washington University（乔治华盛顿大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Department of Electrical and Computer Engineering（电气与计算机工程系）；Princeton University（普林斯顿大学）
Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$. We establish that $RW_p$ defines a valid metric and demonstrate that this type of metric is more intrinsic than the classical Wasserstein distance. A bi-level algorithm is designed to compute the general $RW_p$ distance between arbitrary discrete distributions. Moreover, when $p = 2$, we show that the optimal coupling matrix is invariant under distributional translation in the discrete setting, and we further propose two algorithms, the $\mathrm{RW}_2$-LP algorithm and the $\mathrm{RW}_2$-Sinkhorn algorithm, to improve the numerical stability of computing $W_2$ distance and the optimal coupling matrix solutions. Finally, we conduct three experiments to validate our theoretical results and algorithms. The first two experiments report that the $\mathrm{RW}_2$-LP algorithm and the $\mathrm{RW}_2$-Sinkhorn algorithm, both with and without normalization, can significantly reduce the numerical errors compared to standard algorithms. The third experiment shows that $RW_p$ algorithms are computationally scalable and applicable to the retrieval of similar thunderstorm patterns in practical applications.
Relative Wasserstein Angle and the Problem of the $W_2$-Nearest Gaussian Distribution
Department of Computer Science, George Washington University, Washington D.C., USA（计算机科学系，乔治·华盛顿大学，华盛顿特区，美国）；MAE, George Washington University, Washington D.C., USA（机械工程与应用科学系，乔治·华盛顿大学，华盛顿特区，美国）
Linear convergence of proximal descent schemes on the Wasserstein space
Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan（日本东京RIKEN先进智能研究中心）；School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK（赫瑞-瓦特大学数学与计算机科学学院）；Maxwell Institute for Mathematical Sciences, Edinburgh, UK（爱丁堡数学科学麦克斯韦研究所）；School of Mathematics, University of Edinburgh, UK（爱丁堡大学数学学院）；School of Mathematics, University of Edinburgh, UK, The Alan Turing Institute, UK（爱丁堡大学数学学院、英国艾伦·图灵研究所）
SWIFT: Scalable Wasserstein Factorization for Sparse Nonnegative Tensors
Georgia Institute of Technology（佐治亚理工学院）；Hong Kong Baptist University（香港浸会大学）；Sutter Health（萨特健康医疗集团）；IQVIA（艾昆纬公司）；Emory University（埃默里大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Hidden States Know Where Reasoning Diverges: Credit Assignment via Span-Level Wasserstein Distance
Beijing University of Posts and Telecommunications（北京邮电大学）；Meituan（美团）；Tianjin University（天津大学）；Renmin University of China（中国人民大学）；The University of Melbourne（墨尔本大学）；University of International Business and Economics（国际经贸大学）
Fused Gromov-Wasserstein Distance with Feature Selection
School of Data Science and Society（数据科学与社会学院）；Division of Computational Social Science（计算社会科学系）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Courant Institute（Courant研究所）；Department of Mathematics（数学系）；New York University（纽约大学）；Duke University（杜克大学）
