We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as clarifying relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate loss bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants. It also suggests new techniques for estimating f-divergences.
Optimal Posteriors for Chi-squared Divergence based PAC-Bayesian Bounds and Comparison with KL-divergence based Optimal Posteriors and Cross-Validation Procedure
Risk Bounds for Mixture Density Estimation on Compact Domains via the $h$-Lifted Kullback--Leibler Divergence
School of Mathematics and Physics（数学与物理学院）；The University of Queensland（昆士兰大学）；Institute of Mathematics for Industry（产业数学研究所）；Kyushu University（九州大学）；School of Computing, Engineering, and Mathematical Sciences（计算、工程与数学科学学院）；La Trobe University（拉筹伯大学）
我们考虑的问题，估计概率密度函数的样本数据的基础上，使用有限的混合密度从一些组件类。为此，我们引入了$h$ -提升Kullback-Leibler（KL）分歧作为标准库尔贝克-莱布勒散度的推广和进行风险最小化的标准。在紧支撑假设下，我们证明了当使用$h$ -提升的库尔贝克-莱布勒散度时，期望估计误差的$\mathcal{O}(1/{\sqrt{n}})$界，推广了Rakhlin等人的结果.（2005年，ESAIM：概率与统计，第9卷）和李和巴伦（1999，Advances in Neural Information ProcessingSystems，Vol.12），以允许不是严格正的密度函数的风险边界。我们开发了一个程序的计算相应的最大$h$ -提升似然估计（$h$ -MLLE）使用的优化最大化框架，并提供实验结果支持我们的理论界。
Probability Link Models with Symmetric Information Divergence
University of Isfahan（伊斯法罕大学）；Institute for Research in Fundamental Sciences（基础科学研究所）；Fox Chase Cancer Center（福克斯·蔡斯癌症中心）；Temple University Health System（天普大学卫生系统）；Northern Illinois University（北伊利诺伊大学）；University of Wisconsin-Milwaukee（威斯康星大学密尔沃基分校）；Temple University（天普大学）
In-Context Learning as Nonparametric Conditional Probability Estimation: Risk Bounds and Optimality
Department of Statistics Beijing Normal University at Zhuhai（北京师范大学珠海分校统计学系）；Department of Statistics and Data Science Hunan University（湖南大学统计学与数据科学系）；School of Science Sun Yat-sen University（中山大学科学学院）
Comparison of static and dynamic random forests models for EHR data in the presence of competing risks: predicting central line-associated bloodstream infection
KU Leuven（鲁汶大学）；University Hospitals Leuven（鲁汶大学医院）；Maastricht University（马斯特里赫特大学）；Leiden University Medical Center（莱顿大学医学中心）
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Institute of Applied and Computational Mathematics（应用与计算数学研究所）；Foundation for Research and Technology - Hellas（希腊研究与技术基金会）；Brown University（布朗大学）
Korteweg-de Vries Institute for Mathematics（科特韦格-德弗里斯数学研究所）；University of Amsterdam（阿姆斯特丹大学）；CAIDAS（卡伊达斯（维尔茨堡大学跨学科人工智能与数据科学中心））；University of Würzburg（维尔茨堡大学）
