Partial Label Learning (PLL) is a typical weakly supervised learning task, which assumes each training instance is annotated with a set of candidate labels containing the ground-truth label. Recent PLL methods adopt identification-based disambiguation to alleviate the influence of false positive labels and achieve promising performance. However, they require all classes in the test set to have appeared in the training set, ignoring the fact that new classes will keep emerging in real applications. To address this issue, in this paper, we focus on the problem of Partial Label Learning with Augmented Class (PLLAC), where one or more augmented classes are not visible in the training stage but appear in the inference stage. Specifically, we propose an unbiased risk estimator with theoretical guarantees for PLLAC, which estimates the distribution of augmented classes by differentiating the distribution of known classes from unlabeled data and can be equipped with arbitrary PLL loss functions. Besides, we provide a theoretical analysis of the estimation error bound of the estimator, which guarantees the convergence of the empirical risk minimizer to the true risk minimizer as the number of training data tends to infinity. Furthermore, we add a risk-penalty regularization term in the optimization objective to alleviate the influence of the over-fitting issue caused by negative empirical risk. Extensive experiments on benchmark, UCI and real-world datasets demonstrate the effectiveness of the proposed approach.
Augmented Functional Random Forests: Classifier Construction and Unbiased Functional Principal Components Importance through Ad-Hoc Conditional Permutations
Faculty of Technological and Innovation Sciences（技术与创新科学学院）；Faculty of Economics and Law（经济与法学院）
Minkowski tensors for point clouds and voxelized data: robust, asymptotically unbiased estimators
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；German Aerospace Center (DLR)（德国航空航天中心）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Friedrich Alexander University Erlangen-Nuremberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
Unbiased estimators for the variance of MMD estimators
最大平均差异（MMD）是在许多应用中有用的概率分布之间的基于核的距离（Gretton et al. 2012），具有令人满意的计算和统计特性的简单估计量。能够有效地估计该估计量的方差，对解决双样本检验中的各种问题都有很大的帮助。为此，Bounliphone等人。（2016）使用U-统计量理论来推导MMD估计量方差的估计量，以及两个这样的估计量之间的差异。然而，他们的估计器丢弃了低阶项，并且不必要地存在偏差。我们在这篇笔记中表明-扩展和纠正Sutherland等人的工作。（2017）-我们可以找到一个真正的无偏估计量，用于平方MMD估计量和两个相关平方MMD估计量之差的实际方差，基本上没有额外的计算成本。
Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions
Department of Statistics and Operations Research（统计与运筹学系）；The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Hanes Hall, UNC-Chapel Hill, NC 27599-3260（UNC-教堂山分校318号哈尼斯楼，NC 27599-3260）
A Generalized Unbiased Risk Estimator for Learning with Augmented Classes
Chongqing University（重庆大学）；University of Electronic Science and Technology of China（电子科技大学）；Zhejiang University（浙江大学）；Nanyang Technological University（南洋理工大学）
Flow Perturbation++: Multi-Step Unbiased Jacobian Estimation for High-Dimensional Boltzmann Sampling
State Key Laboratory of Information Photonics（信息光子学与光通信国家重点实验室）；Optical Communications, Beijing University of Posts（光通信，北京邮电大学）；School of Physical Science（物理科学学院）；Technology, Beijing University of Posts（技术学院，北京邮电大学）
