标题： 具有概率集合的多标签问题中的怀疑二元推理 显示英文标题

标题： Skeptical binary inferences in multi-label problems with sets of probabilities

摘要： 本文中，我们研究了针对多标签问题进行分布鲁棒且持怀疑态度的推理问题，或者更一般地，针对布尔向量的问题。 所谓分布鲁棒，我们的意思是考虑一组可能的概率分布；而所谓持怀疑态度，我们的理解是只考虑在这个集合内对每种分布都成立的推理。 只要所考虑的集合足够大，这样的推理将提供部分预测。 我们特别研究了汉明损失（Hamming loss）的情况，这是多标签问题中的常见损失函数，展示了在这种情况下如何进行持怀疑态度的推理。 我们的实验结果分为三个部分： (1) 第一部分通过合成数据集表明了我们理论结果所带来的计算收益； (2) 第二部分表明我们的方法在那些难以预测的实例上产生了相关的谨慎性，而其精确对应的方法在此失败； (3) 最后一部分通过实验证明了我们的方法在处理不完美信息（由降采样程序生成）方面比部分弃权[31]和拒绝规则表现得更好。 显示英文摘要

摘要： In this paper, we consider the problem of making distributionally robust, skeptical inferences for the multi-label problem, or more generally for Boolean vectors. By distributionally robust, we mean that we consider a set of possible probability distributions, and by skeptical we understand that we consider as valid only those inferences that are true for every distribution within this set. Such inferences will provide partial predictions whenever the considered set is sufficiently big. We study in particular the Hamming loss case, a common loss function in multi-label problems, showing how skeptical inferences can be made in this setting. Our experimental results are organised in three sections; (1) the first one indicates the gain computational obtained from our theoretical results by using synthetical data sets, (2) the second one indicates that our approaches produce relevant cautiousness on those hard-to-predict instances where its precise counterpart fails, and (3) the last one demonstrates experimentally how our approach copes with imperfect information (generated by a downsampling procedure) better than the partial abstention [31] and the rejection rules.