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.

本文探讨了分布鲁棒的怀疑推断在多标签问题中的应用，特别是在 Hamming 损失方面，表明我们的方法可以在某些情况下提供有用的推断，并证明在处理不完整信息时比其它方法更优。

在具有概率集合的多标签问题中进行怀疑二元推断

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

The goal in extreme multi-label classification is to learn a classifier which
can assign a small subset of relevant labels to an instance from an extremely
large set of target labels. Datasets in extreme classification exhibit a long
tail of labels which have small number of positive training instances. In this
work, we pose the learning task in extreme classification with large number of
tail-labels as learning in the presence of adversarial perturbations. This view
motivates a robust optimization framework and equivalence to a corresponding
regularized objective.
Under the proposed robustness framework, we demonstrate efficacy of Hamming
loss for tail-label detection in extreme classification. The equivalent
regularized objective, in combination with proximal gradient based
optimization, performs better than state-of-the-art methods on propensity
scored versions of precision@k and nDCG@k(upto 20% relative improvement over
PFastreXML - a leading tree-based approach and 60% relative improvement over
SLEEC - a leading label-embedding approach). Furthermore, we also highlight the
sub-optimality of a sparse solver in a widely used package for large-scale
linear classification, which is interesting in its own right. We also
investigate the spectral properties of label graphs for providing novel
insights towards understanding the conditions governing the performance of
Hamming loss based one-vs-rest scheme vis-\`a-vis label embedding methods.

本文探讨了在存在对抗扰动的情况下的极端分类中的学习任务，并提出了一种鲁棒优化框架和相应的正则化目标，发现 Hamming 损失可作为尾标签检测的有效方法。通过结合正则化目标和基于 Proximal 梯度的优化方法，相对于 PFastreXML 和 SLEEC 等现有方法在 precision@k 和 nDCG@k 上提供了优异的性能。同时，我们还研究了标签图的谱特性，提供了新的洞察力以了解 Hamming 损失的一对多方法和标签嵌入方法之间性能的条件限制。