Supervised learning aims to train a classifier under the assumption that
training and test data are from the same distribution. To ease the above
assumption, researchers have studied a more realistic setting:
out-of-distribution (OOD) detection, where test data may come from classes that
are unknown during training (i.e., OOD data). Due to the unavailability and
diversity of OOD data, good generalization ability is crucial for effective OOD
detection algorithms, and corresponding learning theory is still an open
problem. To study the generalization of OOD detection, this paper investigates
the probably approximately correct (PAC) learning theory of OOD detection that
fits the commonly used evaluation metrics in the literature. First, we find a
necessary condition for the learnability of OOD detection. Then, using this
condition, we prove several impossibility theorems for the learnability of OOD
detection under some scenarios. Although the impossibility theorems are
frustrating, we find that some conditions of these impossibility theorems may
not hold in some practical scenarios. Based on this observation, we next give
several necessary and sufficient conditions to characterize the learnability of
OOD detection in some practical scenarios. Lastly, we offer theoretical support
for representative OOD detection works based on our OOD theory.

基于 PAC 学习理论，本研究探讨了超出分布检测的可学习性，给出了不同场景下学习 OOD 检测的必要和充分条件，并从理论上支持了一些 OOD 检测方法。

关于外部分布检测的可学习性

On the Learnability of Out-of-distribution Detection

Binarizing belief aggregation addresses how to rationally aggregate
individual probabilistic beliefs into collective binary beliefs. Similar to the
development of judgment aggregation theory, formulating axiomatic requirements,
proving impossibility theorems, and identifying exact agenda conditions of
impossibility theorems are natural and important research topics in binarizing
belief aggregation. Building on our previous research on impossibility
theorems, we use an agenda-theoretic approach to generalize the results and to
determine the necessary and sufficient level of logical interconnection between
the issues in an agenda for the impossibility theorems to arise. We demonstrate
that (1) path-connectedness and even-negatability constitute the exact agenda
condition for the oligarchy result stating that binarizing belief aggregation
satisfying proposition-wise independence and deductive closure of collective
beliefs yields the oligarchies under minor conditions; (2)
negation-connectedness is the condition for the triviality result obtained by
adding anonymity to the oligarchy result; and (3) blockedness is the condition
for the impossibility result, which follows by adding completeness and
consistency of collective beliefs. Moreover, we compare these novel findings
with existing agenda-theoretic characterization theorems in judgment
aggregation and belief binarization.

本文旨在研究如何将单个概率信念合理地聚合为集体二元信念，采用议程理论方法推广了此前的研究成果，得出了使 “寡头统治” 成立的议程条件，还研究了附加了匿名性和完备性一致性后的易证无解和不可避免结果。