We present a general, efficient technique for providing contextual
predictions that are "multivalid" in various senses, against an online sequence
of adversarially chosen examples $(x,y)$. This means that the resulting
estimates correctly predict various statistics of the labels $y$ not just
marginally -- as averaged over the sequence of examples -- but also
conditionally on $x \in G$ for any $G$ belonging to an arbitrary intersecting
collection of groups $\mathcal{G}$.
We provide three instantiations of this framework. The first is mean
prediction, which corresponds to an online algorithm satisfying the notion of
multicalibration from Hebert-Johnson et al. The second is variance and higher
moment prediction, which corresponds to an online algorithm satisfying the
notion of mean-conditioned moment multicalibration from Jung et al. Finally, we
define a new notion of prediction interval multivalidity, and give an algorithm
for finding prediction intervals which satisfy it. Because our algorithms
handle adversarially chosen examples, they can equally well be used to predict
statistics of the residuals of arbitrary point prediction methods, giving rise
to very general techniques for quantifying the uncertainty of predictions of
black box algorithms, even in an online adversarial setting. When instantiated
for prediction intervals, this solves a similar problem as conformal
prediction, but in an adversarial environment and with multivalidity guarantees
stronger than simple marginal coverage guarantees.

提出了一种通用的有效技术，用于提供多值上下文预测，可以针对在线选择的对手样例 $(x,y)$ 在各种意义上提供 ' 多个有效性 '，其中结果估计正确地预测标签 y 的各种统计信息，甚至在线对抗情况下运用此算法也可以给黑盒算法的预测的不确定性提供非常通用的技巧。

在线多值学习：均值、矩和预测区间

Online Multivalid Learning: Means, Moments, and Prediction Intervals

In this paper, we propose Latent Relation Language Models (LRLMs), a class of
language models that parameterizes the joint distribution over the words in a
document and the entities that occur therein via knowledge graph relations.
This model has a number of attractive properties: it not only improves language
modeling performance, but is also able to annotate the posterior probability of
entity spans for a given text through relations. Experiments demonstrate
empirical improvements over both a word-based baseline language model and a
previous approach that incorporates knowledge graph information. Qualitative
analysis further demonstrates the proposed model's ability to learn to predict
appropriate relations in context.

提出了一种基于知识图谱关系的潜在关系语言模型 (Latent Relation Language Models, LRLMs), 该模型不仅能提高语言建模性能，还能添加实体跨度的后验概率，实验结果表明该模型的性能优于基准模型和之前的知识图谱信息存在的模型，定性分析进一步证明了所提议的模型在上下文中预测适当的关系的能力。