From Proper Scoring Rules to Max-Min Optimal Forecast Aggregation
From Proper Scoring Rules to Max-Min Optimal Forecast Aggregation
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从适当的评分规则到最大-最小最优预测聚合
DOI：
10.1145/3465456.3467599
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Roughgarden, Tim
中科院分区：
文献类型：
--
作者：
Neyman, Eric;Roughgarden, Tim
本文在两个看似不相关的预测问题之间建立了很强的联系：激励相容预测启发和预测聚合。正确的计分规则是解决前一个问题的众所周知的办法。对于每个这样的规则，我们将相应的聚合方法关联起来，将专家预测和专家权重映射到“共识预测”，我们称之为相对于s的准算术(QA)池。我们用几种方式证明这种对应关系的合理性：关于两个研究最充分的评分规则(二次和对数)的QA池对应于两个研究最充分的预测聚合方法(线性和对数)；给定用于付款的评分规则，转包几个专家，根据他们的权重按比例支付他们的预测代理，最好使用相对于S的QA池来聚合专家的报告，这意味着这种策略最大化了其最坏情况下的利润(超过可能的结果)；使用QA池的聚集者的得分在专家权重中是凹陷的(因此，可以使用在线梯度下降来从重复实验中学习合适的专家权重，并且遗憾程度较低)；所有QA合并方法的类都具有一套自然的公理(推广了柯尔莫戈洛夫关于准算术平均的经典工作)。来源：这项工作得到了计算和通信基础部门[GRANT CCF-1813188]、陆军研究办公室[GRANT W911NF1910294]和研究生教育部门[GRANT DGE-2036197]的支持。补充材料：电子伴侣可在https://doi.org/10.1287/opre.2022.2414.上获得
This paper forges a strong connection between two seemingly unrelated forecasting problems: incentive-compatible forecast elicitation and forecast aggregation. Proper scoring rules are the well-known solution to the former problem. To each such rules, we associate a corresponding method of aggregation, mapping expert forecasts and expert weights to a “consensus forecast,” which we callquasi-arithmetic (QA) poolingwith respect tos. We justify this correspondence in several ways: QA pooling with respect to the two most well-studied scoring rules (quadratic and logarithmic) corresponds to the two most well-studied forecast aggregation methods (linear and logarithmic); given a scoring rulesused for payment, a forecaster agent who subcontracts several experts, paying them in proportion to their weights, is best off aggregating the experts’ reports using QA pooling with respect tos, meaning this strategy maximizes its worst-case profit (over the possible outcomes); the score of an aggregator who uses QA pooling is concave in the experts’ weights (as a consequence, online gradient descent can be used to learn appropriate expert weights from repeated experiments with low regret); and the class of all QA pooling methods is characterized by a natural set of axioms (generalizing classical work by Kolmogorov on quasi-arithmetic means).Funding:This work was supported by the Division of Computing and Communication Foundations [Grant CCF-1813188], the Army Research Office [Grant W911NF1910294], and the Division of Graduate Education [Grant DGE-2036197].Supplemental Material:The e-companion is available at https://doi.org/10.1287/opre.2022.2414.
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DOI：
10.1145/1386790.1386813
发表时间：
2008-07
期刊：
--
影响因子：
--
作者：
Nicolas S. Lambert;David M. Pennock;Y. Shoham
通讯作者：
Nicolas S. Lambert;David M. Pennock;Y. Shoham
影响因子：
5.9
作者：
Hanson, R
通讯作者：
Hanson, R
扩展实数的线性函数
DOI：
--
发表时间：
2021
期刊：
arXiv.org
影响因子：
--
作者：
Bo Waggoner
通讯作者：
Bo Waggoner
基于广义brier评分的最优概率聚合
影响因子：
1.2
作者：
Christian J. Feldbacher;G. Schurz
通讯作者：
G. Schurz
平均值。
影响因子：
56.9
作者：
E. Hayes
通讯作者：
E. Hayes