In this paper we combine the theory of probability aggregation with results of machine learning theory concerning the optimality of predictions under expert advice. In probability aggregation theory several characterization results for linear aggregation exist. However, in linear aggregation weights are not fixed, but free parameters. We show how fixing such weights by success-based scores, a generalization of Brier scoring, allows for transferring the mentioned optimality results to the case of probability aggregation.

中文翻译：

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基于广义brier评分的最优概率聚合

在本文中，我们将概率聚合理论与机器学习理论的结果相结合，关于专家建议下预测的最优性。在概率聚集理论中，存在一些线性聚集的表征结果。然而，在线性聚合中，权重不是固定的，而是自由参数。我们展示了如何通过基于成功的分数来固定这些权重，这是 Brier 评分的概括，允许将提到的最优性结果转移到概率聚合的情况下。