Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a network. Agents iteratively form and communicate beliefs about an unknown state of the world with their neighbors using a learning rule. Existing approaches assume agents have access to precise statistical models (in the form of likelihoods) for the state of the world. However, in many situations, such models must be learned from finite data. We propose a social learning rule that takes into account uncertainty in the statistical models using second-order probabilities. Therefore, beliefs derived from uncertain models are sensitive to the amount of past evidence collected for each hypothesis. These beliefs characterize whether or not the hypotheses are consistent with the true state of the world. We explicitly show the dependency of the generated beliefs with respect to the amount of prior evidence. Furthermore, as the amount of prior evidence goes to infinity, learning occurs and is consistent with traditional social learning theory.

中文翻译：

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具有不确定模型的非贝叶斯社会学习

非贝叶斯社会学习理论提供了一个框架，该框架为一组通过网络交互的代理建模分布式推理。代理使用学习规则与邻居迭代地形成和传达关于世界未知状态的信念。现有方法假设代理可以访问世界状态的精确统计模型（以可能性的形式）。但是，在许多情况下，此类模型必须从有限数据中学习。我们提出了一种社会学习规则，该规则使用二阶概率将统计模型中的不确定性考虑在内。因此，来自不确定模型的信念对为每个假设收​​集的过去证据的数量很敏感。这些信念表征了假设是否与世界的真实状态一致。我们明确地展示了生成的信念对先验证据数量的依赖性。此外，随着先前证据的数量趋于无穷，学习就会发生，并且与传统的社会学习理论是一致的。