This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. In this work, we examine the classification task with limited observations during the decision-making phase, which requires a non-asymptotic performance analysis. We establish a condition for consistent training and derive an upper bound on the probability of error for classification. The results clarify the dependence on the statistical properties of the data and the combination policy used over the graph. They also establish the exponential decay of the probability of error with respect to the number of unlabeled samples.

翻译：本文研究了社会机器学习框架下的错误概率，该框架包含独立的训练阶段和基于图结构的协同决策阶段。该框架旨在以分布式方式对未标记数据流进行分类。本研究针对决策阶段观测数据有限条件下的分类任务，这需要进行非渐近性能分析。我们建立了训练一致性的条件，并推导出分类错误概率的上界。研究结果明确了错误概率对数据统计特性及图结构上组合策略的依赖关系，同时证明了错误概率随未标记样本数量呈指数衰减的特性。