The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the GA is obtained in closed form. In this case, sensitivity is the performance difference with respect to an arbitrary alternative algorithm. This description enables the development of explicit expressions involving the training errors and test errors of GAs trained with different datasets. Using these tools, dataset aggregation is studied and different figures of merit to evaluate the generalization capabilities of GAs are introduced. For particular sizes of such datasets and parameters of the GAs, a connection between Jeffrey's divergence, training and test errors is established.

翻译：本文从解析角度刻画了吉布斯算法（GA）对训练数据的依赖性。通过采用期望经验风险作为性能度量指标，得到了GA灵敏度的闭式表达式。在此情况下，灵敏度是指相对于任意备选算法的性能差异。该描述使得能够推导出基于不同数据集训练的GA的训练误差与测试误差的显式表达式。利用这些工具，研究了数据集聚合问题，并引入了用于评估GA泛化能力的多种品质因数。针对特定规模的数据集及GA参数，建立了杰弗里斯散度、训练误差与测试误差之间的关联。