Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and epistemic uncertainties, which represent the inherent randomness in the data-generating process and the variability due to insufficient data, respectively. They analyzed those uncertainties in an information-theoretic way, assuming that the model is well-specified and treating the model's parameters as latent variables. However, the existing information-theoretic analysis of uncertainty cannot explain the widely believed property of uncertainty, known as the sensitivity between the test and training data. It implies that when test data are similar to training data in some sense, the epistemic uncertainty should become small. In this work, we study such uncertainty sensitivity using our novel decomposition method for the predictive uncertainty. Our analysis successfully defines such sensitivity using information-theoretic quantities. Furthermore, we extend the existing analysis of Bayesian meta-learning and show the novel sensitivities among tasks for the first time.

Bayesian inference中的不确定性推断及其分解方法的研究。首次定义了测试数据和训练数据之间的敏感性，并扩展了Bayesian meta-learning的分析。

不确定性中测试数据敏感性的信息论分析