We propose a novel computationally low-cost method for estimating the predictive risks of Bayesian methods for arbitrary loss functions. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin generalization errors. We present theoretical guarantees of the proposed method, clarifying the connection between the widely applicable information criterion, the Bayesian sensitivity analysis, and the infinitesimal jackknife approximation of Bayesian leave-one-out cross validation. An application to differentially-private learning is also discussed.

翻译：我们提出了一个新的低成本计算方法,用于估算贝叶斯人任意损失功能方法的预测风险。拟议方法使用后置变量,并提供了Gibbs和插件概括错误的估算数据。我们为拟议方法提供了理论保障,澄清了广泛适用的信息标准、贝叶斯敏感度分析与巴伊西亚人放假一出交叉验证的无限粗略乳酪近似值之间的联系。还讨论了对差别化私人学习的应用。