适用于一般损失函数的后验协方差信息准则
Posterior covariance information criterion for general loss functions
AI总结：
本文提出利用后验协方差以低成本估计广义贝叶斯推断的一般预测度量，给出 Gibbs 与插件泛化误差估计量、理论保证及多类应用。
摘要：
我们提出了一种新颖且计算成本较低的方法，用于估计广义贝叶斯推断的一般预测度量。所提方法利用后验协方差，并给出 Gibbs 泛化误差和插件泛化误差的估计量。我们给出了该方法的理论保证，阐明了其与贝叶斯敏感性分析以及贝叶斯留一交叉验证的无穷小刀切法近似之间的联系。我们展示了该方法的若干应用，包括差分隐私保护学习、贝叶斯分层建模、存在影响观测值时的贝叶斯回归，以及广泛适用信息准则的偏差缩减。文中还讨论了其在高维情形下的适用性。
英文摘要：
We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin generalisation errors. We present theoretical guarantees of the proposed method, clarifying the connection to the Bayesian sensitivity analysis and the infinitesimal jackknife approximation of Bayesian leave-one-out cross validation. We illustrate several applications of our methods, including applications to differential privacy-preserving learning, the Bayesian hierarchical modeling, the Bayesian regression in the presence of influential observations, and the bias reduction of the widely-applicable information criterion. The applicability in high dimensions is also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
