论文标题
一般损失功能的后协方差信息标准
Posterior covariance information criterion for general loss functions
论文作者
论文摘要
我们提出了一种新颖的计算低成本方法，用于估计广义贝叶斯推断的一般预测度量。所提出的方法利用后协方差，并提供Gibbs和插件通用错误的估计器。我们介绍了所提出的方法的理论保证，阐明了与贝叶斯灵敏度分析的连接以及贝叶斯剩余交叉验证的无限折刀近似。我们说明了我们的方法的几种应用，包括应用于差异性隐私学习的应用，贝叶斯分层建模，在存在影响力观察的情况下的贝叶斯回归以及降低广泛适用的信息标准的偏见。还讨论了高维度的适用性。
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.
