论文标题
使用经验贝叶斯神经网络的非参数回归的不确定性定量
Uncertainty Quantification for nonparametric regression using Empirical Bayesian neural networks
论文作者
论文摘要
我们为神经网络的方法提出了一种新的两步经验贝叶斯型。我们在非参数回归模型的上下文中表明，该过程（最多达到对数因素）提供了感兴趣的基础功能参数的最佳恢复，并提供了贝叶斯可信集，并具有频繁的覆盖范围保证。该方法只需要拟合一次神经网络一次，因此它比引导类型方法要快得多。我们证明了我们的方法对合成数据的适用性，观察良好的估计属性和可靠的不确定性定量。
We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional parameter of interest and provides Bayesian credible sets with frequentist coverage guarantees. The approach requires fitting the neural network only once, hence it is substantially faster than Bootstrapping type approaches. We demonstrate the applicability of our method over synthetic data, observing good estimation properties and reliable uncertainty quantification.
