Loss-Based Variational Bayes Prediction

We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach constructs a posterior predictive using a variational approximation to a generalized posterior that is directly focused on predictive accuracy. The theoretical behavior of the new prediction approach is analyzed and a form of optimality demonstrated. Applications to both simulated and empirical data using high-dimensional Bayesian neural network and autoregressive mixture models demonstrate that the approach provides more accurate results than various alternatives, including misspecified likelihood-based predictions. Supplementary materials for this article are available online.

本文提出一种适配高参数模型的贝叶斯预测新方法，该方法对模型误设具有鲁棒性。针对一类高维（但参数化）预测模型，该新方法通过对直接聚焦预测精度的广义后验进行变分近似，构建后验预测分布。本文分析了该新预测方法的理论性质，并证明了其某一形式的最优性。通过将该方法应用于高维贝叶斯神经网络（Bayesian neural network）与自回归混合模型（autoregressive mixture models）的模拟数据与实测数据实验，结果表明该方法相较包括基于误设似然的预测在内的多种对比方法，能够获得更精准的预测结果。本文的补充材料可在线获取。