Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the validity of the conventional Bayesian update. We present a scalable Bayesian nonparametric learning routine that enables posterior sampling through the optimization of suitably randomized objective functions. A Dirichlet process prior on the unknown data distribution accounts for model misspecification, and admits an embarrassingly parallel posterior bootstrap algorithm that generates independent and exact samples from the nonparametric posterior distribution. Our method is particularly adept at sampling from multimodal posterior distributions via a random restart mechanism. We demonstrate our method on Gaussian mixture model and sparse logistic regression examples.

本文提出了一种可扩展的贝叶斯非参数学习方法，通过优化适当随机化的目标函数实现后验抽样，一个未知数据分布的狄利克雷过程先验考虑到了模型建立错误，并允许具有尴尬并行事后自举算法的非参数后验分布的独立和精确的样本生成，从而特别擅长从多峰后验分布中抽样。

使用后验自助法从多模式后验中进行可伸缩的非参数采样