Bayesian methods are appealing in their flexibility in modeling complex data and their ability to capture uncertainty in parameters. However, when Bayes' rule does not result in closed-form, most approximate Bayesian inference algorithms lacks either scalability or rigorous guarantees. To tackle this challenge, we propose a scalable yet simple algorithm, Particle Mirror Descent (PMD), to iteratively approximate the posterior density. PMD is inspired by stochastic functional mirror descent where one descends in the density space using a small batch of data points at each iteration, and by particle filtering where one uses samples to approximate a function. We prove result of the first kind that, after $T$ iterations, PMD provides a posterior density estimator that converges in terms of $KL$-divergence to the true posterior in rate $O(1/\sqrt{T})$. We show that PMD is competitive to several scalable Bayesian algorithms in mixture models, Bayesian logistic regression, sparse Gaussian processes and latent Dirichlet allocation.

提出一种名为 Particle Mirror Descent 的算法，可以在处理复杂数据时应用于贝叶斯方法的后验密度概率估计。该算法具有可证明的鲁棒性，可在推断贝叶斯后验分布时用于大规模数据集中。

基于粒子镜面下降的可证明贝叶斯推断