Scalable and Robust Bayesian Inference via the Median Posterior
Scalable and Robust Bayesian Inference via the Median Posterior
复制标题
DOI：
--
复制
发表时间：
2014-06
期刊：
影响因子：
--
通讯作者：
Stanislav Minsker;Sanvesh Srivastava;Lizhen Lin;D. Dunson
中科院分区：
文献类型：
--
作者：
Stanislav Minsker;Sanvesh Srivastava;Lizhen Lin;D. Dunson
许多针对海量数据的贝叶斯学习方法受益于处理小观察子集。特别是，通过随机近似在可扩展贝叶斯学习方面取得了重大进展。然而，分布式计算环境中的贝叶斯学习方法通常是特定于问题或分布的，并且使用临时技术。我们提出了一种新颖的贝叶斯推理通用方法，该方法可扩展且对数据损坏具有鲁棒性。我们的技术基于以下思想：将数据分成几个不重叠的子组，评估给定每个独立子组的后验分布，然后组合结果。我们的主要贡献是提出的聚合步骤，该步骤基于查找子集后验分布的几何中值。提出的理论和数值结果证实了我们方法的优势。
Many Bayesian learning methods for massive data benefit from working with small subsets of observations. In particular, significant progress has been made in scalable Bayesian learning via stochastic approximation. However, Bayesian learning methods in distributed computing environments are often problem- or distributionspecific and use ad hoc techniques. We propose a novel general approach to Bayesian inference that is scalable and robust to corruption in the data. Our technique is based on the idea of splitting the data into several non-overlapping subgroups, evaluating the posterior distribution given each independent subgroup, and then combining the results. Our main contribution is the proposed aggregation step which is based on finding the geometric median of subset posterior distributions. Presented theoretical and numerical results confirm the advantages of our approach.