Robust and Scalable Bayes via a Median of Subset Posterior Measures
Robust and Scalable Bayes via a Median of Subset Posterior Measures
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发表时间：
2014-03
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通讯作者：
Stanislav Minsker;Sanvesh Srivastava;Lizhen Lin;D. Dunson
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作者：
Stanislav Minsker;Sanvesh Srivastava;Lizhen Lin;D. Dunson
我们提出了一种新的贝叶斯分析方法，该方法对数据中的异常值具有可证明的健壮性，并且通常比标准方法具有计算优势。我们的技术是基于将数据分成不重叠的子组，评估给定每个独立子组的后验分布，然后合并所产生的测量。我们方法的主要创新点是提出的聚合步骤，它基于对概率度量空间中的中位数的评估，该空间配备了一组合适的距离，可以在实践中快速有效地评估。我们给出了理论和数值证据来说明我们的方法所取得的改进。
We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups, evaluating the posterior distribution given each independent subgroup, and then combining the resulting measures. The main novelty of our approach is the proposed aggregation step, which is based on the evaluation of a median in the space of probability measures equipped with a suitable collection of distances that can be quickly and efficiently evaluated in practice. We present both theoretical and numerical evidence illustrating the improvements achieved by our method.