Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent
Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent
复制标题
通过贪婪迭代测地线上升构建贝叶斯核心集
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Tamara Broderick
中科院分区：
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作者：
Trevor Campbell;Tamara Broderick
连贯的不确定性定量是贝叶斯方法的关键强度。但是，在追求可伸缩性时，近似贝叶斯后推断的现代算法通常会牺牲准确的后部不确定性估计。这项工作表明，以前的贝叶斯核心结构算法 - 构建了一个近似数据集的数据的较小，加权的子集 - 也不例外。我们证明了这些算法尺寸尺寸尺寸尺寸尺寸，从而导致低估后不确定性。为了解决这一缺点，我们开发了一种贪婪的迭代地球上升（GIGA），这是一种新型贝叶斯核心结构的算法，可最佳地缩放核心对数型类似。 GIGA提供后近似误差的几何衰减，这是核心大小的函数，并保持其前身的快速运行时间。本文以合成数据集和实际数据集对GIGA的验证结束，表明与以前的核心构建体相比，它通过数量级减少了后近似误差。
Coherent uncertainty quantification is a key strength of Bayesian methods. But modern algorithms for approximate Bayesian posterior inference often sacrifice accurate posterior uncertainty estimation in the pursuit of scalability. This work shows that previous Bayesian coreset construction algorithms---which build a small, weighted subset of the data that approximates the full dataset---are no exception. We demonstrate that these algorithms scale the coreset log-likelihood suboptimally, resulting in underestimated posterior uncertainty. To address this shortcoming, we develop greedy iterative geodesic ascent (GIGA), a novel algorithm for Bayesian coreset construction that scales the coreset log-likelihood optimally. GIGA provides geometric decay in posterior approximation error as a function of coreset size, and maintains the fast running time of its predecessors. The paper concludes with validation of GIGA on both synthetic and real datasets, demonstrating that it reduces posterior approximation error by orders of magnitude compared with previous coreset constructions.