插即用分割的吉布斯采样器:在贝叶斯推理中嵌入深度生成先验
概括
本研究介绍了一种新的随机插即用 (PnP) 算法,用于高效的后部分布采样. 它使用深度生成模型进行贝叶斯否定,提供与以前方法不同的置信区间.
科学领域:
- 计算统计的计算统计.
- 机器学习 机器学习
- 图像处理 图像处理
背景情况:
- 后分布采样在贝叶斯推理中至关重要,但在计算上具有挑战性.
- 现有的plug-and-play (PnP) 方法经常产生点估计,并且需要明确的先验.
- 深度生成模型提供了强大的先前表示,但将其整合到采样中仍然是一个活跃的研究领域.
研究的目的:
- 引入一种新型的随机插即用 (PnP) 采样算法,以实现高效的后部分布采样.
- 为了利用可变分割和深度生成模型来完成贝叶斯式否定任务.
- 为了使贝叶斯估计器能够提供置信区间,提高不确定性量化.
主要方法:
- 开发了一种基于分割吉布斯采样 (SGS) 的随机PNP算法.
- 灵感来自半方位分割 (HQS) 和交替方向乘法 (ADMM) 的方法.
- 基于扩散的综合最先进的生成模型,用于贝叶斯否认子问题.
主要成果:
- 拟议的SGS算法有效地从后部分布中取样.
- 该方法在预先训练的生成模型中隐式编码了先前信息,避免了明确的先前选择.
- 与确定性PNP方法不同,随机方法提供了最小的额外计算成本的置信区间.
结论:
- 随机PNP采样策略对于图像处理任务是有效的.
- 该算法提供了一种原则性的方法,将深度生成模型纳入贝叶斯推理中.
- 这种方法通过提供置信区间来增强贝叶斯估计中的不确定性量化.
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