贝叶斯计算与生成扩散模型通过多级蒙特卡洛计算
Luke Shaw1, Abdul-Lateef Haji-Ali2, Marcelo Pereyra2
1Universitat Jaume I, Castello de la Plana, Spain.
概括
生成式扩散模型加速贝叶斯反向问题,但在计算上是昂贵的. 本研究介绍了一种多级蒙特卡洛策略,以显著降低贝叶斯计算中扩散模型采样的计算成本.
科学领域:
- 计算数学是指计算数学.
- 机器学习 机器学习
- 科学成像科学成像
背景情况:
- 生成性扩散模型为贝叶斯反向问题提供了准确的解决方案.
- 扩散模型需要大量的函数评估,这导致蒙特卡洛集成和不确定性定量化的高计算成本.
- 像计算成像这样的大规模问题加剧了这些成本,原因是昂贵的神经网络评估.
研究的目的:
- 提出一种新的多级蒙特卡罗 (MLMC) 策略,以减少使用扩散模型进行贝叶斯计算的计算成本.
- 在反向问题中解决与扩散模型采样相关的高计算费用,特别是在定量成像中.
主要方法:
- 开发了一个针对扩散模型量身定制的多级蒙特卡洛策略.
- 在扩散模型中利用了固有的成本准确性权衡.
- 配对不同准确度的扩散模型,以最大限度地降低整体计算成本.
主要成果:
- 通过扩散模型实现了贝叶斯计算的计算成本的显著降低.
- 在三个基准成像问题中,与标准技术相比,证明了[公式:参见文本]到[公式:参见文本]的成本降低.
- 保持了最终准确性,同时大幅降低了计算需求.
结论:
- 拟议的MLMC策略有效地减少了用于贝叶斯反向问题的扩散模型的计算负担.
- 这种方法提供了一个计算效率高的解决方案,用于不确定性量化大规模应用程序,如计算成像.
- 该方法使得扩散模型在苛刻的科学领域的应用更加可行.
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