Adaptive Monte Carlo augmented with normalizing flows.
Adaptive Monte Carlo augmented with normalizing flows.
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DOI：
10.1073/pnas.2109420119
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发表时间：
2022-03-08
影响因子：
11.1
通讯作者：
Vanden-Eijnden E
中科院分区：
文献类型：
--
作者：
Gabrié M;Rotskoff GM;Vanden-Eijnden E
蒙特卡罗方法是从概率分布中采样数据的工具，广泛应用于物理科学，应用数学和贝叶斯统计。然而，在许多情况下，由于分布模式之间的缓慢“混合”，使用蒙特卡罗在计算上是禁止的，除非使用手动调整的算法来加速该方案。基于生成模型的机器学习技术为特定系统设计有效方案的挑战提供了一种引人注目的替代方案。在这里，我们形式化的蒙特卡洛增强与规范化的流，并表明，有限的先验数据和物理启发的算法，我们可以大大加快采样与生成模型。物理科学、机器学习和统计推断中的许多问题都需要从高维多模态概率分布中进行采样。马尔可夫链蒙特卡罗（MCMC）算法，这项任务的无处不在的工具，通常依赖于随机的本地更新来传播给定系统的配置的方式，确保生成的配置将根据目标概率分布渐近分布。在高维设置多个相关的亚稳盆地，当地的方法需要巨大的计算工作量或复杂设计的重要性采样策略，以捕捉信息，例如，相对人口的盆地。在这里，我们分析了自适应MCMC，它增强了MCMC采样与非局部过渡内核参数化生成模型称为规范化流。我们专注于一个没有预先存在的数据的设置，这是常见的情况下，MCMC使用的问题。我们的方法使用1）MCMC策略，将从任何标准转换内核获得的局部移动与从生成模型获得的局部移动混合以加速采样，以及2）以这种方式生成的数据以适应生成模型并提高其在MCMC算法中的功效。我们提供了一个理论分析，该算法的收敛性能和数值研究其效率，特别是在其倾向于快速平衡亚稳模式，其粗略的位置是已知的先验，但各自的概率权重不。我们表明，我们的算法可以有效地采样跨越大的自由能障碍，提供显着的加速相对于传统的MCMC算法。
Monte Carlo methods, tools for sampling data from probability distributions, are widely used in the physical sciences, applied mathematics, and Bayesian statistics. Nevertheless, there are many situations in which it is computationally prohibitive to use Monte Carlo due to slow “mixing” between modes of a distribution unless hand-tuned algorithms are used to accelerate the scheme. Machine learning techniques based on generative models offer a compelling alternative to the challenge of designing efficient schemes for a specific system. Here, we formalize Monte Carlo augmented with normalizing flows and show that, with limited prior data and a physically inspired algorithm, we can substantially accelerate sampling with generative models. Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multimodal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this task, typically rely on random local updates to propagate configurations of a given system in a way that ensures that generated configurations will be distributed according to a target probability distribution asymptotically. In high-dimensional settings with multiple relevant metastable basins, local approaches require either immense computational effort or intricately designed importance sampling strategies to capture information about, for example, the relative populations of such basins. Here, we analyze an adaptive MCMC, which augments MCMC sampling with nonlocal transition kernels parameterized with generative models known as normalizing flows. We focus on a setting where there are no preexisting data, as is commonly the case for problems in which MCMC is used. Our method uses 1) an MCMC strategy that blends local moves obtained from any standard transition kernel with those from a generative model to accelerate the sampling and 2) the data generated this way to adapt the generative model and improve its efficacy in the MCMC algorithm. We provide a theoretical analysis of the convergence properties of this algorithm and investigate numerically its efficiency, in particular in terms of its propensity to equilibrate fast between metastable modes whose rough location is known a priori but respective probability weight is not. We show that our algorithm can sample effectively across large free energy barriers, providing dramatic accelerations relative to traditional MCMC algorithms.
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