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Hamiltonian Adaptive Importance Sampling
IEEE Signal Processing Letters ( IF 3.9 ) Pub Date : 2021-03-26 , DOI: 10.1109/lsp.2021.3068616
Ali Mousavi , Reza Monsefi , Victor Elvira

Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of this proposal is key for achieving a high performance. In adaptive IS (AIS) methods, a set of proposals is iteratively improved. AIS is a relevant and timely methodology although many limitations remain yet to be overcome, e.g., the curse of dimensionality in high-dimensional and multi-modal problems. Moreover, the Hamiltonian Monte Carlo (HMC) algorithm has become increasingly popular in machine learning and statistics. HMC has several appealing features such as its exploratory behavior, especially in high-dimensional targets, when other methods suffer. In this letter, we introduce the novel Hamiltonian adaptive importance sampling (HAIS) method. HAIS implements a two-step adaptive process with parallel HMC chains that cooperate at each iteration. The proposed HAIS efficiently adapts a population of proposals, extracting the advantages of HMC. HAIS can be understood as a particular instance of the generic layered AIS family with an additional resampling step. HAIS achieves a significant performance improvement in high-dimensional problems w.r.t. state-of-the-art algorithms. We discuss the statistical properties of HAIS and show its high performance in two challenging examples.

中文翻译:

哈密​​顿自适应重要性抽样

重要性采样(IS)是一种强大的蒙特卡洛(MC)方法,用于近似积分,例如在贝叶斯推理的情况下。在IS中,样本是从所谓的提案分配中模拟出来的,因此,选择该提案是实现高性能的关键。在自适应IS(AIS)方法中,一组提议被迭代地改进。AIS是一种相关且及时的方法,尽管仍有许多局限性有待克服,例如,在高维和多模式问题中对维数的诅咒。此外,汉密尔顿蒙特卡洛(HMC)算法在机器学习和统计中已变得越来越流行。HMC具有一些吸引人的功能,例如其探索行为,尤其是在高维目标中,其他方法会受到影响。在这封信中,我们介绍了新颖的哈密顿自适应重要性抽样(HAIS)方法。HAIS通过并行的HMC链实现了两步自适应过程,这些链在每次迭代时都会协作。提议的HAIS有效地适应了众多提议,从而充分利用了HMC的优势。可以将HAIS理解为通用分层AIS系列的特定实例,并带有额外的重采样步骤。HAIS通过最先进的算法在高维问题上实现了显着的性能提升。我们讨论了HAIS的统计属性,并在两个具有挑战性的示例中展示了其高性能。HAIS可以理解为具有附加重采样步骤的通用分层AIS系列的特定实例。HAIS通过最先进的算法在高维问题上实现了显着的性能提升。我们讨论了HAIS的统计属性,并在两个具有挑战性的示例中展示了其高性能。可以将HAIS理解为通用分层AIS系列的特定实例,并带有额外的重采样步骤。HAIS通过最先进的算法在高维问题上实现了显着的性能提升。我们讨论了HAIS的统计属性,并在两个具有挑战性的示例中展示了其高性能。
更新日期:2021-04-23
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