论文标题
基于粒子的快速增量更光滑符合粒子吉布斯
Particle-based, rapid incremental smoother meets particle Gibbs
论文作者
论文摘要
基于粒子的快速增量更平滑（巴黎）是一种顺序的蒙特卡洛技术，允许在Feynman-kac路径分布下有效地在线近似加性功能的期望。在弱假设下，该算法具有线性计算复杂性和有限的内存要求。它还带有许多非质合界和收敛结果。但是，基于自称的重要性抽样，巴黎估计量是有偏见的。它的偏见与颗粒数量成反比，但在适当的混合条件下已发现与时间范围线性生长。在这项工作中，我们提出了巴黎粒子吉布斯（PPG）采样器，其复杂性本质上与巴黎的复杂性相同，并且显着降低了给定计算复杂性的偏差，以差异的适度增加。从某种意义上说，该方法是一种包装器，它使用粒子吉布斯内部环中的巴黎算法来形成靶向数量的偏置版本。我们通过理论结果证实了PPG算法，包括有关偏差和方差以及偏差不平等的新界限。我们通过支持我们主张的数值实验来说明我们的理论结果。
The particle-based, rapid incremental smoother (PARIS) is a sequential Monte Carlo technique allowing for efficient online approximation of expectations of additive functionals under Feynman--Kac path distributions. Under weak assumptions, the algorithm has linear computational complexity and limited memory requirements. It also comes with a number of non-asymptotic bounds and convergence results. However, being based on self-normalised importance sampling, the PARIS estimator is biased; its bias is inversely proportional to the number of particles but has been found to grow linearly with the time horizon under appropriate mixing conditions. In this work, we propose the Parisian particle Gibbs (PPG) sampler, whose complexity is essentially the same as that of the PARIS and which significantly reduces the bias for a given computational complexity at the price of a modest increase in the variance. This method is a wrapper in the sense that it uses the PARIS algorithm in the inner loop of particle Gibbs to form a bias-reduced version of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. We illustrate our theoretical results with numerical experiments supporting our claims.
