On the role of interaction in sequential Monte Carlo algorithms
On the role of interaction in sequential Monte Carlo algorithms
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DOI：
10.3150/14-bej666
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
N. Whiteley;Anthony Lee;K. Heine
中科院分区：
文献类型：
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作者：
N. Whiteley;Anthony Lee;K. Heine
介绍了一种基于参数重采样机制的序贯蒙特卡罗算法的一般形式。我们发现，在研究算法的收敛性质时，一个被广泛用于监测算法退化程度的适当推广的有效样本量(ESS)概念是自然出现的。然后，我们能够用ESS的算法控制来表述时间一致收敛的充分条件，而ESS又可以通过自适应地调节粒子之间的相互作用来实现。这导致我们提出了新的算法，在某种意义上说，这些算法是精确的、可证明的稳定的，并且设计来避免阻碍标准算法并行化的交互程度。作为一个副产品，我们证明了流行的自适应重采样粒子滤波的时间一致收敛。
We introduce a general form of sequential Monte Carlo algorithm defined in terms of a parameterized resampling mechanism. We find that a suitably generalized notion of the Effective Sample Size (ESS), widely used to monitor algorithm degeneracy, appears naturally in a study of its convergence properties. We are then able to phrase sufficient conditions for time-uniform convergence in terms of algorithmic control of the ESS, in turn achievable by adaptively modulating the interaction between particles. This leads us to suggest novel algorithms which are, in senses to be made precise, provably stable and yet designed to avoid the degree of interaction which hinders parallelization of standard algorithms. As a byproduct, we prove time-uniform convergence of the popular adaptive resampling particle filter.