论文标题
去序列化的蒙特卡洛：平行粒子更光滑
De-Sequentialized Monte Carlo: a parallel-in-time particle smoother
论文作者
论文摘要
粒子SmoOther是SMC（顺序蒙特卡洛）算法，旨在近似从状态空间模型观察到的状态的联合分布。我们提出了DSMC（De-Sequientional Monte Carlo），这是一种新的粒子，可以在并行体系结构上处理$ \ Mathcal {o}（\ log t）$时间的$ t $观测值。这与标准粒子湿度相比，其复杂性在$ t $中是线性的。我们得出DSMC的$ \ MATHCAL {L} _p $收敛结果，具有显式的上限，多项式为$ t $。然后，我们讨论如何通过（i）设计良好的提案分布来减少DSMC计算的平滑估计值的方差，以在算法的初始化时对颗粒进行采样，以及（ii）使用懒惰重采样以增加DSMC中使用的颗粒数量。最后，我们基于DSMC设计了一个粒子Gibbs采样器，该采样器能够在$ \ Mathcal {O}（\ log（t））$上的状态空间模型中执行参数推断。
Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to approximate the joint distribution of the states given observations from a state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new particle smoother that is able to process $T$ observations in $\mathcal{O}(\log T)$ time on parallel architecture. This compares favourably with standard particle smoothers, the complexity of which is linear in $T$. We derive $\mathcal{L}_p$ convergence results for dSMC, with an explicit upper bound, polynomial in $T$. We then discuss how to reduce the variance of the smoothing estimates computed by dSMC by (i) designing good proposal distributions for sampling the particles at the initialization of the algorithm, as well as by (ii) using lazy resampling to increase the number of particles used in dSMC. Finally, we design a particle Gibbs sampler based on dSMC, which is able to perform parameter inference in a state-space model at a $\mathcal{O}(\log(T))$ cost on parallel hardware.
