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.

翻译：粒子滑动器是SMC(Contal Monte Carlo)算法,旨在接近州空间模型观测结果的联合分布。我们提出dSMC(不按顺序排列的Monte Carlo),这是一个新的粒子滑动器,能够用美元处理在平行结构上的T$的观测,比标准粒子滑动器(其复杂性为线性)要好。我们为dSMC(dSMC)得出$\mathcal{L ⁇ p$的趋同结果,以美元为明确的上装,多元值为$T$。然后我们讨论如何减少dSMC计算平滑估算值的差异,办法是(一)设计在算法初始化时取样颗粒的好建议分布,以及(二)使用懒惰的抽样增加dSMC中使用的粒子数量。最后,我们根据dSMC设计了一个粒子吉布采样器,能够以$\mathcal{O}硬件(T)平行成本在州空间模型上执行参数。