A sequential smoothing algorithm with linear computational cost

Abstract

In this paper we propose a new particle smoother that has a computational complexity of O(N ), where N is the number of particles. This compares favourably with the O(N 2 ) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify in many existing algorithms.Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and on the analysis of an athletics data set, that our new method also substantially outperforms the simple FilterSmoother (the only other smoother with computational cost that is linear in the number of particles).

Adaptive Importance Sampling for Control and Inference

“…In some cases significant accelerations can be made, e.g. [12,24], but implementing these may be cumbersome [42].…”

An Overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models

“…More recently, an importance sampling type approach has also been proposed in [22] to reduce the computational complexity to O (N T ); see [6] for a similar idea developed in the context of belief propagation. It is demonstrated experimentally in [7] that this procedure outperforms significantly the forward filtering-backward smoothing approach.…”

“…This poor approximation of p ( x 0:n | y 0:n ) induces a poor approximation of p(s n (x 0:n , y 0:n )|y 0:n ) and the errors do built up over time. Results such as (22) suggest that the approximation error increases at least quadratically with n. A convincing example of this degeneracy problem for sufficient statistics is given in [2]. However, these methods cannot completely be ruled out.…”

A Backward-Simulation Based Rao-Blackwellized Particle Smoother for Conditionally Linear Gaussian Models

“…For this reason, various alternative particle smoothers have been proposed. One possible approach is to approximate the two-filter formula using particle methods [Kitagawa, 1996, Briers et al, 2010, Fearnhead et al, 2010. The disadvantage of such two-filter type smoothers is that the construction of the backward filter can be quite troublesome.…”

“…Another possible approach for the RBPS is to use the two-filter formula, and form the smoothing solution by combining two RBPFs, one running forward and one backwards in time [Briers et al, 2010, Fearnhead et al, 2010.…”