TY - JOUR
T1 - Particle Smoothing in Continuous Time: A Fast Approach via Density Estimation
AU - Murray, Lawrence
AU - Storkey, Amos
PY - 2011/3
Y1 - 2011/3
N2 - We consider the particle smoothing problem for state-space models where the transition density is not available in closed form, in particular for continuous-time, nonlinear models expressed via stochastic differential equations (SDEs). Conventional forward-backward and two-filter smoothers for the particle filter require a closed-form transition density, with the linear-Gaussian Euler-Maruyama discretization usually applied to the SDEs to achieve this. We develop a pair of variants using kernel density approximations to relieve the dependence, and in doing so enable use of faster and more accurate discretization schemes such as Runge-Kutta. In addition, the new methods admit arbitrary proposal distributions, providing an avenue to deal with degeneracy issues. Experimental results on a functional magnetic resonance imaging (fMRI) deconvolution task demonstrate comparable accuracy and significantly improved runtime over conventional techniques.
AB - We consider the particle smoothing problem for state-space models where the transition density is not available in closed form, in particular for continuous-time, nonlinear models expressed via stochastic differential equations (SDEs). Conventional forward-backward and two-filter smoothers for the particle filter require a closed-form transition density, with the linear-Gaussian Euler-Maruyama discretization usually applied to the SDEs to achieve this. We develop a pair of variants using kernel density approximations to relieve the dependence, and in doing so enable use of faster and more accurate discretization schemes such as Runge-Kutta. In addition, the new methods admit arbitrary proposal distributions, providing an avenue to deal with degeneracy issues. Experimental results on a functional magnetic resonance imaging (fMRI) deconvolution task demonstrate comparable accuracy and significantly improved runtime over conventional techniques.
UR - http://www.scopus.com/inward/record.url?scp=79951655062&partnerID=8YFLogxK
U2 - 10.1109/TSP.2010.2096418
DO - 10.1109/TSP.2010.2096418
M3 - Article
SN - 1053-587X
VL - 59
SP - 1017
EP - 1026
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 3
ER -