Adaptive stopping for fast particle smoothing

Abstract

Particle smoothing is useful for offline state inference and parameter learning in nonlinear/non-Gaussian state-space models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles. One approach to tackle this issue is to use rejection-sampling-based FFBS (RS-FFBS), which asymptotically reaches linear complexity. In practice, however, the constants can be quite large and the actual gain in computational time limited. In this contribution, we develop a hybrid method, governed by an adaptive stopping rule, in order to exploit the benefits, but avoid the drawbacks, of RS-FFBS. The resulting particle smoother is shown in a simulation study to be considerably more computationally efficient than both FFBS and RS-FFBS.

On Particle Methods for Parameter Estimation in State-Space Models

“…In some applications, the rejection sampling procedure can be computationally costly as the acceptance probability can be very small for some particles; see, for example, Section 4.3 in [75] for empirical results. This has motivated the development of hybrid procedures combining FF-BSa and rejection sampling [85]. We can also directly approximate the marginals {p θ (x n |y 0 : T )} T n=0 .…”

A two filter particle smoother for Wiener state-space systems

“…Since p(x T ) has quadratically increasing variance (see (12)) this is impractical, though, as this density would propose many particles in irrelevant areas of the state space. However, we know that the forward filter is generally capable of keeping the particles in the interesting area.…”

“…Update the prior statistics according to (12) 3) Initialize the backward filter using (25), (28) and (30) 4) For t = T − 1, . .…”

Joint Vehicle Trajectory and Model Parameter Estimation Using Road Side Sensors

“…Instead, we chose to combine the above Rao-Blackwellized smoothing strategy with the rejection sampling based smoother proposed in [25] which asymptotically (as M S → ∞) scales with O(T · M S ). Further, in order to avoid getting trapped inside the rejection sampling phase of the smoother, we also implement adaptive stopping as proposed in [39]. Finally, it is very important to point out that the smoothed weight in (30) is only used for the rejection sampling (Step 7f)) and categorical sampling (Step 8c)) stages but not as the weights of the smoothed particles.…”