Finite Sample L_2 Bounds for Sequential Monte Carlo and Adaptive Path Selection

by   Joseph Marion, et al.

We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the L_2 distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first finite sample convergence result for SMC that does not require an upper bound on the importance weights. Using this bound we show that careful selection of the interpolating distributions can lead to substantial improvements in the computational complexity of the algorithm. This result also justifies the adaptive selection of SMC distributions using the relative effective sample size commonly used in the literature and we establish conditions guaranteeing the approximation accuracy of the adaptive SMC approach. We then demonstrate empirically that this procedure provides nearly-optimal sequences of distributions in an automatic fashion for realistic examples.



There are no comments yet.


page 1

page 2

page 3

page 4


Finite Sample Complexity of Sequential Monte Carlo Estimators

We present bounds for the finite sample error of sequential Monte Carlo ...

Lugsail lag windows and their application to MCMC

Lag windows are commonly used in the time series, steady state simulatio...

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

The finite size of Monte Carlo samples carries intrinsic uncertainty tha...

Adaptive Sequential SAA for Solving Two-stage Stochastic Linear Programs

We present adaptive sequential SAA (sample average approximation) algori...

A Uniform-in-P Edgeworth Expansion under Weak Cramér Conditions

This paper provides a finite sample bound for the error term in the Edge...

Measuring Sample Path Causal Influences with Relative Entropy

We present a sample path dependent measure of causal influence between t...

Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint

We consider the problem of sequential sampling from a finite number of i...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.