Unifying Sequential Monte Carlo with Resampling Matrices
For researchers using SMC, this provides a theoretical foundation to choose resampling schemes, though the practical impact is incremental.
The paper presents a theoretical framework using resampling matrices to unify and compare resampling schemes in Sequential Monte Carlo, identifying the optimal scheme with lowest error and providing new asymptotic error formulas.
Sequential Monte Carlo (SMC) is a class of algorithms that approximate high-dimensional expectations of a Markov chain. SMC algorithms typically include a resampling step. There are many possible ways to resample, but the relative advantages of different resampling schemes remains poorly understood. Here, a theoretical framework for comparing resampling schemes is presented. The framework uses resampling matrices to provide a simple description for the SMC resampling step. The framework identifies the matrix resampling scheme that gives the lowest possible error. The framework leads to new asymptotic error formulas that can be used to compare different resampling schemes.