An Adaptive Resample-Move Algorithm for Estimating Normalizing Constants
This work addresses the suboptimal variance in normalizing constant estimation for probabilistic modeling, offering a more efficient and easier-to-tune method for researchers and practitioners in machine learning and statistics.
The paper tackled the problem of estimating normalizing constants for probabilistic model comparison by introducing an adaptive version of the Resample-Move algorithm that adjusts particle numbers based on variance needs. The result showed that Adaptive Resample-Move achieved smaller variance and used less computational resources than fixed-particle Resample-Move or Annealed Importance Sampling in benchmarks on Gaussian Process Classification and Restricted Boltzmann Machine applications.
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard choice of using a fixed number of particles at each iteration is suboptimal because some steps will contribute disproportionately to the variance of the estimate. We introduce an adaptive version of the Resample-Move algorithm, in which the particle set is adaptively expanded whenever a better approximation of an intermediate distribution is needed. The algorithm builds on the expression for the optimal number of particles and the corresponding minimum variance found under ideal conditions. Benchmark results on challenging Gaussian Process Classification and Restricted Boltzmann Machine applications show that Adaptive Resample-Move (ARM) estimates the normalizing constant with a smaller variance, using less computational resources, than either Resample-Move with a fixed number of particles or Annealed Importance Sampling. A further advantage over Annealed Importance Sampling is that ARM is easier to tune.