Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Incorporating the ChEES Criterion into Sequential Monte Carlo Samplers

Andrew Millard, Joshua Murphy, Daniel Frisch, Simon Maskell

TL;DR

This work addresses efficient Bayesian sampling by integrating Change in the Estimator of the Expected Square (ChEES) into Sequential Monte Carlo (SMC) to create SMC-ChEES, a GPU-friendly gradient-based proposal. By jittering trajectory lengths with quasi-random sequences (e.g., Halton, Sobol) and optimizing during a warm-up, the method aims to match or surpass No-U-Turn Sampler (NUTS) performance while reducing computational load. Across Gaussian, ill-conditioned Gaussian, banana, and German Credit tasks, SMC-ChEES delivers substantially higher effective samples per gradient evaluation than NUTS, with the best RNGs being 1-d Halton and 1-d Sobol; however, some challengers like the ill-conditioned case reveal limits in trajectory-depth tuning. The results suggest ChEES-based proposals within SMC offer a practical, scalable alternative for GPU-accelerated Bayesian inference, with future work on step-size adaptation and broader real-world testing.

Abstract

Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the parameter space of interest if the additional hyper-parameters are chosen well. The No-U-Turn Sampler (NUTS) is a variant of HMC which is extremely effective at selecting these hyper-parameters but is slow to run and is not suited to GPU architectures. An alternative to NUTS, Change in the Estimator of the Expected Square HMC (ChEES-HMC) was shown not only to run faster than NUTS on GPU but also sample from posteriors more efficiently. Sequential Monte Carlo (SMC) samplers are another sampling method which instead output weighted samples from the posterior. They are very amenable to parallelisation and therefore being run on GPUs while having additional flexibility in their choice of proposal over MCMC. We incorporate (ChEEs-HMC) as a proposal into SMC samplers and demonstrate competitive but faster performance than NUTS on a number of tasks.

Incorporating the ChEES Criterion into Sequential Monte Carlo Samplers

TL;DR

This work addresses efficient Bayesian sampling by integrating Change in the Estimator of the Expected Square (ChEES) into Sequential Monte Carlo (SMC) to create SMC-ChEES, a GPU-friendly gradient-based proposal. By jittering trajectory lengths with quasi-random sequences (e.g., Halton, Sobol) and optimizing during a warm-up, the method aims to match or surpass No-U-Turn Sampler (NUTS) performance while reducing computational load. Across Gaussian, ill-conditioned Gaussian, banana, and German Credit tasks, SMC-ChEES delivers substantially higher effective samples per gradient evaluation than NUTS, with the best RNGs being 1-d Halton and 1-d Sobol; however, some challengers like the ill-conditioned case reveal limits in trajectory-depth tuning. The results suggest ChEES-based proposals within SMC offer a practical, scalable alternative for GPU-accelerated Bayesian inference, with future work on step-size adaptation and broader real-world testing.

Abstract

Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the parameter space of interest if the additional hyper-parameters are chosen well. The No-U-Turn Sampler (NUTS) is a variant of HMC which is extremely effective at selecting these hyper-parameters but is slow to run and is not suited to GPU architectures. An alternative to NUTS, Change in the Estimator of the Expected Square HMC (ChEES-HMC) was shown not only to run faster than NUTS on GPU but also sample from posteriors more efficiently. Sequential Monte Carlo (SMC) samplers are another sampling method which instead output weighted samples from the posterior. They are very amenable to parallelisation and therefore being run on GPUs while having additional flexibility in their choice of proposal over MCMC. We incorporate (ChEEs-HMC) as a proposal into SMC samplers and demonstrate competitive but faster performance than NUTS on a number of tasks.

Paper Structure

This paper contains 16 sections, 25 equations, 4 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Markov Chain Monte Carlo
  3. Hamiltonian Monte Carlo
  4. No-U-Turn Sampler
  5. Change in the Estimator of the Expected Square
  6. Sequential Monte Carlo
  7. Proposals in SMC
  8. SMC-ChEES
  9. Random Number Generators (RNGs)
  10. Experimental Set-up
  11. Gaussian
  12. Ill-conditioned Gauss
  13. Rosenbrock Distribution
  14. German Credit
  15. Results
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Number of effective samples per gradient evaluation per iteration for the four experiments.
  • Figure 2: MSE of the mean and variance estimates for the 5-dimensional Gaussian distribution obtained by the different proposals.
  • Figure 3: MSE of the mean and variance estimates for the 100-dimensional Ill-conditioned Gaussian distribution obtained by the different proposals.
  • Figure 4: Position of all samples for the last 20 iterations of the banana distribution.