Transformed Samplers with Variance Reduction

Key points

• Control variates reduce the variance of the resulting estimates, but a good control variate requires solving the Poisson equation of the sampler, which rarely admits a closed-form solution.1
• Exact solutions are available when the sampler's kernel has a known spectral decomposition on a simple reference density.1
• A bijection, such as a normalizing flow, is trained so that the target becomes close to the reference in a latent space, and we show that Markov kernels and their Poisson solutions are transformed by any bijection.1
• Experiments on synthetic targets and real posteriors compare the procedure against state-of-the-art samplers and control variates.1

Sources (1)

• [1]Transformed Samplers with Variance Reduction
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 08:16 PM

  Markov chain Monte Carlo (MCMC) methods are the standard tool for computing expectations under complex probability distributions.

  Control variates reduce the variance of the resulting estimates, but a good control variate requires solving the Poisson equation of the sampler, which rarely admits a closed-form solution.

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