Flexible O(|S|)-cost control variates for complex log-densities

Develop control variates for subsampling-based pseudomarginal MCMC that are sufficiently flexible to accurately approximate highly complex log-likelihood contributions while maintaining per-iteration computational cost O(|S|), and establish corresponding variance and bias guarantees.

Background

The chapter shows that accurate control variates are crucial for effective subsampling and pseudomarginal performance, with existing second-order Taylor expansions working well in many but not all settings.

For models with highly complex log-densities, even grouped second-order expansions can be inadequate. The authors therefore identify the need for more flexible control variates that preserve the computational scaling as an explicit open problem.