Efficient acquisition rules for model-based approximate Bayesian computation
This work addresses a specific bottleneck in Bayesian inference for researchers using ABC, offering an incremental improvement over existing methods.
The paper tackles the high computational cost of Approximate Bayesian Computation (ABC) by proposing a method to intelligently select simulation locations to minimize uncertainty in the posterior density estimation, resulting in more accurate approximations compared to common Bayesian optimization strategies.
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.