Bayesian Learning of Conditional Kernel Mean Embeddings for Automatic Likelihood-Free Inference
This work addresses the challenge of hyperparameter tuning in approximate Bayesian computation for researchers in fields like ecology, offering an incremental improvement in automation and efficiency.
The paper tackles the problem of tuning hyperparameters in likelihood-free inference, which is crucial for balancing accuracy and efficiency, by introducing KELFI, a framework that automatically learns these hyperparameters to improve inference accuracy with limited simulation budgets, demonstrating improved accuracy and efficiency on ecological inference problems.
In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they demand large quantities of simulation calls. Critically, hyperparameters that determine measures of simulation discrepancy crucially balance inference accuracy and sample efficiency, yet are difficult to tune. In this paper, we present kernel embedding likelihood-free inference (KELFI), a holistic framework that automatically learns model hyperparameters to improve inference accuracy given limited simulation budget. By leveraging likelihood smoothness with conditional mean embeddings, we nonparametrically approximate likelihoods and posteriors as surrogate densities and sample from closed-form posterior mean embeddings, whose hyperparameters are learned under its approximate marginal likelihood. Our modular framework demonstrates improved accuracy and efficiency on challenging inference problems in ecology.