  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.
