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Many areas of science make extensive use of computer simulators thatimplicitly encode intractable likelihood functions of complex systems.Classical statistical methods are poorly suited for these so-calledlikelihood-free inference (LFI) settings, especially outside asymptotic andlow-dimensional regimes. At the same time, traditional LFI methods - such asApproximate Bayesian Computation or more recent machine learning techniques -do not guarantee confidence sets with nominal coverage in general settings(i.e., with high-dimensional data, finite sample sizes, and for any parametervalue). In addition, there are no diagnostic tools to check the empiricalcoverage of confidence sets provided by such methods across the entireparameter space. In this work, we propose a unified and modular inferenceframework that bridges classical statistics and modern machine learningproviding (i) a practical approach to the Neyman construction of confidencesets with frequentist finite-sample coverage for any value of the unknownparameters; and (ii) interpretable diagnostics that estimate the empiricalcoverage across the entire parameter space. We refer to the general frameworkas likelihood-free frequentist inference (LF2I). Any method that defines a teststatistic can leverage LF2I to create valid confidence sets and diagnosticswithout costly Monte Carlo samples at fixed parameter settings. We study thepower of two likelihood-based test statistics (ACORE and BFF) and demonstratetheir empirical performance on high-dimensional, complex data. Code isavailable at https://github.com/lee-group-cmu/lf2i.

Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference