Many areas of science make extensive use of computer simulators that implicitly encode likelihood functions of complex systems. Classical statistical methods are poorly suited for these so-called likelihood-free inference (LFI) settings, outside the asymptotic and lowdimensional regimes. Although new machine learning methods, such as normalizing flows, have revolutionized the sample efficiency and capacity of LFI methods, it remains an open question whether they produce reliable measures of uncertainty.This paper presents a statistical framework for LFI that unifies classical statistics with modern machine learning to: (1) efficiently construct frequentist confidence sets and hypothesis tests with finite-sample guarantees of nominal coverage (type I error control) and power; (2) provide practical diagnostics for assessing empirical coverage over the entire parameter space. We refer to our framework as likelihood-free frequentist inference (LF2I). Any method that estimates a test statistic, like the likelihood ratio, can be plugged into our framework to create valid confidence sets and compute diagnostics, without costly Monte Carlo samples at fixed parameter settings. In this work, we specifically study the power of two test statistics (ACORE and BFF), which, respectively, maximize versus integrate an odds function over the parameter space. Our study offers multifaceted perspectives on the challenges in LF2I.

The world is not static: This causes real-world time series to change over time through external, and potentially disruptive, events such as macroeconomic cycles or the COVID-19 pandemic. We present an adaptive sampling strategy that selects the part of the time series history that is relevant for forecasting. We achieve this by learning a discrete distribution over relevant time steps by Bayesian optimization. We instantiate this idea with a two-step method that is pre-trained with uniform sampling and then training a lightweight adaptive architecture with adaptive sampling. We show with synthetic and real-world experiments that this method adapts to distribution shift and significantly reduces the forecasting error of the base model for three out of five datasets.

The vast majority of modern machine learning targets prediction problems, with algorithms such as Deep Neural Networks revolutionizing the accuracy of point predictions for high-dimensional complex data. Predictive approaches are now used in many domain sciences to directly estimate internal parameters of interest in theoretical simulator-based models. In parallel, common alternatives focus on estimating the full posterior using modern neural density estimators such as normalizing flows. However, an open problem in simulation-based inference (SBI) is how to construct properly calibrated confidence regions for internal parameters with nominal conditional coverage and high power. Many SBI methods are indeed known to produce overly confident posterior approximations, yielding misleading uncertainty estimates. Similarly, existing approaches for uncertainty quantification in deep learning provide no guarantees on conditional coverage. In this work, we present WALDO, a novel method for constructing correctly calibrated confidence regions in SBI. WALDO reframes the well-known Wald test and uses Neyman inversion to convert point predictions and posteriors from any prediction or posterior estimation algorithm to confidence sets with correct conditional coverage, even for finite sample sizes. As a concrete example, we demonstrate how a recently proposed deep learning prediction approach for particle energies in high-energy physics can be recalibrated using WALDO to produce confidence intervals with correct coverage and high power.Preprint. Under review.