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Simulation-based inference enables learning the parameters of a model evenwhen its likelihood cannot be computed in practice. One class of methods usesdata simulated with different parameters to infer models of thelikelihood-to-evidence ratio, or equivalently the posterior function. Here weframe the inference task as an estimation of an energy function parametrizedwith an artificial neural network. We present an intuitive approach where theoptimal model of the likelihood-to-evidence ratio is found by maximizing thelikelihood of simulated data. Within this framework, the connection between thetask of simulation-based inference and mutual information maximization isclear, and we show how several known methods of posterior estimation relate toalternative lower bounds to mutual information. These distinct objectivefunctions aim at the same optimal energy form and therefore can be directlybenchmarked. We compare their accuracy in the inference of model parameters,focusing on four dynamical systems that encompass common challenges in timeseries analysis: dynamics driven by multiplicative noise, nonlinearinteractions, chaotic behavior, and high-dimensional parameter space.

MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories