  Simulation-Based Inference (SBI) is a common name for an emerging family of
approaches that infer the model parameters when the likelihood is intractable.
Existing SBI methods either approximate the likelihood, such as Approximate
Bayesian Computation (ABC) or directly model the posterior, such as Sequential
Neural Posterior Estimation (SNPE). While ABC is efficient on low-dimensional
problems, on higher-dimensional tasks, it is generally outperformed by SNPE,
which leverages function approximation. In this paper, we propose
Pseudo-Likelihood Inference (PLI), a new method that brings neural
approximation into ABC, making it competitive on challenging Bayesian system
identification tasks. By utilizing integral probability metrics, we introduce a
smooth likelihood kernel with an adaptive bandwidth that is updated based on
information-theoretic trust regions. Thanks to this formulation, our method (i)
allows for optimizing neural posteriors via gradient descent, (ii) does not
rely on summary statistics, and (iii) enables multiple observations as input.
In comparison to SNPE, it leads to improved performance when more data is
available. The effectiveness of PLI is evaluated on four classical SBI
benchmark tasks and on a highly dynamic physical system, showing particular
advantages on stochastic simulations and multi-modal posterior landscapes.
