Pseudo-Likelihood Inference
This work addresses a bottleneck in Bayesian inference for researchers and practitioners dealing with complex models, offering a competitive method that is incremental by building on existing ABC and SNPE approaches.
The paper tackles the challenge of Simulation-Based Inference (SBI) for intractable likelihoods by proposing Pseudo-Likelihood Inference (PLI), which integrates neural approximation into Approximate Bayesian Computation (ABC) to improve performance on high-dimensional and complex tasks, showing advantages in stochastic simulations and multi-modal posteriors.
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.