Pseudo-Likelihood Inference

• URL: http://arxiv.org/abs/2311.16656v1
• Date: Tue, 28 Nov 2023 10:17:52 GMT
• Title: Pseudo-Likelihood Inference
• Authors: Theo Gruner, Boris Belousov, Fabio Muratore, Daniel Palenicek, Jan Peters
• Abstract summary: Pseudo-Likelihood Inference (PLI) is a new method that brings neural approximation into ABC, making it competitive on challenging Bayesian system identification tasks. PLI allows for optimizing neural posteriors via gradient descent, does not rely on summary statistics, and enables multiple observations as input. The effectiveness of PLI is evaluated on four classical SBI benchmark tasks and on a highly dynamic physical system.
• Score: 16.934708242852558
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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