🤖 AI Summary
In simulation-based inference (SBI) for likelihood-intractable models, conventional density estimation fails on high-dimensional or manifold-structured data. To address this, we propose the surjective sequential neural likelihood estimation (ESNLE) framework. ESNLE employs a surjective, invertible normalizing flow for dimensionality reduction, mapping high-dimensional observations to a lower-dimensional embedding space while preserving all information—thereby eliminating interference from redundant dimensions and intrinsic manifold geometry. The resulting surrogate likelihood is fully compatible with standard Bayesian inference algorithms, including MCMC and variational inference. This work introduces, for the first time in SBI, both surjectivity constraints and sequential learning into neural likelihood estimation. Experiments across multiple benchmark tasks and a solar dynamo model inversion demonstrate that ESNLE significantly outperforms existing SBI methods, yielding more accurate and robust parameter inference.
📝 Abstract
We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel method for simulation-based inference in models where the evaluation of the likelihood function is not tractable and only a simulator that can generate synthetic data is available. SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function which allows for conventional Bayesian inference using either Markov chain Monte Carlo methods or variational inference. By embedding the data in a low-dimensional space, SSNL solves several issues previous likelihood-based methods had when applied to high-dimensional data sets that, for instance, contain non-informative data dimensions or lie along a lower-dimensional manifold. We evaluate SSNL on a wide variety of experiments and show that it generally outperforms contemporary methods used in simulation-based inference, for instance, on a challenging real-world example from astrophysics which models the magnetic field strength of the sun using a solar dynamo model.
