Simulation-Based Inference via Regression Projection and Batched Discrepancies

TL;DR

This paper introduces a lightweight, simulation-based inference method that uses regression projections and batch discrepancies to efficiently estimate parameters, with formal guarantees and practical demonstrations.

Contribution

The paper formalizes a regression-based simulation inference approach, proving its consistency, stability, and asymptotic behavior, and illustrates its advantages and limitations through experiments.

Findings

Method produces a self-normalized pseudo-posterior.

Consistency and stability are formally established.

Experiments demonstrate computational efficiency and identification limits.

Abstract

We analyze a lightweight simulation-based inference method that infers simulator parameters using only a regression-based projection of the observed data. After fitting a surrogate linear regression once, the procedure simulates small batches at the proposed parameter values and assigns kernel weights based on the resulting batch-residual discrepancy, producing a self-normalized pseudo-posterior that is simple, parallelizable, and requires access only to the fitted regression coefficients rather than raw observations. We formalize the construction as an importance-sampling approximation to a population target that averages over simulator randomness, prove consistency as the number of parameter draws grows, and establish stability in estimating the surrogate regression from finite samples. We then characterize the asymptotic concentration as the batch size increases and the bandwidth shrinks, showing that the pseudo-posterior concentrates on an identified set determined by the chosen projection, thereby clarifying when the method yields point versus set identification. Experiments on a tractable nonlinear model and on a cosmological calibration task using the DREAMS simulation suite illustrate the computational advantages of regression-based projections and the identifiability limitations arising from low-information summaries.