Simulation-Based Inference with Quantile Regression
He Jia
We present Neural Quantile Estimation (NQE), a novel Simulation-Based
Inference (SBI) method based on conditional quantile regression. NQE
autoregressively learns individual one dimensional quantiles for each posterior
dimension, conditioned on the data and previous posterior dimensions. Posterior
samples are obtained by interpolating the predicted quantiles using monotonic
cubic Hermite spline, with specific treatment for the tail behavior and
multi-modal distributions. We introduce an alternative definition for the
Bayesian credible region using the local Cumulative Density Function (CDF),
offering substantially faster evaluation than the traditional Highest Posterior
Density Region (HPDR). In case of limited simulation budget and/or known model
misspecification, a post-processing broadening step can be integrated into NQE
to ensure the unbiasedness of the posterior estimation with negligible
additional computational cost. We demonstrate that the proposed NQE method
achieves state-of-the-art performance on a variety of benchmark problems.