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.

翻译：我们提出神经分位数估计（NQE），一种基于条件分位数回归的新型仿真推断（SBI）方法。NQE通过自回归方式学习后验分布每个维度上的一维分位数，这些分位数以观测数据和先验后验维度为条件。通过使用单调三次埃尔米特样条对预测的分位数进行插值获取后验样本，并针对尾部行为和多峰分布进行特殊处理。我们引入基于局部累积密度函数（CDF）的贝叶斯可信区域替代定义，其评估速度显著快于传统最高后验密度区域（HPDR）。在仿真预算有限或已知模型设定偏差的情况下，可整合后处理扩展步骤至NQE，以极小的额外计算成本确保后验估计的无偏性。实验表明，所提出的NQE方法在多个基准问题上取得了最先进的性能。