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.

翻译：我们提出仿射射流序贯神经似然估计(SSNL)，这是一种用于似然函数不可计算、仅可通过模拟器生成合成数据的模型进行模拟推断的新方法。SSNL拟合一个降维的仿射射流归一化流模型，并作为替代似然函数，从而允许使用马尔可夫链蒙特卡罗方法或变分推断进行传统贝叶斯推断。通过将数据嵌入低维空间，SSNL解决了以往基于似然方法在高维数据集（例如包含非信息性数据维度或沿低维流形分布的数据集）中应用时存在的若干问题。我们在多种实验场景下评估SSNL，结果表明，在模拟推断领域，该方法普遍优于现有方法——例如在基于太阳发电机模型模拟太阳磁场强度的具有挑战性的天体物理学真实案例中。