We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not computed directly. The ISN uses a backend neural network that models a scalar function called the inferostatic potential $\varphi$. In addition, we introduce new strategies, respectively called Kernel Score Estimation (KSE) and Kernel Likelihood Ratio Estimation (KLRE), to learn the score and the likelihood ratio functions from simulated data. We illustrate the new techniques with some toy examples and compare to existing approaches in the literature. We mention en passant some new loss functions that optimally incorporate latent information from simulations into the training procedure.

翻译：我们提出了一种直观的、基于机器学习的方法来进行多参数推理，称为InferoStatic网络（ISN）方法，用于在概率密度可采样但无法直接计算的情况下对分数和似然比估计器进行建模。ISN使用一个后端神经网络来建模一个称为“静态势”$\varphi$的标量函数。此外，我们引入了分别称为核分数估计（KSE）和核似然比估计（KLRE）的新策略，以从模拟数据中学习分数和似然比函数。我们通过一些示例说明了这些新技术，并与文献中现有的方法进行了比较。我们顺便提到了一些新的损失函数，这些函数能够最优地将模拟中的潜在信息纳入训练过程。