论文提出期望对数密度比（ELDR）估计新框架
Estimating Implicit Expected Log Density Ratios
搞生成建模或强化学习的朋友看看，密度比估计原来很多场景其实该用 ELDR 来做
arXiv 论文提出期望对数密度比（ELDR）概念，指出许多隐式密度问题虽然常用密度比估计（DRE）处理，实际属于 ELDR 估计任务。作者证明了有限样本下 ELDR 估计的根本性限制，并说明典型 DRE 方法并不适合 ELDR 估计。论文还提出对部分 DRE 方法的简单修改，让收敛到积分分布的样本进入训练数据，基准测试显示可降低 ELDR 估计误差。
Estimating Implicit Expected Log Density Ratios
When exact probabilities cannot be computed, \emph{density ratio estimation (DRE)} is a key subroutine in the wide range of applications where density ratios appear, from experimental design to generative modelling and reinforcement learning. In this paper, we introduce the concept of an \emph{expected log density ratio (ELDR)}: log density ratios that are integrated under some third, possibly distinct measure. We show many problems with implicit densities where DRE is naïvely used are actually ELDR estimation tasks, and prove fundamental limitations on finite-sample ELDR estimation. Based on these results, we argue that the typical DRE-based approaches are unsuitable for ELDR estimation, and provide some foundational motivation towards bespoke ELDR estimators. To demonstrate, we propose a simple modification to some DRE methods that allows samples convergent to the integral distribution to appear in training data. We show through benchmarks that this can improve ELDR estimation error.