估计隐式期望对数密度比（ELDR）：arXiv 新研究揭示密度比估计方法的适用边界
Estimating Implicit Expected Log Density Ratios
AI 导读
一篇 arXiv 论文提出期望对数密度比（ELDR）概念，即在某种第三测度下积分的对数密度比，并指出许多隐式密度下朴素使用密度比估计（DRE）的问题实为 ELDR 估计任务。作者证明了有限样本 ELDR 估计的根本性限制，认为典型基于 DRE 的方法不适用，并提出对部分 DRE 方法的简单改进，使收敛到积分分布的样本可进入训练数据。基准测试显示该改进可降低 ELDR 估计误差。
正文 · 原文
Abstract: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.38151 [cs.LG] |
| (or arXiv:2610.38151v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.38151 arXiv-issued DOI via DataCite |
Submission history
From: Avi Amalanshu [view email]
[v1]
Wed, 28 Oct 2026 01:35:32 UTC (5,553 KB)
来源：arXiv cs.AI · arxiv.org