arXiv cs.AI· Avi Amalanshu, Chandler Squires, Yizhou Lu, Pradeep Ravikumar·· 14 小时前AI 评分18
密度比估计新视角：期望对数密度比（ELDR）的估计方法与局限
Estimating Implicit Expected Log Density Ratios
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论文提出期望对数密度比（ELDR）概念，即在第三种测度下积分的对数密度比，并证明有限样本 ELDR 估计存在根本性限制，指出常规密度比估计（DRE）方法并不适用于 ELDR 任务。作者提出对部分 DRE 方法做简单修改，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。
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