Skip to content

Estimating Implicit Expected Log Density Ratios

Avi Amalanshu Chandler Squires Yizhou Lu Pradeep Ravikumar
Oct 2026
Artificial Intelligence Machine Learning Data Science

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 na\"ively 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.

View source

Similar papers

#artificial intelligence Conference Open access Jun 2018

Gibson Env: Real-World Perception for Embodied Agents

This paper investigates developing real-world perception for active agents, proposes Gibson Environment for this purpose, and showcases a set of perceptual tasks learned therein.

F. Xia, Amir Zamir, Zhi-Yang He et al. · 1,069 citations · ⚡112
#computer vision Review Sep 2017

Agile Software Development Methods: Review and Analysis

This publication proposes a definition and a classification of agile software development approaches and analyses ten software development methods that can be characterized as being "agile" against the defined criterion.

P. Abrahamsson, O. Salo, Jussi Ronkainen et al. · 727 citations · ⚡54
#computer vision Jun 2008

The impact of agile practices on communication in software development

The study shows that agile practices improve both informal and formal communication, but indicates that, in larger development situations involving multiple external stakeholders, a mismatch of adequate communication mechanisms can sometimes even hinder the communication.

M. Pikkarainen, Jukka Haikara, O. Salo et al. · 401 citations · ⚡48
#machine learning Review Open access Oct 2014

Software development in startup companies: A systematic mapping study

The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.

Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al. · 394 citations · ⚡54

Diffusion models as plug-and-play priors

The possibility of inferring high-dimensional data inference in a model that consists of a prior and an auxiliary differentiable constraint given some additional information is considered, thereby allowing a range of potential applications in adapting models to new domains and tasks.

Alexandros Graikos, Esmeralda S. Whitammer, N. Jojic et al. · 316 citations · ⚡15

Related blog posts

We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.