Density Ratio Estimation

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Density ratio estimation learns how likely an example is under one distribution relative to another, making it possible to reweight data or compare distributions without modeling each one fully. Approaches include classifier-based and variational estimation, kernel and spectral methods, and newer score-, flow-, and Stein-based techniques. Ratios are used for covariate-shift adaptation, importance-weighted evaluation and conformal prediction, offline reinforcement learning, simulation-based inference, and data selection for model alignment. A central tension is that accurate ratios can be hard to estimate when distributions differ greatly, while clipping or regularization improves stability but may introduce bias or weaken guarantees.

Latest papers

26 papers4 papers in the last four weeks, up 33% on the four weeks before. 0.0% of all new papers.

Backward Conformal Prediction under Covariate Shift
Oct 12, 2026Amin Meghrazi, Yuanyuan LiConformal Prediction Weighted Conformal Prediction
The Ohio State University · Munich RE
Density Ratio Estimation with Stein Displacement Fields
Oct 8, 2026Song LiuDensity Ratio Estimation Distribution Shift
University of Bristol
Learning What to Forget: Distributional Unlearning for LLM Representation Spaces
Sep 30, 2026Pinaki Mohanty, Haoran Tang, Maggie Makar +1Density Ratio Estimation Machine Unlearning
Department of Computer Science, College of Science & College of Engineering, Purdue University, West Lafayette, IN, USA · Computer Science and Engineering Division, University of Michigan, Ann Arbor, MI, USA
Learning Conditional Expectation Operators via Functional Newton Updates
Sep 28, 2026Thiago Ramos, Alek Fröhlich, Daniel Perazzo +1Density Ratio Estimation Low-Rank Approximation
Federal University of São Carlos · CSML, Istituto Italiano di Tecnologia and University of Genoa · CSML, Istituto Italiano di Tecnologia and University College London
Density-Ratio Rescoring for Imbalanced Classification Using Raking Duals and Classifier Scores
Sep 20, 2026Dongha Kim, Seunghwan ParkClass-Imbalanced Learning Density Ratio Estimation
School of Mathematics, Statistics and Data Science, Sungshin Women’s University, 2, Bomun-ro 34da-gil, Seongbuk-gu, Seoul, 02844, Republic of Korea · Department of Information Statistics, Kangwon National University, 1, Kangwondaehak-gil, Chuncheon-si, Gangwon-do, 24341, Republic of Korea
Turn-level Multiscale Density Ratio Estimation for LLM Agents
Sep 15, 2026Zishuo Zhao, Kai Chen, Ao Li +1LLM Agent Training LLM Alignment
Alibaba Group
Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression
Sep 14, 2026Ren-Rui Liu, Zheng-Chu GuoKernel Regression Distribution Shift
School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China
When Can Conditional Flow Matching Replace Pointwise Negative Log-Likelihood?
Aug 28, 2026Yansen Han, Hongxin Sun, Tao LinFlow Matching Conditional Flow Matching
Zhejiang University · Westlake University · Fudan University
Fitted Occupancy-Ratio Evaluation without Bellman Completeness
Jul 6, 2026Lars van der Laan, Nathan KallusOff-Policy Evaluation Offline RL
Stanford University · Netflix · Cornell University
Sampling Bias Compensation for Robust Evaluation of Audio Classification Systems with Partially Labeled Evaluation Datasets
Jul 5, 2026Javier Naranjo-Alcazar, Annamaria Mesaros, Tuomas Virtanen +1Importance Sampling Density Ratio Estimation
Instituto Tecnologico de Informatica (ITI), Valencia, Spain · Tampere University, Tampere, Finland
Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model
Jul 2, 2026Francis BachSpectral Regularization Density Ratio Estimation
SIERRA · Inria - Ecole Normale Sup´erieure PSL Research University
Causal Density Functions
May 30, 2026Sridhar MahadevanCausal Effect Estimation Density Ratio Estimation
Research Professor, University of Massachusetts, Amherst · Adobe Research San Jose, CA
Density-Ratio Losses for Post-Hoc Learning to Defer
May 19, 2026Alexander Soen, Ragnar Thobaben, Joakim Jaldén +1Learning to Defer Density Ratio Estimation
KTH⋄ · Google Research†
Anytime PAC-Bayes for Constrained Density-Ratio Networks under Covariate Shift
May 17, 2026Paulo Akira F. Enabe, Rodrigo ProvasiPAC-Bayesian Generalization Bounds Domain Adaptation
Escola Politénica University of São Paulo Department of Structural and Geotechnical Engineering
TokenRatio: Principled Token-Level Preference Optimization via Ratio Matching
May 12, 2026Truong Nguyen, Tien-Phat Nguyen, Linh Ngo Van +3Pairwise Preference Learning LLM Alignment
Hanoi University of Science and Technology · University of Stuttgart · German Research Center for Artificial Intelligence +3
Adaptive TD-Lambda for Cooperative Multi-agent Reinforcement Learning
May 12, 2026Yue Deng, Zirui Wang, Yin ZhangTemporal-Difference Learning Density Ratio Estimation
1Zhongguancun Academy, Beijing, China · College of Computer Science and Technology, Zhejiang University
A Spectral Framework for Closed-Form Relative Density Estimation
May 11, 2026Francis BachDensity Ratio Estimation Spectral Methods
SIERRA · Inria - Ecole Normale Supérieure · PSL Research University
Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts
May 3, 2026James Wang, Surbhi GoelDistribution Shift Robustness Weighted Conformal Prediction
Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA 19104, USA.
LatentDiff: Scaling Semantic Dataset Comparison to Millions of Images
Apr 28, 2026James Flora, Kowshik Thopalli, Akshay R. Kulkarni +2Distribution Shift Distribution Shift Detection
School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon, USA · Lawrence Livermore National Laboratory, Livermore, California, USA · University of California San Diego, California, USA
One-Step Score-Based Density Ratio Estimation
Apr 12, 2026Wei Chen, Qibin Zhao, John Paisley +2Density Ratio Estimation Efficient Inference
School of Mathematics, South China University of Technology, Guangzhou 510006, China · Tensor Learning Team, RIKEN Center for Advanced Intelligence Project, Tokyo 103-0027, Japan · Department of Electrical Engineering, Columbia University, New York, NY 10027, USA +1
Time-Series Classification with Multivariate Statistical Dependence Features
Apr 8, 2026Yao Sun, Bo Hu, Jose PrincipeMultivariate Time Series Classification Density Ratio Estimation
Department of Electrical and Computer Engineering, University of Florida, Gainesville, USA
Relative Density Ratio Optimization for Stable and Statistically Consistent Model Alignment
Apr 6, 2026Hiroshi Takahashi, Tomoharu Iwata, Atsutoshi Kumagai +4LLM Alignment Preference Alignment
NTT, Inc. · NTT DOCOMO, INC.
Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation
Mar 31, 2026Ren-Rui Liu, Jun Fan, Lei Shi +1Density Ratio Estimation Statistical Learning Theory
School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China · Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong · School of Mathematical Sciences and Shanghai, Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China
Conditional Neural Bayes Ratio Estimation for Experimental Design Optimisation
Mar 27, 2026S. A. K. Leeney, T. Gessey-Jones, W. J. Handley +3Bayesian Experimental Design Simulation-Based Inference
Cavendish Astrophysics, University of Cambridge, Cambridge CB3 0HE, UK. · Kavli Institute for Cosmology, University of Cambridge, Cambridge CB3 0HA, UK. · PhysicsX, London, UK. +1
Towards Reliable Simulation-based Inference
Mar 9, 2026Arnaud DelaunoySimulation-Based Inference Probability Calibration
Department of Electrical Engineering and Computer Science, Faculty of Applied Sciences
Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics
Feb 27, 2026Egor Antipov, Alessandro Palma, Lorenzo Consoli +3Density Ratio Estimation
Institute of Computational Biology, Helmholtz Munich · School of Computation Information and Technology, Technical University of Munich · Munich Center for Machine Learning (MCML) +2

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Backward Conformal Prediction under Covariate Shift

Amin Meghrazi, Yuanyuan Li

The Ohio State University · Munich RE

Conformal Prediction Weighted Conformal Prediction Covariate Shift Density Ratio Estimation

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Backward conformal prediction (BCP) fixes the size of a prediction set and estimates its miscoverage, but assumes calibration and test data are exchangeable. We extend BCP to covariate shift through importance weighting, preserving its guarantees when the density ratio is known. We show that BCP's tight miscoverage report depends only on the relative weight assigned to missed calibration examples, explaining why a better domain classifier can sometimes produce a worse estimate. Motivated by the fact that BCP depends only on nonconformity scores, we propose estimating density ratios on sorted score vectors rather than high-dimensional inputs. We prove that this approach recovers the same report asymptotically under an interpretable condition and characterize the resulting bias otherwise. Experiments with simulated and benchmark distribution shifts show that the proposed method improves BCP's miscoverage estimates, while score-based weighting consistently yields more accurate estimates than embedding-based weighting.