mlsanityData to 7 Oct 2026

Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation

arXiv 2006.06979 ↗First posted 12 Jun 2020cs.LG cs.CV stat.MLcited by 43

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Abstract (arXiv)

Density ratio estimation (DRE) is at the core of various machine learning tasks such as anomaly detection and domain adaptation. In existing studies on DRE, methods based on Bregman divergence (BD) minimization have been extensively studied. However, BD minimization when applied with highly flexible models, such as deep neural networks, tends to suffer from what we call train-loss hacking, which is a source of overfitting caused by a typical characteristic of empirical BD estimators. In this paper, to mitigate train-loss hacking, we propose a non-negative correction for empirical BD estimators. Theoretically, we confirm the soundness of the proposed method through a generalization error bound. Through our experiments, the proposed methods show a favorable performance in inlier-based outlier detection.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jun 2020.

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Citing papers per year: 2021: 6; 2022: 4; 2023: 9; 2024: 5; 2025: 14; 2026: 5.

43 papers.

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  1. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Modelscited by 98
  2. 2023Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regressioncited by 17
  3. 2023Adapting to Continuous Covariate Shift via Online Density Ratio Estimationcited by 15
  4. 2021Deep Bregman Divergence for Contrastive Learning of Visual Representationscited by 13
  5. 2023Towards a Unified Analysis of Kernel-based Methods Under Covariate Shiftcited by 12
  6. 2025Dequantified Diffusion-Schr"odinger Bridge for Density Ratio Estimationcited by 11
  7. 2023Utility Theory of Synthetic Data Generationcited by 8
  8. 2023Computing high-dimensional optimal transport by flow neural networkscited by 8
  9. 2025Direct Bias-Correction Term Estimation for Average Treatment Effect Estimationcited by 8
  10. 2021Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimationcited by 7
  11. 2021Learning Causal Models from Conditional Moment Restrictions by Importance Weightingcited by 7
  12. 2021Meta-Learning for Relative Density-Ratio Estimationcited by 6
31 more
  1. 2023Federated Learning under Covariate Shifts with Generalization Guaranteescited by 6
  2. 2025Direct Density Ratio Optimization: A Statistically Consistent Approach to Aligning Large Language Modelscited by 6
  3. 2025Learning from positive and unlabeled examples -Finite size sample boundscited by 6
  4. 2025Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regressioncited by 6
  5. 2021A Unified Framework for Multi-distribution Density Ratio Estimationcited by 5
  6. 2024Overcoming Saturation in Density Ratio Estimation by Iterated Regularizationcited by 5
  7. 2025Projection Pursuit Density Ratio Estimationcited by 5
  8. 2025Direct Debiased Machine Learning via Bregman Divergence Minimizationcited by 5
  9. 2022Approximate Data Deletion in Generative Modelscited by 3
  10. 2023Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimationcited by 3
  11. 2026A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimationcited by 3
  12. 2021Estimation of Local Average Treatment Effect by Data Combinationcited by 2
  13. 2023Asymptotically Unbiased Synthetic Control Methods by Moment Matchingcited by 2
  14. 2024Meta-learning for Positive-unlabeled Classificationcited by 2
  15. 2024Binary Losses for Density Ratio Estimationcited by 2
  16. 2024Bounds on Lp errors in density ratio estimation via f-divergence loss functionscited by 2
  17. 2025A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regressioncited by 2
  18. 2025Riesz Regression As Direct Density Ratio Estimationcited by 2
  19. 2022Generalized Balancing Weights via Deep Neural Networkscited by 1
  20. 2023Automatic Debiased Learning from Positive, Unlabeled, and Exposure Datacited by 1
  21. 2024Alpha-divergence loss function for neural density ratio estimationcited by 1
  22. 2025Two-sample comparison through additive tree models for density ratioscited by 1
  23. 2022Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metricscited by 0
  24. 2025Learning from Double Positive and Unlabeled Data for Potential-Customer Identificationcited by 0
  25. 2025A Conditional Distribution Equality Testing Framework using Deep Generative Learningcited by 0
  26. 2025Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inferencecited by 0
  27. 2025Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contaminationcited by 0
  28. 2026genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regressioncited by 0
  29. 2026Relative Density Ratio Optimization for Stable and Statistically Consistent Model Alignmentcited by 0
  30. 2026AUC Maximization from Biased Positive-unlabeled Data with Confidencecited by 0
  31. 2026Importance Weighting for Unlabeled-unlabeled Learning under Distribution Shiftcited by 0