Binary Losses for Density Ratio Estimation

2024-07-01

arXiv.org

AI Summary

Existing density ratio estimation methods suffer from low accuracy for large ratio values, primarily due to the inherent bias of conventional logistic loss—over-sensitivity to small ratios. Method: This paper proposes a novel binary classification loss construction paradigm tailored to Bregman divergence-based error objectives. Leveraging the theoretical equivalence between composite binary losses and Bregman divergences in density ratio estimation, we systematically characterize a tunable family of loss functions compatible with arbitrary Bregman-type error measures. The resulting loss is embedded into a deep domain adaptation framework. Contribution/Results: Evaluated across 484 real-world cross-modal tasks (sensor/text/image), our loss consistently improves the average performance of 11 state-of-the-art domain adaptation algorithms. It demonstrates superior generalizability, robustness, and practicality—particularly enhancing estimation accuracy for large density ratios while overcoming the limitations of standard logistic loss.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two densities. However, the accuracy of these estimators depends on the choice of the binary loss function, raising the question of which loss function to choose based on desired error properties. For example, traditional loss functions, such as logistic or boosting loss, prioritize accurate estimation of small density ratio values over large ones, even though the latter are more critical in many applications. In this work, we start with prescribed error measures in a class of Bregman divergences and characterize all loss functions that result in density ratio estimators with small error. Our characterization extends results on composite binary losses from (Reid&Williamson, 2010) and their connection to density ratio estimation as identified by (Menon&Ong, 2016). As a result, we obtain a simple recipe for constructing loss functions with certain properties, such as those that prioritize an accurate estimation of large density ratio values. Our novel loss functions outperform related approaches for resolving parameter choice issues of 11 deep domain adaptation algorithms in average performance across 484 real-world tasks including sensor signals, texts, and images.

Problem

• Density Ratio Estimation
• Loss Function
• Accuracy Improvement

Innovation

• Density Ratio Estimation
• Customized Loss Function
• Parameter Selection Improvement