BAPE: Learning an Explicit Bayes Classifier for Long-tailed Visual Recognition

2025-06-29

AI Summary

To address gradient imbalance and suboptimal Bayesian decision-making in visual recognition under long-tailed class distributions, this paper proposes Bayesian Posterior Explicit Estimation (BAPE). BAPE abandons implicit probabilistic modeling and instead performs direct point estimation of posterior probability parameters, explicitly constructing a Bayes-optimal classifier. It is the first method to instantiate this paradigm in long-tailed learning. Crucially, BAPE introduces a distribution-adaptive mechanism that incurs no additional computational overhead, enabling generalization to test distributions with arbitrary imbalance factors. Orthogonal to existing approaches, BAPE requires no modification to backbone architectures. Extensive experiments on CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist demonstrate consistent and significant improvements in generalization performance across mainstream backbones—including ResNet and ResNeXt—while maintaining simplicity and efficiency.

Technology Category

• Machine Learning: Bayesian Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

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

Abstract

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by emph{implicitly} estimating the posterior probabilities, emph{e.g.}, by minimizing the Softmax cross-entropy loss. This simple methodology has been proven effective for meticulously balanced academic benchmark datasets. However, it is not applicable to the long-tailed data distributions in the real world, where it leads to the gradient imbalance issue and fails to ensure the Bayes optimal decision rule. To address these challenges, this paper presents a novel approach (BAPE) that provides a more precise theoretical estimation of the data distributions by emph{explicitly} modeling the parameters of the posterior probabilities and solving them with point estimation. Consequently, our method directly learns the Bayes classifier without gradient descent based on Bayes' theorem, simultaneously alleviating the gradient imbalance and ensuring the Bayes optimal decision rule. Furthermore, we propose a straightforward yet effective emph{distribution adjustment} technique. This method enables the Bayes classifier trained from the long-tailed training set to effectively adapt to the test data distribution with an arbitrary imbalance factor, thereby enhancing performance without incurring additional computational costs. In addition, we demonstrate the gains of our method are orthogonal to existing learning approaches for long-tailed scenarios, as they are mostly designed under the principle of emph{implicitly} estimating the posterior probabilities. Extensive empirical evaluations on CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist demonstrate that our method significantly improves the generalization performance of popular deep networks, despite its simplicity.

Problem

• Explicitly models posterior probabilities for long-tailed data
• Ensures Bayes optimal decision rule without gradient descent
• Adapts to arbitrary test distributions without extra cost

Innovation

• Explicitly models posterior probabilities parameters
• Directly learns Bayes classifier without gradient descent
• Proposes distribution adjustment for test data adaptation