[Paper Review] Deep Anti-Regularized Ensembles provide reliable out-of-distribution uncertainty quantification

Antoine de Mathelin, François Deheeger+2 more|arXiv (Cornell University)|Apr 8, 2023

Adversarial Robustness in Machine Learning47 references4 citations

TL;DR

This paper proposes Deep Anti-Regularized Ensembles (DARE), a method that enhances out-of-distribution (OOD) uncertainty quantification in deep learning by penalizing small weights during training to increase output variance outside the training domain, while maintaining in-distribution accuracy via a dynamic loss control. DARE achieves state-of-the-art OOD detection performance without requiring OOD data or hyperparameter tuning.

ABSTRACT

We consider the problem of uncertainty quantification in high dimensional regression and classification for which deep ensemble have proven to be promising methods. Recent observations have shown that deep ensemble often return overconfident estimates outside the training domain, which is a major limitation because shifted distributions are often encountered in real-life scenarios. The principal challenge for this problem is to solve the trade-off between increasing the diversity of the ensemble outputs and making accurate in-distribution predictions. In this work, we show that an ensemble of networks with large weights fitting the training data are likely to meet these two objectives. We derive a simple and practical approach to produce such ensembles, based on an original anti-regularization term penalizing small weights and a control process of the weight increase which maintains the in-distribution loss under an acceptable threshold. The developed approach does not require any out-of-distribution training data neither any trade-off hyper-parameter calibration. We derive a theoretical framework for this approach and show that the proposed optimization can be seen as a "water-filling" problem. Several experiments in both regression and classification settings highlight that Deep Anti-Regularized Ensembles (DARE) significantly improve uncertainty quantification outside the training domain in comparison to recent deep ensembles and out-of-distribution detection methods. All the conducted experiments are reproducible and the source code is available at \url{https://github.com/antoinedemathelin/DARE}.

Motivation & Objective

• To address the critical limitation of deep ensembles producing overconfident predictions on out-of-distribution (OOD) data.
• To resolve the trade-off between increasing ensemble diversity for OOD regions and preserving accurate in-distribution predictions.
• To develop a method that enhances uncertainty quantification without relying on OOD training data or complex hyperparameter calibration.
• To provide a theoretically grounded, practical approach for reliable uncertainty estimation in real-world deep learning deployments.

Proposed method

• Introduces an anti-regularization term that penalizes small weights during training to promote large-weight networks.
• Employs a dynamic control process that activates weight increases only when the training loss remains above a threshold, ensuring in-distribution accuracy is preserved.
• Treats the optimization as a 'water-filling' problem, theoretically framing the balance between weight magnitude and generalization.
• Applies the method to fully-connected networks with piecewise linear activations, and extends it to residual networks by replacing the final layer with a DARE head.
• Uses mean squared error loss and logits-based uncertainty scores instead of softmax to preserve the effect of weight scaling on uncertainty.
• Employs a simple, scalable training protocol that does not require additional OOD data or validation-based hyperparameter tuning.

Experimental results

Research questions

• RQ1 Can anti-regularization of small weights improve out-of-distribution uncertainty quantification in deep ensembles?
• RQ2 How can ensemble diversity be increased outside the training domain without degrading in-distribution performance?
• RQ3 Can a dynamic weight control mechanism maintain training loss while promoting large weights and high output variance?
• RQ4 Does the proposed method outperform existing deep ensemble and OOD detection techniques without using OOD data or hyperparameter tuning?

Key findings

• DARE significantly improves OOD uncertainty quantification, reducing out-of-distribution NLL by 2.4 compared to standard deep ensembles on the camera-shift experiment.
• In the weather-shift experiment, DARE achieves the best ECE score, demonstrating superior calibration for OOD data.
• On CIFAR10 with Fashion-MNIST as OOD, DARE improves AUROC by 34 points compared to baseline deep ensembles, with only a 2-point drop in in-distribution accuracy.
• For Fashion-MNIST with SVHN as OOD, DARE achieves an 8-point AUROC improvement over the baseline, maintaining strong in-distribution performance.
• The method remains effective even when applied to a ResNet32 backbone by replacing the final layer with a DARE-optimized fully-connected head.
• Experiments show that setting λ=0 (no anti-regularization) leads to minimal weight increase, while λ=1 causes loss explosion, confirming the necessity of the dynamic control mechanism.