[Paper Review] Improving model calibration with accuracy versus uncertainty optimization

Ranganath Krishnan, Omesh Tickoo|arXiv (Cornell University)|Dec 14, 2020

Adversarial Robustness in Machine LearningComputer Science49 references60 citations

TL;DR

The paper introduces AvUC, a differentiable accuracy versus uncertainty calibration loss, to train models to be confident on accurate predictions and uncertain on inaccurate ones, improving calibration under distributional shift, with a post-hoc AvUTS option.

ABSTRACT

Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. Uncertainty calibration is a challenging problem as there is no ground truth available for uncertainty estimates. We propose an optimization method that leverages the relationship between accuracy and uncertainty as an anchor for uncertainty calibration. We introduce a differentiable accuracy versus uncertainty calibration (AvUC) loss function that allows a model to learn to provide well-calibrated uncertainties, in addition to improved accuracy. We also demonstrate the same methodology can be extended to post-hoc uncertainty calibration on pretrained models. We illustrate our approach with mean-field stochastic variational inference and compare with state-of-the-art methods. Extensive experiments demonstrate our approach yields better model calibration than existing methods on large-scale image classification tasks under distributional shift.

Motivation & Objective

• Motivation: calibrated uncertainty is essential for safety-critical AI systems and robust decisions under dataset shift.
• Goal: develop a differentiable AvUC loss that ties accuracy and uncertainty to improve calibration without sacrificing accuracy.
• Aim: enable both training-time calibration (SVI-AvUC) and post-hoc calibration (AvUTS) for pretrained models.
• Approach: apply AvUC within a loss-calibrated inference framework and evaluate on large-scale image classification under distributional shift.

Proposed method

• Define AvU categories (AC, AU, IC, IU) to formalize accuracy and uncertainty relationships.
• Introduce differentiable AvU proxies and AvUC loss to optimize the AvU utility during training.
• Integrate AvUC as a penalty term in loss-calibrated ELBO (SVI-AvUC) with a weighting hyperparameter β.
• Provide a post-hoc calibration method (AvUTS) by optimizing AvUC via temperature scaling on pretrained models.
• Demonstrate applicability to mean-field stochastic variational inference and compare with baselines like Temp scaling, Ensembles, Dropout.

Experimental results

Research questions

• RQ1 Can a differentiable AvUC loss yield better calibrated uncertainties without sacrificing accuracy under distributional shift?
• RQ2 Does AvUC improve both in-distribution calibration and calibration under dataset shift across large-scale datasets?
• RQ3 Is post-hoc AvUTS competitive with training-time AvUC for pretrained models?
• RQ4 How does AvUC affect distributional shift detection and uncertainty-based evaluation metrics?

Key findings

• SVI-AvUC achieves better model calibration (lower ECE and UCE) than baselines under distributional shift while maintaining comparable accuracy to ensembles.
• SVI-AvUC improves confidence-accuracy relationships and uncertainty quality across multiple metrics on ImageNet and CIFAR10 under corrupted shifts.
• AvUTS provides post-hoc uncertainty calibration improvements over the baseline SVI and vanilla models, as shown by lower calibration errors.
• AvUC-based methods enhance distributional shift detection performance using predictive uncertainty, outperforming several competing methods.
• Table-like results indicate SVI-AvUC yields superior calibration and uncertainty metrics compared to Temp scaling, Dropout, and Enlightened Bayesian baselines across shift intensities.
• AVUC methods improve both calibrated confidence and uncertainty measures under distributional shift.