Improving Calibration and Robustness of Probability Estimates for Pre-trained Classifiers

Core Concepts

The core message of this article is that quantile-based probability estimates (QUANTPROB) can provide more robust and well-calibrated probabilities compared to the standard softmax probabilities, especially under distribution shifts and corruptions.

Abstract

The article addresses the problem of assigning meaningful probabilities to the predictions of a pre-trained classifier. The authors argue that the standard softmax probabilities often lack reliability and do not generalize well across small distortions.
To address this, the authors propose an innovative approach called QUANTPROB that leverages quantile regression techniques to construct quantile representations for any pre-trained classifier. The key idea is to establish a novel duality property between quantiles and probabilities, which allows them to compute quantile-based probabilities without modifying the original network.
The authors show that QUANTPROB preserves the calibration errors across distortions, unlike the standard softmax probabilities or post-hoc calibration techniques. Experiments on CIFAR10C and CIFAR100C datasets demonstrate that the expected calibration error (ECE) of QUANTPROB remains constant as the severity of corruptions increases, while the ECE of softmax probabilities degrades significantly.
The authors also discuss the limitations of trying to achieve minimal calibration error across all distributions, and highlight that the goal of having constant calibration error across distortions is a more practical and desirable property for real-world applications.

Stats

The calibration error of QUANTPROB remains constant across distortions, while the calibration error of softmax probabilities increases significantly as the severity of corruptions increases.
The accuracy of QUANTPROB is comparable to or better than softmax probabilities across different levels of corruption.

Quotes

"Between the choice of having a minimum calibration error on original distribution which increases across distortions or having a (possibly slightly higher) calibration error which is constant across distortions, we prefer the latter."
"Quantile probabilities (QUANTPROB), obtained from Quantile representations, preserve the calibration errors across distortions, since quantile probabilities generalize better than the naive Softmax probabilities."

Key Insights Distilled From

QuantProb: Generalizing Probabilities along with Predictions for a Pre-trained Classifier

by Aditya Chall... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2304.12766.pdf

Deeper Inquiries

What are the potential trade-offs between the constant calibration error property of QUANTPROB and other desirable properties like minimal calibration error or computational efficiency

One potential trade-off of the constant calibration error property of QUANTPROB is the compromise on achieving minimal calibration error. While constant calibration error across distortions provides stability and reliability in predictions, it may not always result in the lowest overall calibration error. This trade-off is important to consider depending on the specific requirements of the application. Additionally, maintaining constant calibration error may require more computational resources and complexity compared to approaches focused solely on minimizing calibration error. Therefore, there could be a trade-off between the simplicity and computational efficiency of the model and the constant calibration error property of QUANTPROB.

How can the QUANTPROB approach be extended to handle multi-class classification problems more effectively

To extend the QUANTPROB approach for multi-class classification problems, one can adapt the algorithm to handle multiple classes simultaneously. Instead of considering binary classification, the quantile representations can be generated for each class in a multi-class setting. This can be achieved by training separate quantile models for each class or by modifying the loss function to accommodate multiple classes. By incorporating the quantile representations for each class, the probabilities can be estimated more effectively for multi-class scenarios, ensuring robustness and calibration across different classes.

Are there any other applications or domains where the robustness and calibration properties of QUANTPROB could be particularly beneficial

The robustness and calibration properties of QUANTPROB can be beneficial in various applications and domains where reliable predictions and uncertainty quantification are crucial. One such domain is healthcare, where accurate predictions and reliable uncertainty estimates are essential for clinical decision-making. QUANTPROB can be applied in medical diagnosis, prognosis, and treatment planning to provide more trustworthy predictions and quantify the uncertainty associated with the predictions. Additionally, in financial services, QUANTPROB can be utilized for risk assessment, fraud detection, and investment decision-making to improve the reliability and accuracy of predictive models. Overall, the robustness and calibration properties of QUANTPROB can enhance the performance and trustworthiness of machine learning models in diverse real-world applications.