Calibrating Deep Neural Network using Euclidean Distance

TL;DR

This paper proposes Focal Calibration Loss (FCL), a new loss function that improves probability calibration in deep neural networks by minimizing Euclidean distance, enhancing reliability without sacrificing accuracy.

Contribution

It introduces FCL, a novel loss function that combines calibration and classification objectives, validated theoretically and empirically on multiple models and datasets.

Findings

FCL outperforms existing calibration methods in accuracy and calibration metrics.

FCL effectively reduces calibration error while maintaining model performance.

Application to CheXNet demonstrates practical benefits in healthcare diagnostics.

Abstract

Uncertainty is a fundamental aspect of real-world scenarios, where perfect information is rarely available. Humans naturally develop complex internal models to navigate incomplete data and effectively respond to unforeseen or partially observed events. In machine learning, Focal Loss is commonly used to reduce misclassification rates by emphasizing hard-to-classify samples. However, it does not guarantee well-calibrated predicted probabilities and may result in models that are overconfident or underconfident. High calibration error indicates a misalignment between predicted probabilities and actual outcomes, affecting model reliability. This research introduces a novel loss function called Focal Calibration Loss (FCL), designed to improve probability calibration while retaining the advantages of Focal Loss in handling difficult samples. By minimizing the Euclidean norm through a strictly proper loss, FCL penalizes the instance-wise calibration error and constrains bounds. We provide theoretical validation for proposed method and apply it to calibrate CheXNet for potential deployment in web-based health-care systems. Extensive evaluations on various models and datasets demonstrate that our method achieves SOTA performance in both calibration and accuracy metrics.