![[2506.10572] Probability Bounding: Post-Hoc Calibration via Box-Constrained Softmax](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2506.10572] Probability Bounding: Post-Hoc Calibration via Box-Constrained Softmax
Summary
The paper introduces Probability Bounding (PB), a novel post-hoc calibration method that uses Box-Constrained Softmax to improve the calibration of neural network probabilities, addressing issues of underconfidence and overconfidence.
Why It Matters
Accurate probability calibration in neural networks is essential for reliable decision-making in various applications. This research provides a new method that enhances the reliability of model predictions, which is crucial for fields like healthcare, finance, and autonomous systems.
Key Takeaways
- Probability Bounding (PB) improves calibration of neural network outputs.
- Introduces Box-Constrained Softmax (BCSoftmax) for better probability bounds.
- Demonstrates effectiveness on four real-world datasets, reducing calibration errors.
- Provides theoretical guarantees for the proposed methods.
- Python implementation available for practical use.
Statistics > Machine Learning arXiv:2506.10572 (stat) [Submitted on 12 Jun 2025 (v1), last revised 23 Feb 2026 (this version, v2)] Title:Probability Bounding: Post-Hoc Calibration via Box-Constrained Softmax Authors:Kyohei Atarashi, Satoshi Oyama, Hiromi Arai, Hisashi Kashima View a PDF of the paper titled Probability Bounding: Post-Hoc Calibration via Box-Constrained Softmax, by Kyohei Atarashi and 3 other authors View PDF HTML (experimental) Abstract:Many studies have observed that modern neural networks achieve high accuracy while producing poorly calibrated probabilities, making calibration a critical practical issue. In this work, we propose probability bounding (PB), a novel post-hoc calibration method that mitigates both underconfidence and overconfidence by learning lower and upper bounds on the output probabilities. To implement PB, we introduce the box-constrained softmax (BCSoftmax) function, a generalization of Softmax that explicitly enforces lower and upper bounds on the output probabilities. While BCSoftmax is formulated as the solution to a box-constrained optimization problem, we develop an exact and efficient algorithm for computing BCSoftmax. We further provide theoretical guarantees for PB and introduce two variants of PB. We demonstrate the effectiveness of our methods experimentally on four real-world datasets, consistently reducing calibration errors. Our Python implementation is available at this https URL. Comments: Subjects: Machine Learning (stat...
