Instance-Wise Monotonic Calibration by Constrained Transformation

TL;DR

This paper introduces a novel class of monotonic post-hoc calibration methods for neural network probabilities, ensuring interpretability, robustness, and state-of-the-art calibration performance through a constrained linear transformation approach.

Contribution

It proposes a family of monotonic calibration methods using a constrained linear transformation, addressing limitations of previous approaches in expressiveness and interpretability.

Findings

Achieves state-of-the-art calibration accuracy on multiple datasets.

Ensures monotonicity, interpretability, and robustness of calibration maps.

Outperforms existing methods in efficiency and effectiveness.

Abstract

Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted probabilities. A key desirable property of the calibration map is instance-wise monotonicity (i.e., preserving the ranking of probability outputs). However, most existing post-hoc calibration methods do not guarantee monotonicity. Previous monotonic approaches either use an under-parameterized calibration map with limited expressive ability or rely on black-box neural networks, which lack interpretability and robustness. In this paper, we propose a family of novel monotonic post-hoc calibration methods, which employs a constrained calibration map parameterized linearly with respect to the number of classes. Our proposed approach ensures expressiveness, robustness, and interpretability while preserving the relative ordering of the probability output by formulating the proposed calibration map as a constrained optimization problem. Our proposed methods achieve state-of-the-art performance across datasets with different deep neural network models, outperforming existing calibration methods while being data and computation-efficient. Our code is available at https://github.com/YunruiZhang/Calibration-by-Constrained-Transformation