用结构化矩阵校准提升多分类概率准确性，解决过拟合问题。
Structured Matrix Scaling for Multi-Class Calibration
- 基于理论推导设计结构化矩阵校准方法
- 在有限数据下实现比温度/向量校准更优的性能
- 适合需要高可靠性概率输出的场景
事后校准方法广泛用于确保分类器提供可信的概率估计。我们指出，基于逻辑回归的参数化校准函数可从二元与多类分类的简单理论设定中自然推导得出，这启发了超越标准温度校准的更表达能力强的校准方法。然而，多类校准中复杂模型引入的大量参数常伴随校准数据有限，易导致过拟合。通过大量实验，我们证明通过结构化正则化、鲁棒预处理和高效优化可有效管理由此产生的偏差-方差权衡。所提方法相较现有基于逻辑回归的校准技术有显著提升。我们提供了高效且易用的开源实现，使其成为温度、向量和矩阵校准的有力替代方案。
原文摘要 · Abstract (English)
Post-hoc recalibration methods are widely used to ensure that classifiers provide faithful probability estimates. We argue that parametric recalibration functions based on logistic regression can be motivated from a simple theoretical setting for both binary and multiclass classification. This insight motivates the use of more expressive calibration methods beyond standard temperature scaling. For multi-class calibration however, a key challenge lies in the increasing number of parameters introduced by more complex models, often coupled with limited calibration data, which can lead to overfitting. Through extensive experiments, we demonstrate that the resulting bias-variance tradeoff can be effectively managed by structured regularization, robust preprocessing and efficient optimization. The resulting methods lead to substantial gains over existing logistic-based calibration techniques. We provide efficient and easy-to-use open-source implementations of our methods, making them an attractive alternative to common temperature, vector, and matrix scaling implementations.
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