h-calibration：基于概率误差有界目标重新思考分类器重校准
h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective
AI总结：
本文提出概率学习框架 h-calibration，通过构造误差有界的规范校准等价目标，设计简单事后校准算法，克服以往方法十大局限并在标准基准上取得最先进性能。
摘要：
深度神经网络在众多学习任务中展现了卓越的性能，但常常遭受校准不良（miscalibration）问题，导致概率输出不可靠。这激发了近期许多旨在缓解校准不良的工作，尤其是事后重校准（post-hoc recalibration）方法，这些方法力求在不牺牲预训练模型分类性能的前提下获得校准后的概率。在本研究中，我们将以往工作归纳为三类通用策略：直觉设计方法、基于分箱（binning）的方法以及基于理想校准形式化的方法。通过理论与实际分析，我们指出了以往方法中十个常见局限。为解决这些局限，我们提出了一种用于校准的概率学习框架，称为 h-calibration，该框架在理论上为具有有界性的规范校准（canonical calibration）构造了等价的学习形式化。在此基础上，我们设计了一种简单而有效的事后校准算法。我们的方法不仅克服了所识别的十个局限，而且通过大量实验验证，其性能显著优于传统方法。我们进一步从理论和实验两方面分析了我们的学习目标与传统 proper scoring rule 的关系及优势。总之，我们的概率框架推导出一个近似等价的、可微分的、用于学习误差有界校准概率的目标，阐明了计算统计量相对于规范校准中理论界限的对应关系与收敛性质。通过在标准事后校准基准上取得最先进性能，验证了其理论有效性。本研究为相关领域中学习可靠似然提供了有价值的参考。
英文摘要：
Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating miscalibration, particularly through post-hoc recalibration methods that aim to obtain calibrated probabilities without sacrificing the classification performance of pre-trained models. In this study, we summarize and categorize previous works into three general strategies: intuitively designed methods, binning-based methods, and methods based on formulations of ideal calibration. Through theoretical and practical analysis, we highlight ten common limitations in previous approaches. To address these limitations, we propose a probabilistic learning framework for calibration called h-calibration, which theoretically constructs an equivalent learning formulation for canonical calibration with boundedness. On this basis, we design a simple yet effective post-hoc calibration algorithm. Our method not only overcomes the ten identified limitations but also achieves markedly better performance than traditional methods, as validated by extensive experiments. We further analyze, both theoretically and experimentally, the relationship and advantages of our learning objective compared to traditional proper scoring rule. In summary, our probabilistic framework derives an approximately equivalent differentiable objective for learning error-bounded calibrated probabilities, elucidating the correspondence and convergence properties of computational statistics with respect to theoretical bounds in canonical calibration. The theoretical effectiveness is verified on standard post-hoc calibration benchmarks by achieving state-of-the-art performance. This research offers valuable reference for learning reliable likelihood in related fields.
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