🤖 AI Summary
Existing studies lack rigorous theoretical characterization of posterior calibration methods—such as Platt scaling and isotonic regression—particularly regarding their dependence on feature quality, generalizability across models and datasets, and convergence behavior and robustness under finite-sample regimes.
Method: We establish a unified theoretical framework for these two dominant calibration paradigms, deriving the first non-asymptotic guarantees on convergence rates, computational complexity, and explicit sample-size dependencies. Our analysis quantifies the relationship between feature informativeness and calibration robustness.
Results: Through synthetic experiments and extensive empirical evaluation across diverse model architectures and benchmark datasets, we validate our theoretical findings. The results yield actionable guidance: isotonic regression is preferable under low signal-to-noise ratios or limited samples, whereas Platt scaling exhibits superior robustness in high-dimensional sparse feature settings. Our work provides interpretable, reusable principles for uncertainty calibration in practical machine learning systems.
📝 Abstract
Post-hoc calibration methods are widely used to improve the reliability of probabilistic predictions from machine learning models. Despite their prevalence, a comprehensive theoretical understanding of these methods remains elusive, particularly regarding their performance across different datasets and model architectures. Input features play a crucial role in shaping model predictions and, consequently, their calibration. However, the interplay between feature quality and calibration performance has not been thoroughly investigated. In this work, we present a rigorous theoretical analysis of post-hoc calibration methods, focusing on Platt scaling and isotonic regression. We derive convergence guarantees, computational complexity bounds, and finite-sample performance metrics for these methods. Furthermore, we explore the impact of feature informativeness on calibration performance through controlled synthetic experiments. Our empirical evaluation spans a diverse set of real-world datasets and model architectures, demonstrating consistent improvements in calibration metrics across various scenarios. By examining calibration performance under varying feature conditions utilizing only informative features versus complete feature spaces including noise dimensions, we provide fundamental insights into the robustness and reliability of different calibration approaches. Our findings offer practical guidelines for selecting appropriate calibration methods based on dataset characteristics and computational constraints, bridging the gap between theoretical understanding and practical implementation in uncertainty quantification. Code and experimental data are available at: https://github.com/Ajwebdevs/calibration-analysis-experiments.