Probabilistic Scores of Classifiers, Calibration is not Enough

TL;DR

This paper argues that traditional calibration metrics are insufficient for probabilistic predictions in binary classification, and demonstrates that optimizing KL divergence with tree-based models improves score alignment with true probabilities.

Contribution

It introduces a focus on optimizing distributional alignment via KL divergence, especially in tree-based models, over traditional calibration metrics.

Findings

Optimizing KL divergence improves score-probability alignment.

Traditional calibration metrics may lead to performance decline.

Tree-based models can be tuned to minimize distributional divergence.

Abstract

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to ensure alignment between predicted probabilities and actual outcomes. However, when score heterogeneity deviates from the underlying data probability distribution, traditional calibration metrics lose reliability, failing to align score distribution with actual probabilities. In this study, we highlight approaches that prioritize optimizing the alignment between predicted scores and true probability distributions over minimizing traditional performance or calibration metrics. When employing tree-based models such as Random Forest and XGBoost, our analysis emphasizes the flexibility these models offer in tuning hyperparameters to minimize the Kullback-Leibler (KL) divergence between predicted and true distributions. Through extensive empirical analysis across 10 UCI datasets and simulations, we demonstrate that optimizing tree-based models based on KL divergence yields superior alignment between predicted scores and actual probabilities without significant performance loss. In real-world scenarios, the reference probability is determined a priori as a Beta distribution estimated through maximum likelihood. Conversely, minimizing traditional calibration metrics may lead to suboptimal results, characterized by notable performance declines and inferior KL values. Our findings reveal limitations in traditional calibration metrics, which could undermine the reliability of predictive models for critical decision-making.