Paper: arXiv 2505.19068

Authors: Dirk Tasche

Abstract

Recalibration of binary probabilistic classifiers to a target prior probability is an important task in areas like credit risk management. However, recalibration of a classifier learned on a training dataset to a target on a test dataset in general is not a well-defined problem because there might be more than one way to transform the original posterior probabilities such that the target is matched. In this paper, methods for recalibration are analysed from a distribution shift perspective. Distribution shift assumptions linked to the area under the curve (AUC) of a probabilistic classifier are found to be useful for the design of meaningful recalibration methods. Two new methods called parametric covariate shift with posterior drift (CSPD) and ROC-based quasi moment matching (QMM) are proposed and tested together with some other methods in an example setting. The outcomes of the test suggest that the QMM methods discussed in the paper can provide appropriately conservative results in evaluations with concave functions like for instance risk weights functions for credit risk.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous mathematical formalization of binary classifier recalibration under distribution shift, introducing two novel techniques (CSPD and ROC-based QMM). While the theoretical foundation and formulation are strong, the empirical evaluation is limited to stylized synthetic/example settings rather than extensive real-world credit backtests.

Research Flowchart

  flowchart TD
    A["Goal: Recalibrate Binary Classifiers to Target Prior Under Distribution Shift"] --> B["Data Inputs: Training Dataset & Test Dataset Target Prior"]
    B --> C["Framework Analysis: Analyze Recalibration via AUC & Distribution Shift Assumptions"]
    C --> D["Method Development: Propose CSPD & ROC-based Quasi Moment Matching (QMM)"]
    D --> E["Empirical Testing: Evaluate Methods in Credit Risk Example Setting"]
    E --> F["Key Outcome: QMM Provides Appropriately Conservative Results for Concave Risk Functions"]