Paper: arXiv 2506.06653

Authors: Dangxing Chen

Abstract

In recent years, machine learning models have achieved great success at the expense of highly complex black-box structures. By using axiomatic attribution methods, we can fairly allocate the contributions of each feature, thus allowing us to interpret the model predictions. In high-risk sectors such as finance, risk is just as important as mean predictions. Throughout this work, we address the following risk attribution problem: how to fairly allocate the risk given a model with data? We demonstrate with analysis and empirical examples that risk can be well allocated by extending the Shapley value framework.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper heavily relies on advanced mathematical frameworks like Shapley value axioms, characteristic functions, and theoretical proofs, resulting in high mathematical complexity. However, the empirical section is described generically with ‘analysis and empirical examples’ without specifying backtests, datasets, or implementation details, indicating low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Risk Attribution Problem: How to fairly allocate risk<br>given a model with data?"] --> B["Methodology<br>Extend Shapley Value Framework<br>(Axiomatic Attribution)"]
  B --> C["Input Data<br>Financial Model Predictions<br>Feature Datasets"]
  C --> D["Computational Process<br>Iterative Feature Combinations<br>Calculate Marginal Risk Contributions"]
  D --> E["Aggregation<br>Sum contributions via Shapley Formula<br>Ensure Efficiency & Symmetry"]
  E --> F["Key Outcomes<br>1. Fair Risk Allocation per Feature<br>2. Interpretable Risk Sensitivity<br>3. Validated on Financial Models"]
  F --> G["Conclusion<br>Risk accurately attributed<br>enhancing model interpretability in finance"]