Learning Counterfactually Invariant Predictors

Francesco Quinzan, Cecilia Casolo, Krikamol Muandet, Yucen Luo, Niki Kilbertus

Abstract: Notions of counterfactual invariance (CI) have proven essential for predictors that are fair, robust, and generalizable in the real world. We propose graphical criteria that yield a sufficient condition for a predictor to be counterfactually invariant in terms of a conditional independence in the observational distribution. In order to learn such predictors, we propose a model-agnostic framework, called Counterfactually Invariant Prediction (CIP), building on the Hilbert-Schmidt Conditional Independence Criterion (HSCIC), a kernel-based conditional dependence measure. Our experimental results demonstrate the effectiveness of CIP in enforcing counterfactual invariance across various simulated and real-world datasets including scalar and multi-variate settings.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

The main improvements of the revised version in response to the reviewers’ comments:
- We added a summary of our main contributions in the introduction section.
- We improved clarity of the Definition 2.2 of counterfactual invariance, together with its relations to D-CI, a.s.-CI and F-CI from Fawkes & Evans, 2023 as well as the strength of our injectivity assumption.
- We clarified the distinction between our theoretical contributions and previous definitions/results we build upon, both in the main paper and in the appendix.
- We added an entire section in the appendix on the computational complexity and runtimes in Appendix F.7 and provide further pointers to how the computational efficiency could be improved.

Main updates after comments of reviewer sMhK:
- We added an additional appendix section (Related work Fawkes & Evans, 2023 - App. A).
- We added a clarification on the necessity of VCF in Sec. 3.5.
- We added further explanation on comparison with CF1 and PSCF at the end of Sec. 4.3.
- We added a paragraph on real-world applications for practitioners in the conclusions (Sec. 5).

Code: https://github.com/ceciliacasolo/CIP.git

Assigned Action Editor: ~Fabio_Stella1

Submission Number: 2317