Iterative Chow Filtering for Learning with Distribution Shift

2026-05-17

AI Summary

This work addresses the challenge of identifying and rejecting anomalous test samples under distribution shift by proposing an Iterative Chow Filtering mechanism based on low-degree Chow parameters, which efficiently filters out out-of-distribution samples when training and test distributions diverge. The key theoretical contribution is the first demonstration that a relatively weak L₁ sandwiching condition suffices for efficient Probably Quasi (PQ) learning, thereby overcoming prior reliance on stronger L₂ assumptions. By integrating Chow parameter estimation with distribution compatibility testing, the method yields the first quasipolynomial-time PQ learning algorithm for DNF formulas under the uniform distribution and achieves exponential improvements for function classes such as constant-depth circuits.

Abstract

Recent work due to Goel et al. gave the first efficient algorithms for learning with distribution shift in the challenging PQ framework. In this setting, a learner receives labeled training examples, unlabeled test examples, and must make correct predictions on the test set but is allowed to abstain from predicting on out-of-distribution points. Their results rely on ${\cal L}_2$ sandwiching approximations, a strong requirement that leads to poor bounds for several basic function classes such as DNF formulas. Here, we show that the weaker notion of ${\cal L}_1$ sandwiching suffices for efficient PQ learning. As a consequence, we obtain the first quasipolynomial-time PQ learning algorithm for DNFs under the uniform distribution and essentially match the guarantees known for ordinary PAC learning. More broadly, our bounds provide exponential improvements for several classes including constant depth circuits and constant degree polynomial threshold functions. Our main technical ingredient is Iterative Chow Filtering, a new procedure that uses low-degree Chow parameters to identify and remove test points incompatible with the training distribution.

Problem

• distribution shift
• PQ learning
• DNF formulas
• Chow parameters
• abstention

Innovation

• Iterative Chow Filtering
• distribution shift
• PQ learning
• L1 sandwiching
• Chow parameters