Source-linked AI summary
Linear unit-tests for invariance discovery
Benjamin Aubin, Agnieszka Słowik, Martin Arjovsky, Leon Bottou, David Lopez-Paz
TL;DR
The paper asks whether invariant-correlation algorithms practically support out-of-distribution generalization. It proposes six linear unit tests and finds that current causal-learning alternatives fail to pass them all, motivating standardized evaluation.
Problem
Current causal-learning algorithms aim to use correlations invariant across training distributions for out-of-distribution generalization, but their practical usefulness remains uncertain.
Method
The paper proposes six low-dimensional linear problems, including scrambled variants, to evaluate distinct out-of-distribution generalization abilities.
Results
No evaluated method performs close to the Oracle on the proposed problems, except IRMv1 and ANDMask on example1.
Takeaways & Limitations
The unit tests and replication code are intended as a transparent, standardized guide for developing and evaluating out-of-distribution generalization algorithms.
Takeaways & Limitations
Training-error-based invariance penalties such as IRM may accept solutions using spurious features when spurious correlations increase rapidly.
Abstract
from arXiv · showhide
There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The purpose of this note is to propose six linear low-dimensional problems -- unit tests -- to evaluate different types of out-of-distribution generalization in a precise manner. Following initial experiments, none of the three recently proposed alternatives passes all tests. By providing the code to automatically replicate all the results in this manuscript (https://www.github.com/facebookresearch/InvarianceUnitTests), we hope that our unit tests become a standard steppingstone for researchers in out-of-distribution generalization.
1 Introduction
Out-of-distribution failures motivate learning invariant correlations across environments, but spurious correlations are easier to learn and can undermine causal approaches. The paper responds with six linear unit tests targeting these failure modes.
- Machine learning systems can fail when deployment conditions differ from training conditions [Szegedy et al., 2013, Rosenfeld et al., 2018, Alcorn et al., 2019].
- Causal proposals seek correlations invariant across training distributions as proxies for out-of-distribution generalization [Peters et al., 2015, Arjovsky et al., 2019, Parascandolo et al., 2020].
- Spurious correlations are often easier to learn than invariant ones, as shown by green backgrounds predicting cows and beige landscapes predicting camels [Arjovsky et al., 2019].Least-effort learning can favor textures over the shapes defining the object.
- Predictors relying on distractor, shortcut, or bait correlations fail under novel conditions.
- The paper introduces six linear problems containing invariant and spurious correlations to test whether algorithms discard the latter and generalize beyond training conditions.It reports that empirical risk minimization absorbs spurious training correlations and that causal algorithms often fail to capture causal invariances.
2 Problems
The paper defines six low-dimensional linear problems that separate invariant from spurious correlations and test whether predictors generalize when shortcut features are disrupted.
- Dataset construction: Test splits shuffle spurious features across examples, so low error requires predictors to ignore shortcut correlations.Train and validation splits follow the structural equations, while test splits shuffle spurious features across examples.
- Dataset construction: The default problems use three environments, 10 total dimensions, and five invariant plus five spurious features, with 10^4 samples per environment.The invariant and spurious dimensions are each five in the default setting.
- Example 1: regression from causes and effects: Example 1 varies the effects of the target across environments while preserving the causes-to-target mapping, and IRM solves this regression problem.The construction uses environment-specific noise variances, including 0.1, 1.5, and 2 for the first three environments.
- Example 2: cows versus camels: Example 2 models cows and camels with invariant foreground information and environment-dependent background correlations, while invariant learning can require large weights.As feature dimension grows, spurious features increasingly permit zero training error, allowing training-error penalties such as IRM to accept spurious solutions.
- Example 3: small invariant margin: Example 3 combines a small-margin invariant classifier with changing large-margin spurious features, so spurious features alone can achieve zero population error while invariant features incur some error.The intended invariant solution may require sacrificing training error to generalize out of distribution.
- Scrambled variations: Scrambled variants apply one fixed random rotation across environments, requiring algorithms to learn a linear representation before identifying the desired invariance.This is why brute-force feature-selection methods such as ICP are not compared on the scrambled problems.
- Evaluation: Table 1 reports test errors for all algorithms, datasets, and environments, using MSE for Example 1 and Example 1s and classification error otherwise.The table uses (d_inv, d_spu, n_env) = (5, 5, 3).
3 Experiments
Experiments compare ERM, IRMv1, IGA, ANDMask, and an Oracle across six linear unit-tests, finding that current methods generally remain far from Oracle and respond differently to environments, scrambling, and spurious dimensions.
- 3.1 Default results: No method approaches Oracle on any proposed problem, except IRMv1 and ANDMask on example1.The results indicate that current causal learning algorithms fail to capture invariances even in low-dimensional linear settings.
- 3.2 Varying the number of environments: IGA generally performs no better than ERM, except on Example2, where increasing δenv improves it without improving scrambled Example2s.
- 3.2 Varying the number of environments: On Example1 and Example1s, ANDMask and IRMv1 approach Oracle, whereas on Example2 and Example2s, ERM outperforms them.
- 3.2 Varying the number of environments: ANDMask and IRMv1 approach optimality on Example3 when nenv ≃ dspu + 1, but scrambling collapses ANDMask while leaving IRMv1 unaffected.At this environment-to-spurious-dimension ratio, no invariant boundary can solve the problem using x_spu alone.
- 3.3 Varying the number of spurious dimensions: Adding spurious dimensions leaves ANDMask and IRMv1 stable on Example1 and Example1s, but IGA fails after one spurious feature; performance declines for all methods on Example3(s) and for δspu ≤ 1 on Example2(s).
4 Outlook
The paper proposes a battery of six synthetic unit-tests for evaluating distinct out-of-distribution generalization abilities. It invites researchers to use and extend them as a transparent, standardized benchmark for new algorithms.
- The unit-tests are designed to evaluate different types of out-of-distribution generalization in a precise, transparent, and standardized manner.