[Paper Review] An Empirical Study of Invariant Risk Minimization

Yo Joong Choe, Jiyeon Ham+1 more|arXiv (Cornell University)|Apr 10, 2020

Risk and Portfolio Optimization14 references21 citations

TL;DR

This paper empirically evaluates Invariant Risk Minimization (IRMv1), a framework for improving out-of-distribution generalization by learning predictors invariant across multiple training environments. It demonstrates that IRMv1 improves OOD performance when environments vary widely, learns approximately invariant representations under approximate invariance, and generalizes to text classification with spurious token-to-label correlations.

ABSTRACT

Invariant risk minimization (IRM) (Arjovsky et al., 2019) is a recently proposed framework designed for learning predictors that are invariant to spurious correlations across different training environments. Yet, despite its theoretical justifications, IRM has not been extensively tested across various settings. In an attempt to gain a better understanding of the framework, we empirically investigate several research questions using IRMv1, which is the first practical algorithm proposed to approximately solve IRM. By extending the ColoredMNIST experiment in different ways, we find that IRMv1 (i) performs better as the spurious correlation varies more widely between training environments, (ii) learns an approximately invariant predictor when the underlying relationship is approximately invariant, and (iii) can be extended to an analogous setting for text classification.

Motivation & Objective

• To empirically evaluate the effectiveness of IRMv1 in out-of-distribution (OOD) generalization across diverse training environments.
• To investigate whether IRMv1 can learn approximately invariant predictors when the underlying causal relationship is approximately invariant.
• To extend IRMv1 to natural language processing by constructing a text-based analog of ColoredMNIST with spurious token-to-label correlations.
• To compare IRMv1’s performance against ERM and baselines in both vision and text classification under controlled spurious correlation settings.
• To provide open-source code to support reproducibility and further research on IRM in multi-environment settings.

Proposed method

• Extends the ColoredMNIST benchmark by varying the degree of spurious correlation (color-to-digit association) across multiple training environments.
• Employs IRMv1, a practical algorithm that minimizes empirical risk plus a gradient penalty term to enforce invariance across environments.
• The gradient penalty term in IRMv1 approximates the condition that the classifier weights are optimal across all environments, promoting invariance.
• Applies the same framework to a text classification task using PunctuatedSST-2, where punctuation marks are used as spurious features correlated with labels.
• Uses a simple bag-of-words model with averaged word embeddings to isolate the effect of the IRMv1 penalty in NLP.
• Conducts hyperparameter search and evaluates models on held-out sets from training environments and an OOD environment with inverted spurious correlation.

Experimental results

Research questions

• RQ1 How does the diversity of spurious correlations across training environments affect IRMv1's OOD generalization performance?
• RQ2 Can IRMv1 learn an approximately invariant predictor when the underlying data-generating process is approximately invariant?
• RQ3 Can the IRMv1 framework be successfully extended to text classification tasks with spurious token-to-label correlations?
• RQ4 How does IRMv1 compare to ERM and oracle baselines in terms of OOD accuracy on both vision and text benchmarks?
• RQ5 What is the impact of varying the strength and direction of spurious correlations on model generalization in multi-environment settings?

Key findings

• IRMv1's OOD generalization performance improves as the spurious correlation varies more widely between training environments.
• IRMv1 learns an approximately invariant predictor when the underlying data-generating process is approximately invariant, as evidenced by consistent performance across environments.
• On the PunctuatedSST-2 text classification benchmark, IRMv1 achieves 61.4% OOD accuracy, nearly matching the oracle model’s 61.5% accuracy.
• ERM performs poorly on OOD data (30.4% accuracy) due to reliance on spurious correlations, while IRMv1 mitigates this by learning invariant representations.
• The IRMv1 penalty effectively reduces model dependence on spurious features in both vision and text tasks, demonstrating its generalizability beyond image classification.
• The results suggest that IRMv1 can be a viable approach for improving OOD generalization in real-world datasets with varying spurious correlations.