Learning Invariant Representations for Algorithmic Fairness and Domain Generalization with Minimax Optimality

Conceitos essenciais

The core message of this work is to develop an invariant risk minimization framework, termed FAIRM, that can achieve both reliable domain generalization and algorithmic fairness in the out-of-distribution (OOD) setting, where the test data distribution differs from the training data distributions.

Resumo

The paper proposes a new invariant risk minimization framework, FAIRM, to address the challenges of domain generalization and algorithmic fairness in machine learning. The key idea is to learn invariant representations that capture the underlying relationships between features and the target variable, while excluding spurious associations that can lead to poor OOD performance and unfair predictions.
The authors first introduce a full-information FAIRM oracle, which is defined at the population level based on all environments. They show that this oracle has desirable properties for domain generalization and multi-calibration, a fairness criterion. To make this oracle practical, the authors then propose an empirical FAIRM that can be realized with finite samples, and provide theoretical guarantees on its OOD performance under mild assumptions.
The authors further adapt the empirical FAIRM to high-dimensional linear models and develop an efficient algorithm. They establish the minimax optimality of the proposed method for domain generalization and its asymptotic multi-calibration in this setting.
Numerical experiments on synthetic data and MNIST demonstrate the advantages of FAIRM over existing methods like Empirical Risk Minimization (ERM), Maximin, and conditional mean-based invariance.

Estatísticas

There exists a positive constant c such that the domain generalization risk of FAIRM is at least cρ smaller than that of ERM, Maximin, and conditional mean-based invariance.
Under certain conditions, the multi-calibration error of empirical FAIRM is bounded by a term that goes to 0 as the sample size increases.

Citações

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Principais Insights Extraídos De

FAIRM

by Sai Li,Linju... às arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01608.pdf

Perguntas Mais Profundas

How can the FAIRM framework be extended beyond linear models to handle more complex data structures and prediction tasks

To extend the FAIRM framework beyond linear models and handle more complex data structures and prediction tasks, several approaches can be considered:

Non-linear Models: Incorporating non-linear models such as neural networks or decision trees can capture more complex relationships in the data. By adapting the FAIRM constraints to these models, the framework can learn invariant representations in a non-linear feature space.

Feature Engineering: Introducing more sophisticated feature engineering techniques, such as kernel methods or deep feature extraction, can enhance the representation learning capabilities of FAIRM. This can help capture intricate patterns in the data that may not be linearly separable.

Ensemble Methods: Leveraging ensemble methods like boosting or bagging can combine multiple models trained using FAIRM to improve prediction performance. By aggregating the outputs of diverse models, the framework can handle diverse and complex data structures more effectively.

Regularization Techniques: Incorporating regularization techniques like L1 or L2 regularization can prevent overfitting and enhance the generalization capabilities of FAIRM in more complex scenarios. Regularization can help control the complexity of the model and improve its robustness.

What are the potential limitations or failure modes of the FAIRM approach, and how can they be addressed

While the FAIRM approach offers several advantages in learning invariant representations for algorithmic fairness and domain generalization, there are potential limitations and failure modes that need to be addressed:

Curse of Dimensionality: In high-dimensional spaces, the performance of FAIRM may deteriorate due to the increased complexity and sparsity of the data. Addressing this limitation may require dimensionality reduction techniques or more sophisticated feature selection methods.

Data Imbalance: FAIRM may struggle with imbalanced datasets, where certain subpopulations are underrepresented. Techniques such as oversampling, undersampling, or using different loss functions can help mitigate this issue.

Model Interpretability: The complex nature of some models used in FAIRM, especially non-linear models, can hinder interpretability. Incorporating explainable AI techniques or model-agnostic interpretability methods can enhance the transparency of the model's decisions.

Adversarial Attacks: FAIRM may be vulnerable to adversarial attacks that manipulate the input data to deceive the model. Robust optimization techniques and adversarial training can help improve the model's resilience against such attacks.

How can the insights from this work on invariant representation learning be applied to other areas of machine learning, such as transfer learning or causal inference

The insights from the FAIRM framework on invariant representation learning can be applied to other areas of machine learning, such as transfer learning and causal inference:

Transfer Learning: In transfer learning, understanding invariant features across different domains is crucial for transferring knowledge effectively. By leveraging the principles of invariant representation learning from FAIRM, transfer learning models can better generalize to new domains while preserving important features.

Causal Inference: In causal inference, identifying causal features that are invariant across different populations or interventions is essential for making reliable causal claims. By adopting the invariance principles of FAIRM, causal inference models can better distinguish between causal and spurious relationships in observational data.

Domain Adaptation: In domain adaptation, where the training and test data come from different distributions, learning invariant representations can help align the domains and improve the model's performance on unseen data. FAIRM's focus on invariance can be beneficial in addressing domain shift challenges in domain adaptation tasks.