Minimax Regret Learning for Data with Heterogeneous Subgroups (2405.01709v1)

Abstract: Modern complex datasets often consist of various sub-populations. To develop robust and generalizable methods in the presence of sub-population heterogeneity, it is important to guarantee a uniform learning performance instead of an average one. In many applications, prior information is often available on which sub-population or group the data points belong to. Given the observed groups of data, we develop a min-max-regret (MMR) learning framework for general supervised learning, which targets to minimize the worst-group regret. Motivated from the regret-based decision theoretic framework, the proposed MMR is distinguished from the value-based or risk-based robust learning methods in the existing literature. The regret criterion features several robustness and invariance properties simultaneously. In terms of generalizability, we develop the theoretical guarantee for the worst-case regret over a super-population of the meta data, which incorporates the observed sub-populations, their mixtures, as well as other unseen sub-populations that could be approximated by the observed ones. We demonstrate the effectiveness of our method through extensive simulation studies and an application to kidney transplantation data from hundreds of transplant centers.

• The paper introduces a minimax regret framework that optimizes worst-case performance across diverse subgroups.
• It formulates loss functions specific to each subgroup and minimizes maximum empirical regret to enhance fairness.
• Real-world tests, including kidney transplantation data, demonstrate improved prediction accuracy and equitable outcomes.

Exploring Minimax Regret Learning in AI Models Across Heterogeneous Sub-Populations

What is Minimax Regret Learning?

Minimax Regret Learning (MMR) refines the approach of training AI models to adapt more effectively across various sub-populations in a dataset, especially when these groups possess inherent variations. Conventional learning methods often aim to minimize the average loss across the entire dataset, which can lead to suboptimal performance on minority groups within the data. MMR shifts the focus towards minimizing the maximum regret, which essentially is about reducing the worst-case scenario losses. This method is particularly valuable when dealing with high-stakes applications such as healthcare and criminal justice where performance equity across groups is crucial.

The Mechanics of MMR

The paper presents a detailed formulation for implementing MMR in a structured learning environment. Here’s a simplified breakdown:

• Formulate Loss Functions: For each data point in the various groups, a loss function dependent on a changeable parameter $\theta$ is defined.
• Compute Empirical Regret: Calculate the regret for each sub-population, which evaluates the difference in risk between using the parameter $\theta$ and the best possible parameter for that specific subgroup.
• Optimize for Worst-Case: The final learning objective becomes minimizing the maximum regret across all subgroups, thus ensuring that the model performs as well as possible in the worst-performing group.

Practical Implications

Strength in Diverse Applications

Rigorously tested through simulations and an application to kidney transplantation data, MMR exhibited consistent strengths:

• Robustness: It offers robust performance, particularly effective in handling outliers or groups with extreme characteristics which are often overlooked.
• Fairness: By focusing on minimizing regrets across groups, MMR inherently aims at equity, making it suitable for domains requiring fairness.

Handling Real-World Heterogeneity

For diseases like chronic kidney disease, patients and treatment effects can significantly vary across different demographics and clinical settings. MMR can harness this heterogeneity, providing a unique tool that can potentially yield better and more fair treatment outcomes across diverse patient sub-populations.

Diving into Specifics with an Example: Kidney Transplantation

The application of MMR to kidney transplantation showcased its efficacy in a real-world healthcare setting involving multiple transplant centers, with varying patient outcomes and treatment efficacies. The results indicated not only improved prediction of patient outcomes but also highlighted MMR's robustness to data perturbations such as measurement errors and inherent data biases among different centers.

Looking Forward: Broader Applications and Extensions

The potential extensions of MMR are vast:

• Broader Medical Applications: Extending beyond transplantation to other areas with similar needs for equity and robustness, such as oncology or chronic disease management.
• Policy Making: In domains like criminal justice or welfare, where decisions critically impact human lives, applying MMR could lead to more equitable outcomes.
• Algorithm Development: Addressing non-convex or non-smooth loss functions could expand MMR's usability further across various machine learning applications.

Conclusion

MMR represents a significant step forward in making learning algorithms not only more accurate on average but also fairer and more robust on an individual group level. As datasets and applications become increasingly complex and heterogeneous, such approaches will be crucial in ensuring that AI systems perform equitably across all spectrums of society.