Learning With Multi-Group Guarantees For Clusterable Subpopulations

Abstract: A canonical desideratum for prediction problems is that performance guarantees should hold not just on average over the population, but also for meaningful subpopulations within the overall population. But what constitutes a meaningful subpopulation? In this work, we take the perspective that relevant subpopulations should be defined with respect to the clusters that naturally emerge from the distribution of individuals for which predictions are being made. In this view, a population refers to a mixture model whose components constitute the relevant subpopulations. We suggest two formalisms for capturing per-subgroup guarantees: first, by attributing each individual to the component from which they were most likely drawn, given their features; and second, by attributing each individual to all components in proportion to their relative likelihood of having been drawn from each component. Using online calibration as a case study, we study a multi-objective algorithm that provides guarantees for each of these formalisms by handling all plausible underlying subpopulation structures simultaneously, and achieve an $O(T^{1/2})$ rate even when the subpopulations are not well-separated. In comparison, the more natural cluster-then-predict approach that first recovers the structure of the subpopulations and then makes predictions suffers from a $O(T^{2/3})$ rate and requires the subpopulations to be separable. Along the way, we prove that providing per-subgroup calibration guarantees for underlying clusters can be easier than learning the clusters: separation between median subgroup features is required for the latter but not the former.

• The paper introduces a multi-objective learning framework that delivers subgroup performance guarantees without needing to explicitly resolve the underlying cluster structure.
• It contrasts traditional 'cluster-then-predict' methods with an approach that reduces error rates from O(T^(2/3)) to O(T^(1/2)), requiring fewer samples for robust predictions.
• It applies multicalibration techniques on exponential family models, offering theoretical insights and practical implications for fairness and reliable AI deployment.

Learning With Multi-Group Guarantees For Clusterable Subpopulations

The paper "Learning With Multi-Group Guarantees For Clusterable Subpopulations" presents a sophisticated approach to handling performance guarantees across multiple subpopulations in machine learning models. The focus is on ensuring that prediction systems not only perform well on average but also provide guarantees for meaningful subgroups within a dataset.

Conceptual Framework

The authors propose a generative model that treats population data as a mixture model, where each component represents a subpopulation. This model allows for the identification of meaningful subpopulations based on the natural clusters that form within the dataset. Two key methods are introduced for providing guarantees per subgroup:

1. Discriminant Error: Each individual is attributed to the component they are most likely drawn from.
2. Likelihood Error: Each individual is attributed to components in proportion to their likelihood of being drawn from each.

Algorithmic Approach

The paper illustrates the inefficiencies of the traditional "Cluster-Then-Predict" paradigm, which often suffers from a $O(T^{2/3})$ error rate due to its reliance on first resolving the cluster structure explicitly. This approach requires a large sample size and clear separation between subpopulations.

Alternatively, the paper leverages a Multi-Objective Learning framework. Here, instead of resolving the precise underlying cluster structures, the authors construct a representative covering of plausible clusterings and provide guarantees for all of them simultaneously. This results in a more efficient $O(T^{1/2})$ error rate, thus demonstrating that achieving per-subgroup guarantees can be significantly easier than learning the cluster structure itself.

Technical Contributions

1. Subpopulation Identification: The authors explore subpopulation structures by focusing on statistically identifiable groups, contrasting with prior work that only considers computational identifiability.
2. Multicalibration for Subgroup Guarantees: They apply multicalibration algorithms to achieve calibration guarantees across multiple subgroups, efficiently managing the complexity of exploring various potential subgroup structures.
3. Applicability to Exponential Families: The theoretical framework is showcased using exponential family distributions, specifically Gaussian mixture models. The dimension of the sufficient statistic plays a crucial role in bounding the pseudodimension necessary for efficient learning and prediction.

Implications and Future Directions

The ability to provide guarantees for endogenous subpopulations without explicitly identifying them presents significant opportunities for advancing fairness, auditing, and accountability in machine learning systems. This approach is particularly relevant in scenarios where subgroup labels are unavailable or unreliable, making it appealing for practical applications in AI deployment.

Future work could explore extending this framework to more complex models and objectives within machine learning. Additionally, investigating the interplay between normative and statistical considerations in defining subgroup relevance could enrich the theoretical underpinnings of fair machine learning.

In summary, the paper presents a compelling framework for learning and prediction with multi-group guarantees, addressing both practical efficiency and theoretical robustness. This advancement offers meaningful insights into subgroup-oriented machine learning, paving the way for more equitable and reliable AI systems.