Conformal Prediction With Conditional Guarantees (2305.12616v4)

Abstract: We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most popular methods only guarantee marginal coverage over the covariates or are restricted to a limited set of conditional targets, e.g. coverage over a finite set of pre-specified subgroups. This paper bridges this gap by defining a spectrum of problems that interpolate between marginal and conditional validity. We motivate these problems by reformulating conditional coverage as coverage over a class of covariate shifts. When the target class of shifts is finite-dimensional, we show how to simultaneously obtain exact finite-sample coverage over all possible shifts. For example, given a collection of subgroups, our prediction sets guarantee coverage over each group. For more flexible, infinite-dimensional classes where exact coverage is impossible, we provide a procedure for quantifying the coverage errors of our algorithm. Moreover, by tuning interpretable hyperparameters, we allow the practitioner to control the size of these errors across shifts of interest. Our methods can be incorporated into existing split conformal inference pipelines, and thus can be used to quantify the uncertainty of modern black-box algorithms without distributional assumptions.

• The paper redefines conditional coverage across covariate shifts to achieve exact finite-sample guarantees in finite-dimensional cases.
• It develops an approach that integrates with split conformal inference, balancing prediction set size with coverage accuracy even when faced with infinite-dimensional shifts.
• It demonstrates the method’s practical utility on real datasets, enhancing reliability and fairness in predictive modeling for diverse applications.

Conformal Prediction with Conditional Guarantees

The paper "Conformal Prediction with Conditional Guarantees" addresses the challenge of constructing distribution-free prediction sets that ensure conditional accuracy in finite samples. The authors, Gibbs, Cherian, and Candès, investigate the limitations of existing methods that typically offer only marginal coverage guarantees or limited conditional coverage for pre-defined subgroups. This paper proposes a method to interpolate between marginal and conditional coverage, thereby extending the applicability of conformal prediction.

Key Contributions

1. Problem Formulation and Motivation: The authors redefine conditional coverage as a problem of coverage across a class of covariate shifts. This reformulation allows for the examination of prediction accuracy under different conditions, specifically focusing on shifts that are representable within a finite-dimensional space.
2. Methodological Advances: By identifying a finite-dimensional class of covariate shifts, the paper shows how exact finite-sample coverage can be achieved for these shifts. In cases with infinite-dimensional shifts, where exact coverage is theoretically unattainable, the paper presents methods to quantify coverage errors. This is achieved by using interpretable hyperparameters that allow practitioners to balance prediction set size with coverage accuracy.
3. Integration with Existing Frameworks: The proposed methods can be embedded into traditional split conformal inference pipelines. This integration implies that the technique can assess the uncertainty of modern black-box algorithms without relying on specific distributional assumptions.
4. Applications and Experimentation: The methodology is demonstrated on several datasets, including the Communities and Crime dataset and the RxRx1 dataset, showcasing the practical utility of the method in achieving robust coverage across various subgroups and experimental settings.

Technical Implications

• Balancing Marginal and Conditional Coverage: The methodology introduces a spectrum of problem formulations between marginal and conditional guarantees, providing a broader framework for predictive coverage analysis. This flexibility is crucial for applications needing precise performance guarantees across subpopulations, such as fairness in algorithmic decision-making.
• Compatibility with Machine Learning Models: By using conformity scores derived from the outputs of various machine learning models, the method enhances the coverage properties of these models. This approach is especially beneficial in high-stakes scenarios where accurate uncertainty quantification is critical, for instance in healthcare and criminal justice.
• Efficiency and Scalability: Through the use of efficient computation techniques, the paper ensures that the proposed approach is scalable to large datasets and complex models, making it practical for real-world applications where computational resources and time are limited.

Potential Impact and Future Directions

This research has the potential to significantly influence the development of robust predictive systems in machine learning. By providing tools for conditional coverage evaluation, it paves the way for more reliable and fair predictive modeling. In the future, further exploration into extending these methodologies to more complex, non-linear covariate shifts could widen their applicability. Additionally, the integration of these methods into automated machine learning workflows could democratize access to robust predictive techniques, bridging the gap between advanced statistical methods and practical, industry-scale deployments.

In summary, this paper presents a compelling advancement in conformal prediction methodologies, offering a nuanced approach to balance and achieve conditional guarantees in predictive modeling. Its implications for fairness, reliability, and robustness in machine learning are substantial, extending its relevance across many domains where precision and accountability are of utmost importance.