CAS: A General Algorithm for Online Selective Conformal Prediction with FCR Control

Core Concepts

Developing the CAS algorithm for online selective conformal prediction to control FCR in real-time predictive tasks.

Abstract

The article introduces the CAS algorithm for online selective conformal prediction to control the false coverage-statement rate (FCR) in real-time predictive tasks. It addresses the issue of temporal multiplicity in selected prediction intervals and provides a framework that ensures exact selection-conditional coverage guarantee. The algorithm wraps around any prediction model and online selection rule to output post-selection prediction intervals, achieving distribution-free regimes. Numerical results confirm the effectiveness of CAS in controlling FCR and narrowing prediction intervals. Abstract: Study on post-selection predictive inference in an online fashion. Importance of controlling real-time FCR in online predictive tasks. Introduction: Real-time selection before prediction allocation. Utilization of conformal inference for valid confidence intervals. Methodology: Development of CAS algorithm for adaptive selection. Calibration set construction based on historical data. Results: CAS achieves exact selection-conditional coverage guarantee. Control of real-time FCR below target level without distribution assumptions. Applications: Illustrative application in drug discovery using machine learning tools. Related Work: Comparison with existing methods like LORD-CI and e-LOND-CI. Conclusion: Organization of paper sections and technical proofs provided in Supplementary Material.

Stats

"Since training large-scale machine learning models is time-consuming, we consider that one pre-trained model bµ is given in this work." "We provide tractable constructions for the calibration set for popular online selection rules." "CAS can achieve an exact selection-conditional coverage guarantee in the finite-sample and distribution-free regimes." "For decision-driven selection rules, we prove that CAS can exactly control the real-time FCR below the target level without any distributional assumption." "For the selection with symmetric thresholds, we also provide an upper bound for the real-time FCR value under mild stability condition on the selection threshold." "To deal with the distribution shift in online data, we adjust the level of prediction intervals whenever the selection happens by leveraging past feedback at each step."

Quotes

Key Insights Distilled From

CAS

by Yajie Bao,Yu... at arxiv.org 03-13-2024

https://arxiv.org/pdf/2403.07728.pdf

Deeper Inquiries

How does CAS compare to other existing algorithms for controlling FCR

CAS outperforms other existing algorithms for controlling FCR in several ways. Firstly, CAS provides a distribution-free framework that can achieve an exact selection-conditional coverage guarantee in both decision-driven selection and online selection with symmetric thresholds. This is a significant advantage as it eliminates the need for stringent distributional assumptions on the data, making CAS more versatile and applicable to various practical tasks without prior knowledge of data distribution. Secondly, CAS can effectively control the real-time FCR below the target level without any distributional assumptions for decision-driven selection rules, which is crucial for maintaining accurate predictive intervals while minimizing miscoverage errors. Additionally, by embedding CAS into dynamic conformal prediction methods like DtACI, long-run FCR control can be achieved with properly chosen parameters under arbitrary distribution shifts.

What are potential limitations or challenges when applying CAS to different datasets or scenarios

When applying CAS to different datasets or scenarios, there are potential limitations or challenges that may arise. One challenge could be related to the assumption of exchangeability between historical decisions and current selections when using full holdout sets. If this assumption does not hold due to complex dependencies between past decisions and new data points, it may impact the accuracy of FCR control using non-adaptive selection strategies. Another limitation could stem from variations in dataset characteristics such as feature distributions or noise levels across different scenarios. These variations might require adjustments or fine-tuning of parameters within CAS to ensure optimal performance and reliable FCR control.

How can insights from this study be applied to improve other areas beyond predictive inference

Insights from this study can be applied beyond predictive inference to improve other areas such as online multiple-testing procedures or adaptive learning algorithms. For instance, the concept of selective conformal prediction introduced in CAS could be extended to enhance error rate controls in online multiple-testing problems where sequential hypothesis testing is involved. By incorporating adaptive calibration techniques similar to those used in CAS, researchers can develop more robust methodologies for managing false discovery rates while accounting for temporal multiplicity issues arising from sequential testing processes.