[Paper Review] Conformal Risk Control

Anastasios N. Angelopoulos, Stephen Bates+3 more|arXiv (Cornell University)|Aug 4, 2022

Statistical Methods in Clinical Trials25 citations

TL;DR

Extends conformal prediction to guarantee the expected risk for any monotone loss, with several distribution-shift and extension variants, plus practical NLP/CV examples.

ABSTRACT

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an $\mathcal{O}(1/n)$ factor. We also introduce extensions of the idea to distribution shift, quantile risk control, multiple and adversarial risk control, and expectations of U-statistics. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.

Motivation & Objective

• Motivate safe deployment by providing statistical guarantees on model post-processing outputs.
• Generalize conformal prediction to bound the expected value of monotone losses rather than just miscoverage.
• Develop a practical, tight algorithm for risk control with finite-sample guarantees.
• Explore extensions to distribution shift, quantile risk, multiple and adversarial risk, and U-statistics.

Proposed method

• Post-process model predictions via a parameterized family of conservative outputs C_lambda with a non-increasing loss L_i(lambda).
• Define the empirical risk R_hat_n(lambda) as the average of L_i(lambda) on calibration data and select lambda_hat to satisfy a risk-constraint-infimum condition (n/(n+1))R_hat_n(lambda)+(B/(n+1)) <= alpha.
• Prove that the chosen lambda_hat yields an expected risk E[L_{n+1}(lambda_hat)] <= alpha under monotone, right-continuous losses with bounded range.
• Show tightness of the risk bound, up to 2B/(n+1), under mild assumptions and discuss monotonicity requirements.
• Relate conformal risk control to standard conformal prediction when the loss is miscoverage, and discuss non-monotone-loss limitations.
• Provide extensions to distribution shift, quantile risk, multi-risk control, adversarial risks, and U-risk control.

Experimental results

Research questions

• RQ1 How can conformal prediction be generalized to guarantee the expected risk for monotone losses beyond miscoverage?
• RQ2 What is the tightness of the risk guarantee and under what conditions does the method hold or fail?
• RQ3 How can the approach be extended to handle distribution shift, quantile risk, multiple risks, and adversarial settings?
• RQ4 How does conformal risk control relate to and differ from classical conformal prediction in practice?
• RQ5 Can practical, real-world tasks in CV/NLP demonstrate effective risk control for non-binary losses?

Key findings

• The proposed conformal risk control guarantees that the expected loss on a new point is at most alpha for any bounded monotone loss function.
• The risk control bound is tight up to an O(1/n) factor, with a derived lower bound showing the limit of improvement.
• The framework subsumes standard conformal prediction when the loss is a miscoverage indicator.
• Extensions enable risk control under distribution shift, quantile risk, multiple risks, adversarial perturbations, and U-statistics.
• Worked examples across tumor segmentation, multilabel classification, hierarchical image classification, and open-domain QA demonstrate controlling FNR, graph distance, and token-level F1-score.