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Conformal Prediction Sets Quantify Information Gain: A Theoretical Perspective
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arXiv Machine Learning
Oct 7
Conformal Prediction Sets Quantify Information Gain: A Theoretical Perspective
Conformal prediction sets, which provide finite‑sample coverage guarantees, are examined from an information‑theoretic perspective. The authors introduce a family of generalized information measures that link set size and coverage to entropy, showing that Shannon mutual information can be expressed exactly in terms of these measures. They prove that, in classification tasks, the reduction in set size due to additional information is bounded by calibration‑dependent members of this family and satisfies a data‑processing inequality, and they empirically demonstrate that set‑size reduction and mutual information can rank features differently in greedy selection.
arXiv Machine Learning
Oct 12
Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry
The paper extends conformal prediction by introducing a geometric view of uncertainty through credal sets, which are families of probability distributions compatible with CP regions. It provides analytical characterisations and efficient algorithms for common credal uncertainty measures, reducing complexity from exponential to linear after sorting p-values. The authors also unify these measures with classical conformal summaries using Tsallis entropy penalties, prove an impossibility theorem for split-conformal regression, and demonstrate through experiments that the new summaries recover ranking information lost by prediction-set size, enabling finer-grained uncertainty assessment.
arXiv Machine Learning
Jul 9
Optimal Conformal Prediction under Epistemic Uncertainty
arXiv:2505. 19033v2 Announce Type: replace-cross Abstract: Conformal prediction (CP) is a widely used frequentist framework to quantify uncertainty by constructing prediction sets with user-specified marginal coverage guarantees.
arXiv Machine Learning
Jun 3
Set-Preserving Calibration from Conformal P-Values to E-Values
arXiv:2606. 03600v1 Announce Type: cross Abstract: Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits.
arXiv Machine Learning
Jun 2
Fundamental bounds on efficiency-confidence trade-off for transductive conformal prediction
arXiv:2509. 04631v2 Announce Type: replace Abstract: Transductive conformal prediction addresses the simultaneous prediction for multiple data points.
arXiv Machine Learning
Jul 21
Isotonic Conformal Prediction
arXiv:2607. 16675v1 Announce Type: cross Abstract: A point prediction that is well calibrated on average can still be systematically biased conditional on its own value, undermining its use in downstream decision-making.