Kernkonzepte
The core message of this paper is to propose a data-driven framework called Partition Learning Conformal Prediction (PLCP) that can improve the conditional validity of prediction sets by learning uncertainty-guided features from the calibration data.
Zusammenfassung
The paper focuses on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. The authors propose PLCP, a framework that aims to improve the conditional validity of prediction sets by learning uncertainty-guided features from the calibration data.
The key algorithmic principles of PLCP are:
- Given a partitioning of the covariate space, the prediction sets for each partition can be constructed using the corresponding (1-α)-quantile of the conditional distribution of the conformity score.
- Given the prediction set values, the partitioning of the covariate space can be learned by assigning each point to the partition whose associated prediction set value is closest to the (1-α)-quantile of the conditional distribution of the conformity score at that point.
PLCP iteratively optimizes these two principles using the finite calibration data. The authors provide theoretical guarantees for the mean squared conditional error (MSCE) of the prediction sets constructed by PLCP in both the infinite and finite data regimes. They also derive implied coverage guarantees (both marginal and conditional) for PLCP.
The experimental results show that PLCP consistently outperforms the Split Conformal method in terms of conditional coverage and interval length across diverse datasets and tasks. PLCP also matches the performance of BatchGCP, which relies on predefined groups, and effectively identifies and covers additional meaningful groups.
Statistiken
The paper does not provide any specific numerical data or statistics. The focus is on the theoretical analysis and algorithmic framework of the proposed PLCP method.
Zitate
"Prior work has shown that it is impossible to construct nontrivial prediction sets with distribution-free, full conditional coverage when we have access to a finite-size calibration set."
"Our algorithmic framework aims at learning such structures in conjunction with constructing the prediction sets in an iterative fashion."
"We introduce the notion of "Mean Squared Conditional Error (MSCE)" defined as MSCE(D, α, C) = E[(cov(X) - (1-α))^2], which measures the deviation of prediction sets C(x) from the full conditional coverage."