Generating High-Quality Prediction Intervals for Regression Tasks via Fuzzy C-Means Clustering-Based Conformal Prediction

Accurately assessing uncertainty and prediction of a regression model is essential for making informed decisions, especially in high-risk tasks. Conformal Prediction (CP) is a powerful distribution-free uncertainty quantification framework for building such models as it is capable to transform a single-point prediction of any machine learning model into a Prediction Interval (PI) with a guarantee of encompassing the true value for specified levels of confidence. On the other hand, to generate high-quality PIs, the PIs should be as narrow as possible while enveloping a certain amount of uncertainty (i.e. confidence level). The generated width of the PIs mainly depends on the nonconformity measure used within the CP. In this study, we propose two novel Fuzzy c-Means Clustering (FCM) based nonconformity measures for CP with nearest neighbors to learn distribution-free and high-quality PIs for regression. The proposed approach generates tight PIs by evaluating the degree of nonconformity of a new data point compared to the so-called calibration points via Fuzzy Sets (FSs). From the calibration dataset, we extract representative FSs via FCM and assign every test point alongside the nearest neighbors within the calibration dataset with membership grades to adapt the nonconformity measure. To evaluate the performance, we present statistical comparisons and demonstrate that the proposed FCM-based nonconformity measures result in high-quality PIs.