Root-finding Approaches for Computing Conformal Prediction Set

Abstract

Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal level without additional assumptions on their distribution. Its computation deplorably requires a refitting procedure for all replacement candidates of the target response. In regression settings, this corresponds to an infinite number of model fits. Apart from relatively simple estimators that can be written as pieces of linear function of the response, efficiently computing such sets is difficult, and is still considered as an open problem. We exploit the fact that, \emph{often}, conformal prediction sets are intervals whose boundaries can be efficiently approximated by classical root-finding algorithms. We investigate how this approach can overcome many limitations of formerly used strategies; we discuss its complexity and drawbacks.

Published in Machine Learning Journal https://rdcu.be/c0nh9

References in corpus (7)

• SCAD-penalized regression in high-dimensional partially linear models
• Testing for Outliers with Conformal p-values
• Complexity Analysis of the Lasso Regularization Path
• Predictive Inference Is Free with the Jackknife+-after-Bootstrap
• Uncertainty Sets for Image Classifiers using Conformal Prediction
• Making learning more transparent using conformalized performance prediction
• Few-shot Conformal Prediction with Auxiliary Tasks