Root-finding Approaches for Computing Conformal Prediction Set

TL;DR

This paper explores root-finding algorithms to efficiently compute conformal prediction sets, especially intervals, addressing computational challenges in regression settings without extensive refitting.

Contribution

It introduces a novel approach using classical root-finding methods to approximate conformal prediction set boundaries, improving efficiency over traditional methods.

Findings

Root-finding algorithms can effectively approximate conformal prediction interval boundaries.

The approach reduces computational complexity compared to refitting procedures.

Discussion of limitations and potential drawbacks of the method.

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.