Root-finding Approaches for Computing Conformal Prediction Set
This addresses a key bottleneck in conformal prediction for practitioners, though it is incremental as it builds on existing interval-based assumptions.
The paper tackles the computational inefficiency of conformal prediction sets, which traditionally require refitting models for many candidates, by proposing root-finding algorithms to approximate interval boundaries, reducing computational burden.
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.