Projected random forests and conformal prediction of circular data

Abstract: We apply split conformal prediction techniques to regression problems with circular responses by introducing a suitable conformity score, leading to prediction sets with adaptive arc length and finite-sample coverage guarantees for any circular predictive model under exchangeable data. Leveraging the high performance of existing predictive models designed for linear responses, we analyze a general projection procedure that converts any linear response regression model into one suitable for circular responses. When random forests serve as basis models in this projection procedure, we harness the out-of-bag dynamics to eliminate the necessity for a separate calibration sample in the construction of prediction sets. For synthetic and real datasets the resulting projected random forests model produces more efficient out-of-bag conformal prediction sets, with shorter median arc length, when compared to the split conformal prediction sets generated by two existing alternative models.