Martim Sousa

Martim Sousa, Ana Maria Tomé, José Moreira

This paper introduces a novel model-agnostic algorithm called adaptive ensemble batch multi-input multi-output conformalized quantile regression (AEnbMIMOCQR} that enables forecasters to generate multi-step ahead prediction intervals for a fixed pre-specified miscoverage rate in a distribution-free manner. Our method is grounded on conformal prediction principles, however, it does not require data splitting and provides close to exact coverage even when the data is not exchangeable. Moreover, the resulting prediction intervals, besides being empirically valid along the forecast horizon, do not neglect heteroscedasticity. AEnbMIMOCQR is designed to be robust to distribution shifts, which means that its prediction intervals remain reliable over an unlimited period of time, without entailing retraining or imposing unrealistic strict assumptions on the data-generating process. Through methodically experimentation, we demonstrate that our approach outperforms other competitive methods on both real-world and synthetic datasets. The code used in the experimental part and a tutorial on how to use AEnbMIMOCQR can be found at the following GitHub repository: https://github.com/Quilograma/AEnbMIMOCQR.

Martim Sousa, Ana Maria Tomé, José Moreira

Conformalized quantile regression is a procedure that inherits the advantages of conformal prediction and quantile regression. That is, we use quantile regression to estimate the true conditional quantile and then apply a conformal step on a calibration set to ensure marginal coverage. In this way, we get adaptive prediction intervals that account for heteroscedasticity. However, the aforementioned conformal step lacks adaptiveness as described in (Romano et al., 2019). To overcome this limitation, instead of applying a single conformal step after estimating conditional quantiles with quantile regression, we propose to cluster the explanatory variables weighted by their permutation importance with an optimized k-means and apply k conformal steps. To show that this improved version outperforms the classic version of conformalized quantile regression and is more adaptive to heteroscedasticity, we extensively compare the prediction intervals of both in open datasets.