Conformal Prediction for Astronomy Data with Measurement Error

TL;DR

This paper adapts conformal prediction techniques to astronomical data with heteroscedastic, non-Gaussian measurement errors, providing finite-sample coverage guarantees for prediction intervals in exoplanet mass estimation.

Contribution

It introduces a tailored conformal prediction method for astronomy data with measurement errors, ensuring reliable prediction intervals with finite-sample guarantees.

Findings

Finite sample control over Type I error probabilities demonstrated.

Effective construction of prediction intervals for unobserved exoplanet masses.

Method applicable under various measurement error assumptions.

Abstract

Astronomers often deal with data where the covariates and the dependent variable are measured with heteroscedastic non-Gaussian error. For instance, while TESS and Kepler datasets provide a wealth of information, addressing the challenges of measurement errors and systematic biases is critical for extracting reliable scientific insights and improving machine learning models' performance. Although techniques have been developed for estimating regression parameters for these data, few techniques exist to construct prediction intervals with finite sample coverage guarantees. To address this issue, we tailor the conformal prediction approach to our application. We empirically demonstrate that this method gives finite sample control over Type I error probabilities under a variety of assumptions on the measurement errors in the observed data. Further, we demonstrate how the conformal prediction method could be used for constructing prediction intervals for unobserved exoplanet masses using established broken power-law relationships between masses and radii found in the literature.