Prediction Sets for High-Dimensional Mixture of Experts Models

Abstract

Large datasets make it possible to build predictive models that can capture heterogenous relationships between the response variable and features. The mixture of high-dimensional linear experts model posits that observations come from a mixture of high-dimensional linear regression models, where the mixture weights are themselves feature-dependent. In this paper, we show how to construct valid prediction sets for an $\ell_1$-penalized mixture of experts model in the high-dimensional setting. We make use of a debiasing procedure to account for the bias induced by the penalization and propose a novel strategy for combining intervals to form a prediction set with coverage guarantees in the mixture setting. Synthetic examples and an application to the prediction of critical temperatures of superconducting materials show our method to have reliable practical performance.