Lifted Coefficient of Determination: Fast model-free prediction intervals and likelihood-free model comparison

Abstract

We propose the lifted linear model, and derive model-free prediction intervals that become tighter as the correlation between predictions and observations increases. These intervals motivate the Lifted Coefficient of Determination, a model comparison criterion for arbitrary loss functions in prediction-based settings, e.g., regression, classification or counts. We extend the prediction intervals to more general error distributions, and propose a fast model-free outlier detection algorithm for regression. Finally, we illustrate the framework via numerical experiments.

Tasks

Reproductions