Lifted Coefficient of Determination: Fast model-free prediction intervals and likelihood-free model comparison
This provides a general framework for prediction intervals and model comparison in various prediction-based settings, though it appears incremental as it builds on existing concepts.
The paper tackles the problem of creating model-free prediction intervals and model comparison criteria for arbitrary loss functions, proposing a lifted linear model that yields tighter intervals as prediction-observation correlation increases and introducing the Lifted Coefficient of Determination for tasks like regression and classification.
We propose the $\textit{lifted linear model}$, and derive model-free prediction intervals that become tighter as the correlation between predictions and observations increases. These intervals motivate the $\textit{Lifted Coefficient of Determination}$, 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.