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

• URL: http://arxiv.org/abs/2410.08958v1
• Date: Fri, 11 Oct 2024 16:27:31 GMT
• Title: Lifted Coefficient of Determination: Fast model-free prediction intervals and likelihood-free model comparison
• Authors: Daniel Salnikov, Kevin Michalewicz, Dan Leonte,
• Abstract summary: We derive model-free prediction intervals that become tighter as the correlation between predictions and observations increases. These intervals motivate the $textitLifted Coefficient of Determination$, a model comparison criterion for arbitrary loss functions. We extend the prediction intervals to more general error distributions, and propose a fast model-free outlier detection algorithm for regression.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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