Conformal Prediction via Regression-as-Classification

Conformal Prediction via Regression-as-Classification

2024 | Etash Guha, Shlok Natarajan, Thomas Möllenhoff, Mohammad Emtiyaz Khan, Eugene Ndiaye
This paper proposes a novel approach to conformal prediction (CP) for regression by converting regression into a classification problem. The method addresses the challenges of constructing reliable prediction intervals when the output distribution is heteroscedastic, multimodal, or skewed. Instead of estimating the output distribution directly, the approach discretizes the output space into bins and treats each bin as a class. A new loss function is designed to preserve the ordering of the continuous output space while incorporating entropy regularization to encourage smoothness in the probability distribution. This allows the method to adapt to various label distributions, including heteroscedasticity and bimodality. The approach is validated on synthetic and real datasets, where it achieves shorter intervals compared to other CP baselines. The method leverages existing CP techniques for classification and applies them to the discretized output space. The resulting conformal sets are built using a conformity score that measures how appropriate an output value is for a given input. The method is shown to be effective in handling complex label distributions and provides reliable prediction intervals. The paper also discusses related works, including other CP methods for regression, and highlights the advantages of the proposed approach in terms of flexibility and accuracy. The experiments demonstrate that the method performs well on various benchmark datasets, achieving the shortest intervals in many cases. The approach is simple to implement and effective in capturing the shape of the output distribution while maintaining the simplicity and efficiency of CP for classification.This paper proposes a novel approach to conformal prediction (CP) for regression by converting regression into a classification problem. The method addresses the challenges of constructing reliable prediction intervals when the output distribution is heteroscedastic, multimodal, or skewed. Instead of estimating the output distribution directly, the approach discretizes the output space into bins and treats each bin as a class. A new loss function is designed to preserve the ordering of the continuous output space while incorporating entropy regularization to encourage smoothness in the probability distribution. This allows the method to adapt to various label distributions, including heteroscedasticity and bimodality. The approach is validated on synthetic and real datasets, where it achieves shorter intervals compared to other CP baselines. The method leverages existing CP techniques for classification and applies them to the discretized output space. The resulting conformal sets are built using a conformity score that measures how appropriate an output value is for a given input. The method is shown to be effective in handling complex label distributions and provides reliable prediction intervals. The paper also discusses related works, including other CP methods for regression, and highlights the advantages of the proposed approach in terms of flexibility and accuracy. The experiments demonstrate that the method performs well on various benchmark datasets, achieving the shortest intervals in many cases. The approach is simple to implement and effective in capturing the shape of the output distribution while maintaining the simplicity and efficiency of CP for classification.
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