Symbolic Quantile Regression for the Interpretable Prediction of Conditional Quantiles

TL;DR

This paper introduces Symbolic Quantile Regression (SQR), a method that uses Symbolic Regression to predict conditional quantiles, providing interpretable models for understanding variable effects across the entire distribution.

Contribution

The paper presents SQR, a novel approach combining symbolic regression with quantile estimation, enabling interpretable predictions of various quantiles in the distribution.

Findings

SQR outperforms transparent models in quantile prediction.

SQR performs comparably to black-box models without losing interpretability.

SQR helps explain differences in target distribution in a case study.

Abstract

Symbolic Regression (SR) is a well-established framework for generating interpretable or white-box predictive models. Although SR has been successfully applied to create interpretable estimates of the average of the outcome, it is currently not well understood how it can be used to estimate the relationship between variables at other points in the distribution of the target variable. Such estimates of e.g. the median or an extreme value provide a fuller picture of how predictive variables affect the outcome and are necessary in high-stakes, safety-critical application domains. This study introduces Symbolic Quantile Regression (SQR), an approach to predict conditional quantiles with SR. In an extensive evaluation, we find that SQR outperforms transparent models and performs comparably to a strong black-box baseline without compromising transparency. We also show how SQR can be used to explain differences in the target distribution by comparing models that predict extreme and central outcomes in an airline fuel usage case study. We conclude that SQR is suitable for predicting conditional quantiles and understanding interesting feature influences at varying quantiles.