Machine and deep learning performance in out-of-distribution regressions

Abstract Machine learning (ML) and deep learning (DL) models are gaining popularity due to their effectiveness in many computational tasks. These models are based on an intuitive, but frequently unsatisfied, assumption that the data used to train these models is well-representing the task at hand. This gives rise to the out-of-distribution (OOD) challenge which can cause an unexpected drop in the data-driven model’s performance. In this study, we evaluate the performance of various ML and DL models in in-distribution (ID) versus OOD prediction. While the degradation in OOD performance is well acknowledged, to the best of our knowledge, this is one of the first studies to quantify it for various models on a large benchmark n = 15 real-world regression datasets. We extensively ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>40</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>000</mml:mn> </mml:mrow> </mml:math> runs) compare the ID versus OOD performance of XGBoost, random forest, K-nearest-neighbors, support vector machine, and linear regression models, as well as AutoML models (Tree-based Pipeline Optimization Tool and AutoKeras). In addition, to tackle this challenge, we propose to integrate a symbolic regression (SR) as a feature engineering method model with an ML or DL model to improve its performance for OOD samples. Our results show that the incorporation of SR-derived features significantly enhances the predictive capabilities of both ML and DL models with 3.70% and 10.20%, on average, of the OOD samples, respectively, without reducing ID performance and in fact improving it to a slightly lower extent. As such, this method can help produce more generalized and robust data-driven models.