cs.LGMar 10, 2026

A Visualization for Comparative Analysis of Regression Models

Authors: Nassime Mountasir, Baptiste Lafabregue, Bruno Albert, Nicolas Lachiche

Organizations: ICube · Laboratoire ICube, Université de Strasbourg, 300 Bd Sébastien Brant, 67400 Illkirch-Graffenstaden, France · ENGLAB, Technology & Strategy Engineering, 3 rue Denis Papin, 67300 Schiltigheim, France

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Abstract

As regression is a widely studied problem, many methods have been proposed to solve it, each of them often requiring setting different hyper-parameters. Therefore, selecting the proper method for a given application may be very difficult and relies on comparing their performances. Performance is usually measured using various metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), or R-squared (R2{}^2). These metrics provide a numerical summary of predictive accuracy by quantifying the difference between predicted and actual values. However, while these metrics are widely used in the literature for summarizing model performance and useful to distinguish between models performing poorly and well, they often aggregate too much information. This article addresses these limitations by introducing a novel visualization approach that highlights key aspects of regression model performance. The proposed method builds upon three main contributions: (1) considering the residuals in a 2D space, which allows for simultaneous evaluation of errors from two models, (2) leveraging the Mahalanobis distance to account for correlations and differences in scale within the data, and (3) employing a colormap to visualize the percentile-based distribution of errors, making it easier to identify dense regions and outliers. By graphically representing the distribution of errors and their correlations, this approach provides a more detailed and comprehensive view of model performance, enabling users to uncover patterns that traditional aggregate metrics may obscure. The proposed visualization method facilitates a deeper understanding of regression model performance differences and error distributions, enhancing the evaluation and comparison process.

Figures & tables

Table 1: MAE and RMSE values for Dataset A
Figure 1: Overview of the three main limitations of aggregate error metrics
Figure 2: Comparison of the predictions and the real values for Dataset A
Figure 3: Comparison of error distributions (left) and predicted vs. real values (right).
Figure 4: Comparison of the errors of Model A1 and Model A10
Figure 5: Representation of the proximity of points with different methods
Figure 6: Visualization with Mahalanobis distance for Model A1 and A10
Figure 7: 2D Error Space for AI4I2020
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