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Fitting Graphs: A Visual Framework for Transparent and Robust Machine Learning Model Selection
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DOI：10.1080/08839514.2026.2678638.png)
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Abstract
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Model developers often rely on cross-validation (CV) to estimate model performance, yet CV – even when repeated multiple times – can produce highly variable results that are difficult to interpret. This paper introduces the fitting graph, an information visualization that helps developers assess model performance, select regularization parameters, and evaluate model robustness. The fitting graph plots the relationship between the regularization parameter (λ) and mean squared error (MSE) across multiple CV repetitions, with a smoothing spline used to estimate the underlying curve. Experiments on several datasets – including the Baseball, Boston Housing, and Parkinson’s datasets – demonstrate that fitting graphs provide a transparent visual summary of model performance behavior across λ values. The spline-estimated curve reliably identifies near-optimal λ values even when only a small number of CV repetitions are performed, substantially reducing computational cost. A case study using an intentionally unstable regression model further shows that the fitting graph can identify stable regions of performance where standard CV often fails. The results indicate that fitting graphs offer a simple and effective visual diagnostic for transparent and robust model development and selection.
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