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This paper argues that linear models often outperform flexible nonlinear models in prediction tasks due to the inherent instability of complex, partially observed data across different environments. The authors suggest that when underlying mechanisms shift between populations or settings, omitting nonlinear components can actually reduce error by avoiding overfitting to spurious correlations specific to a single context. Model selection should therefore prioritize cross-environment stability rather than maximizing accuracy on static training datasets alone.
Why Linear Models Can Still Work in a Complex and Changing World
arXiv:2610.13404v1 Announce Type: new Abstract: Linear models can predict well in complex domains even when underlying mechanisms are nonlinear. We argue that this can occur because the complexity of the world exceeds the complexity that can be learned reliably from finite, partially observed data. Flexible models can exploit curvature, thresholds, and interactions that fit one hospital, period, population, policy setting, or measurement process but fail elsewhere. When this instability lies mainly in the nonlinear component, omitting it can give linear models lower prediction error in a new environment. We connect this claim to work on simple linear rules, bias and variance, regularization, best linear prediction, measurement error, distribution shift, invariance, Rashomon sets, and underspecification. Proposition 1 gives a simple squared-error case in which a nonlinear rule learned in the training environment raises target error because it transfers too weakly; finite-sample estimation error can strengthen this result. Partial observation alone is not enough: the link between observed variables and unobserved factors must vary across environments. Stable nonlinear structure favors flexible models, and linear models remain vulnerable to linear spurious relationships. Model complexity should therefore be chosen by cross-environment stability as well as training-data accuracy.
Abstract:Linear models can predict well in complex domains even when underlying mechanisms are nonlinear. We argue that this can occur because the complexity of the world exceeds the complexity that can be learned reliably from finite, partially observed data. Flexible models can exploit curvature, thresholds, and interactions that fit one hospital, period, population, policy setting, or measurement process but fail elsewhere. When this instability lies mainly in the nonlinear component, omitting it can give linear models lower prediction error in a new environment. We connect this claim to work on simple linear rules, bias and variance, regularization, best linear prediction, measurement error, distribution shift, invariance, Rashomon sets, and underspecification. Proposition 1 gives a simple squared-error case in which a nonlinear rule learned in the training environment raises target error because it transfers too weakly; finite-sample estimation error can strengthen this result. Partial observation alone is not enough: the link between observed variables and unobserved factors must vary across environments. Stable nonlinear structure favors flexible models, and linear models remain vulnerable to linear spurious relationships. Model complexity should therefore be chosen by cross-environment stability as well as training-data accuracy.
Machine Learning (cs.LG)
arXiv:2610.13404 [cs.LG]
(or arXiv:2610.13404v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.13404 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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