Measurement noise limits the advantage of nonlinear models over linear models in biomedical prediction

Flexible machine-learning models such as deep networks and gradient-boosted trees gain no consistent advantage over simple linear regression on biomedical tabular data because measurement noise erases nonlinear structure faster than linear structure, according to an analysis posted to arXiv on 16 June 2026 [1]. Marc-Andre Schulz assembles classical results from measurement-error statistics, psychometrics, and Gaussian analysis into an exact excess-risk identity to explain why linear and logistic regression repeatedly match or beat far more flexible models when both are given the same features [1][2]. The core mechanism is attenuation: additive noise blurs the population-optimal predictor, and because blurring removes a function’s fine, rapidly varying detail before its broad shape, it erases nonlinear structure faster than linear structure [2]. A degree-𝑘 interaction is attenuated by the 𝑘-th power of feature reliability, while the linear part is attenuated only once [2]. At the reliabilities typical of biomedical measurement, the nonlinear advantage can vanish even when the underlying biology is strongly nonlinear [2]. The paper argues that the usual reaction — treating the tie as a model-side shortfall to be fixed with more data, a better architecture, or tuning — cannot help when the binding limit is the measurement rather than the model [2]. What the noise removes cannot be recovered by a larger cohort or a more flexible model, only by better measurement [2]. The nonlinearity is hidden, not absent, and a tie between linear and flexible models is not by itself a verdict on the biology [2]. Measurement reliability is identified as one of three conditions, alongside sample size and feature representation, that must align for a flexible model to help [2]. Together they leave only a narrow window that most biomedical tasks fall outside [2]. Across 140 UK Biobank tasks, the gap between flexible and linear models, where it exists, carries the predicted noise signature, and the three conditions can be separated by intervention but not by a benchmark alone [2]. Linear models have a long history in classification and prediction. Linear discriminant analysis, for instance, finds a linear combination of features that characterizes or separates two or more classes of objects or events and is closely related to analysis of variance and regression analysis [5]. The new work does not dispute the utility of such methods but provides a formal framework for understanding when more complex models cannot outperform them [2]. The findings carry implications for the broader deployment of foundation models in biomedicine. Foundation models — large machine-learning models trained on vast datasets so they can be applied across a wide range of use cases — are being developed for fields including radiology, ophthalmology, and genomics [9]. If measurement noise rather than model capacity is the binding constraint, simply scaling up model size or training data may yield diminishing returns without parallel improvements in measurement fidelity [2].