Measurement Noise Limits Nonlinear Model Advantage in Biomedical Prediction.

In the realm of biomedical tabular data, it is frequently observed that advanced, flexible models like deep networks, gradient-boosted trees, and kernel methods perform comparably to, or are even outperformed by, simpler linear and logistic regression models when using the same features. The common assumption is that this indicates a model deficiency, suggesting a need for more data, improved architectures, or better tuning to capture inherent nonlinear structures. However, this paper posits that such fixes are ineffective when the primary limitation stems from measurement noise, a frequent issue in biomedicine. Additive noise blurs the optimal predictor, and because fine, rapidly varying details of a function are erased before its broader shape, nonlinear structures are lost more quickly than linear ones. Specifically, a degree-$k$ interaction is attenuated by the $k$-th power of feature reliability, while the linear component is attenuated only once. At the typical reliability levels of biomedical measurements, the potential advantage of nonlinear models can disappear entirely, even when the underlying biological processes are highly nonlinear. What is lost due to noise cannot be recovered by simply increasing cohort size or employing more flexible models; only improved measurement quality can restore it. The nonlinearity is thus hidden, not absent, and a performance tie between linear and flexible models does not inherently negate the biological nonlinearity. Drawing from classical measurement-error statistics, psychometrics, and Gaussian analysis, the authors assemble these insights into an exact excess-risk identity. Measurement reliability is identified as one of three crucial conditions—alongside sample size and feature representation—that must align for a flexible model to offer a benefit. Most biomedical tasks, the paper concludes, fall outside this narrow window. An analysis across 140 UK Biobank tasks reveals that any existing gap between flexible and linear models carries the predicted noise signature, and these three conditions can be isolated through intervention, but not solely through benchmarking.