Determining the required sample size for machine learning prediction models is challenging. Conventional power analysis assumes a pre‑specified predictor‑outcome relationship and effect structure, which nonlinear models do not provide due to their complex prediction surfaces.
We introduce a framework that first approximates a nonlinear model with localized linear representations and then evaluates statistical power within these regions to infer the necessary sample size.
The procedure consists of:
- Training the full nonlinear model;
- Sampling points in the input space and obtaining local linear coefficients $\beta$ via a Taylor expansion;
- Using the linear‑model power formula $$Power = \Phi\left(\frac{\sqrt{n}\,|\beta|}{\sigma} - z_{1-\alpha/2}\right)$$ to solve for the required sample size $n$;
- Aggregating the upper bounds of $n$ across all local regions to produce a global sample size recommendation.
This approach balances model complexity with statistical interpretability and works for both regression and classification tasks.
Simulation studies show that the power estimates from local linear approximations deviate less than 5% from those of the true nonlinear models under various noise levels.
Review