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Is R2R^{2} a useful metric for non-linear models (RF, GBM, neural nets)?

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Answer

  • It's a valid summary but has caveats: (1) R2R^{2} is not scale-free per dataset — it depends on Var(y)\operatorname{Var}(y) — so comparing across datasets is misleading; (2) it's easy to inflate by adding features and can overstate goodness for wiggly models on small data; (3) it doesn't reflect calibration or heteroscedastic errors.
  • Prefer RMSE / MAE / quantile loss for absolute quality, MASE for time series comparison, and Bayesian criteria (AIC, BIC) for model selection.
Check yourself — multiple choice
  • R2R^{2} is meaningless for non-linear models
  • Valid but limited — prefer RMSE/MAE/quantile loss for absolute quality; MASE for cross-dataset comparison
  • R2R^{2} is always the best regression metric
  • R2R^{2} only works for linear regression

R2R^{2} is a valid summary but data-dependent; complement with RMSE/MAE/MASE.

#metrics-regression

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