Bagged Polynomial Regression and Neural Networks

Climate and environmental applications increasingly rely on high-dimensional prediction from remote sensing and other scientific data. Neural networks (NN) can deliver strong accuracy in these settings, but they are often hard to audit and hard to align with domain knowledge. As an alternative, we propose bagged polynomial regression with random projections (BPR), an econometrics-native ensemble that averages many regularized low-degree polynomial models fit on randomly selected covariate groups. We provide novel finite-sample and asymptotic risk bounds and show how covariate partitioning can improve rates for smooth target functions by controlling dictionary basis growth. Rate improvements may be particularly relevant for the estimation of marginal effects. In an application to satellite-based crop classification using optical and radar imagery, BPR matches NN accuracy while remaining straightforward to diagnose. We provide practical transparency tools, coefficient summaries and partial-dependence diagnostics, that show BPR captures intuitive feature relationships that NNs do not.