Title: Bagged Polynomial Regression and Neural Networks

Abstract:

High-dimensional prediction derived from remote sensing and other scientific datasets is becoming increasingly critical for climate and environmental applications. While neural networks (NN) are capable of delivering robust accuracy in such contexts, they frequently suffer from a lack of auditability and difficulty in aligning with established domain knowledge. To address these limitations, we introduce bagged polynomial regression with random projections (BPR), an ensemble method rooted in econometrics that averages numerous regularized, low-degree polynomial models trained on randomly selected subsets of covariates.

We establish new finite-sample and asymptotic risk bounds, demonstrating that covariate partitioning can enhance convergence rates for smooth target functions by managing the growth of the dictionary basis. These improvements in rate are especially significant for estimating marginal effects. In a case study involving satellite-based crop classification using both optical and radar imagery, BPR achieves accuracy levels comparable to neural networks while remaining easy to diagnose. Furthermore, we offer practical transparency tools—including coefficient summaries and partial-dependence diagnostics—that reveal BPR’s ability to capture intuitive feature relationships, a capability that neural networks often lack.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC