# Bagged Polynomial Regression and Neural Networks

arXiv: https://arxiv.org/abs/2205.08609 · HTML: https://mlsanity.com/paper/2205.08609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 6 of 6)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Iterative Random Forests to detect predictive and stable high-order interactions](https://mlsanity.com/paper/1706.08457/) (2017)
- [Simultaneous Corn and Soybean Yield Prediction from Remote Sensing Data Using Deep Transfer Learning](https://mlsanity.com/paper/2012.03129/) (2020)
- [Polynomial Regression As an Alternative to Neural Nets](https://mlsanity.com/paper/1806.06850/) (2018)
- [Neural Networks and Polynomial Regression. Demystifying the Overparametrization Phenomena](https://mlsanity.com/paper/2003.10523/) (2020)
- [Non-Parametric Inference Adaptive to Intrinsic Dimension](https://mlsanity.com/paper/1901.03719/) (2019)

## Abstract (arXiv)

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.