Bagged Polynomial Regression and Neural Networks

TL;DR

It is demonstrated that BPR performs as well as neural networks in crop classification using satellite data, a setting where prediction accuracy is critical and interpretability is often required for addressing research questions.

Abstract

Series and polynomial regression are able to approximate the same function classes as neural networks. However, these methods are rarely used in practice, although they offer more interpretability than neural networks. In this paper, we show that a potential reason for this is the slow convergence rate of polynomial regression estimators and propose the use of \textit{bagged} polynomial regression (BPR) as an attractive alternative to neural networks. Theoretically, we derive new finite sample and asymptotic $L^2$ convergence rates for series estimators. We show that the rates can be improved in smooth settings by splitting the feature space and generating polynomial features separately for each partition. Empirically, we show that our proposed estimator, the BPR, can perform as well as more complex models with more parameters. Our estimator also performs close to state-of-the-art prediction methods in the benchmark MNIST handwritten digit dataset. We demonstrate that BPR performs as well as neural networks in crop classification using satellite data, a setting where prediction accuracy is critical and interpretability is often required for addressing research questions.

Figures (2)

• Figure 1: Finite sample rates and the choice of partition number $B$.
• Figure 2: Test Accuracy By Number of Estimators.

Theorems & Definitions (6)

• Theorem 1: $L^2$ rates
• Definition 1: Partitioned Polynomial Regression
• Corollary 1.1: Optimized rate for Partitioned Polynomial Regression
• Theorem A.1: Rudelson and Vershynin 2007
• proof
• proof