Neural Networks as Linear Regression: An Introduction for Statisticians

2026-06-22

AI Summary

This study addresses the challenge classical frequentist statisticians face in understanding neural networks by proposing a reconstruction of neural networks through the lens of linear regression. By simplifying network architecture and integrating statistical interpretability techniques, the approach reformulates deep learning models into a modeling paradigm familiar to statisticians. The method preserves the expressive power of neural networks while offering intuitive parameter interpretations and customizable pathways, thereby significantly lowering the cognitive barrier for statisticians entering the field of deep learning. The resulting framework balances theoretical rigor with practical usability, fostering meaningful integration and methodological exchange between traditional statistics and modern deep learning.

Abstract

Neural networks are a commonly used prediction tool in computer science and statistics. However, the barrier to entry of this interesting field remains high, particularly for classical statisticians trained in a frequentist perspective. In this letter, we demystify neural networks by describing networks that approximate a linear regression and describe common customizations that provide a foundation for further study.

Problem

• neural networks
• linear regression
• statisticians
• frequentist perspective
• barrier to entry

Innovation

• neural networks
• linear regression
• statistical interpretation
• frequentist perspective
• model demystification