Eigen for Statistical and Machine Learning Computing: A Lightweight C++ Tutorial with Python Bindings

TL;DR

This paper provides a practical tutorial on using Eigen, a C++ linear algebra library, with Python bindings to implement common statistical and machine learning algorithms efficiently.

Contribution

It offers a clear, example-driven guide for researchers to develop C++ implementations of ML algorithms with Python integration, focusing on readability and practicality.

Findings

Demonstrates kernel ridge regression implementation

Shows matrix factorization with stochastic gradient descent

Includes data conversion between NumPy and Eigen

Abstract

This note provides a lightweight tutorial on using Eigen, a C++ template library for linear algebra, to implement statistical and machine learning algorithms. The emphasis is practical rather than methodological: we show how common matrix operations, decomposition-based solvers, and vectorized updates can be written in readable C++ and then connected to Python through pybind11. Two examples are used throughout the tutorial: kernel ridge regression and matrix factorization with stochastic gradient descent. The examples are intentionally small enough to be studied as code, but they contain many operations that appear in larger research software projects, including kernel matrix construction, regularized linear system solving, row-wise updates, and NumPy--Eigen data conversion. The goal is to provide a reproducible starting point for researchers who want to move from mathematical formulas to efficient C++ implementations while retaining a convenient Python workflow.