Comparing the Moore-Penrose Pseudoinverse and Gradient Descent for Solving Linear Regression Problems: A Performance Analysis
It provides practical guidance for machine learning researchers and practitioners on selecting between direct and iterative solvers for linear regression, but it is incremental as it compares well-established methods without introducing new techniques.
This paper compares the Moore-Penrose pseudoinverse and gradient descent for solving linear regression problems, analyzing their computational complexity and empirical performance on synthetic and real-world datasets to identify conditions where each method excels in terms of time, stability, and accuracy.
This paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method. Linear regression is a cornerstone of predictive modeling, and the choice of solver can significantly impact efficiency and accuracy. I review and discuss the theoretical underpinnings of both methods, analyze their computational complexity, and evaluate their empirical behavior on synthetic datasets with controlled characteristics, as well as on established real-world datasets. My results delineate the conditions under which each method excels in terms of computational time, numerical stability, and predictive accuracy. This work aims to provide practical guidance for researchers and practitioners in machine learning when selecting between direct, exact solutions and iterative, approximate solutions for linear regression tasks.