@misc{10481/108560,
year = {2024},
url = {https://hdl.handle.net/10481/108560},
abstract = {Introduction: Regression analysis is a central topic in statistical modeling, aimed at estimating the relationships between a dependent variable, commonly referred to as the response variable, and one or more
independent variables, i.e., explanatory variables. Linear regression is by far the most popular method for
performing this task in various fields of research, such as data integration and predictive modeling when
combining information from multiple sources. Objectives: Classical methods for solving linear regression problems, such as Ordinary Least Squares (OLS), Ridge, or Lasso regressions, often form the foundation for more advanced machine learning (ML) techniques, which have been successfully applied, though without a formal definition of statistical significance. At most, permutation or analyses based on empirical measures (e.g., residuals or accuracy) have been conducted, leveraging the greater sensitivity of ML estimations for detection. Methods: In this paper, we introduce Statistical Agnostic Regression (SAR) for evaluating the statistical significance of ML-based linear regression models. This is achieved by analyzing concentration inequalities of the actual risk (expected loss) and considering the worst-case scenario. To this end, we define a threshold that ensures there is sufficient evidence, with a probability of at least 1 g, to conclude the existence of a linear relationship in the population between the explanatory (feature) and the response (label) variables. Conclusions: Simulations demonstrate that the proposed agnostic (non-parametric) test can perform an analysis of variance comparable to the classical multivariate F-test for the slope parameter, without relying on the underlying assumptions of classical methods. A power analysis on a putative regression task revealed an overinflated false positive rate in standard ML methods, whereas the SAR test exhibited excellent control. Moreover, the residuals computed using this method represent a trade-off between those obtained from ML approaches and classical OLS.},
organization = {MICIU/AEI/10.13039/501100011033, PID2022-137451OB-I00},
organization = {CIN/AEI/10.13039/501100011033 FSE+, PID2022-137451OB-I00 and PID2022-137629OA-I00},
organization = {Programa Iberoamericano de Ciencia y Tecnología para el Desarrollo (CYTED), 225RT0169},
publisher = {Elsevier},
keywords = {Ordinary least squares},
keywords = {K-fold cross-validation},
keywords = {Linear support vector machines},
title = {Statistical agnostic regression: A machine learning method to validate regression models},
doi = {10.1016/j.jare.2025.04.026},
author = {Gorriz Sáez, Juan Manuel and Ramírez, J. and Segovia Román, Fermín and Jiménez Mesa, Carmen and Martínez Murcia, Francisco Jesús and Suckling, John},
}