City Research Online

Abstract

We propose the statistical modeling approach to supervised learning (i.e., predicting labels from features) as an alternative to algorithmic machine learning (ML). The approach is demonstrated by employing a multivariate general linear model (MGLM) describing the effects of labels on features, possibly accounting for covariates of no interest, in combination with prior distributions on the model parameters. ML "training" is translated into estimating the MGLM parameters via Bayesian inference and ML "testing" or application is translated into Bayesian model comparison—a reciprocal relationship we refer to as multivariate Bayesian inversion (MBI). We devise MBI algorithms for the standard cases of supervised learning, discrete classification and continuous regression, derive novel classification rules and regression predictions, and use practical examples (simulated and real data) to illustrate benefits of the statistical modeling approach: interpretability, incorporation of prior knowledge, probabilistic predictions. We close by discussing further advantages, disadvantages, and the future potential of MBI.

Publication Type:	Article
Additional Information:	© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publisher Keywords:	Supervised learning, Multivariate analysis, General linear models, Bayesian inference, Marginal likelihood, Model comparison
Subjects:	B Philosophy. Psychology. Religion > BF Psychology H Social Sciences > HA Statistics T Technology > T Technology (General)
Departments:	School of Health & Medical Sciences School of Health & Medical Sciences > Department of Psychology & Neuroscience
SWORD Depositor:	Symplectic Administrator

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