2018/05/18 by Karl Friston, Thomas Parr, Friston, Karl +3 · 19 citations
Computer Science · Mathematics · #Artificial intelligence #Bayes factor #Bayes' theorem #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Bayesian inference #Bayesian probability #Computer science #Context (archaeology) #Gaussian Processes and Bayesian Inference #Machine learning #Mathematics #Prior probability #Probabilistic logic #Reduction (mathematics) #stat.ME
paper · pdf · doi:10.48550/arxiv.1805.07092
published in arXiv (Cornell University) (Cornell University) · The manuscript has been thoroughly updated, including more detailed explanations, additional derivations and three worked examples
openalex publication_date 2018/05/18 · arxiv created 2019/10/14 · arxiv updated 2019/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in their priors. In the setting of variational Bayes this has an analytical solution, which finesses the problem of scoring large model spaces in model comparison or structure learning. In this technical note, we review Bayesian model reduction and provide the relevant equations for several discrete and continuous probability distributions. We provide worked examples in the context of multivariate linear regression, Gaussian mixture models and dynamical systems (dynamic causal modelling). These examples are accompanied by the Matlab scripts necessary to reproduce the results. Finally, we briefly review recent applications in the fields of neuroimaging and neuroscience. Specifically, we consider structure learning and hierarchical or empirical Bayes that can be regarded as a metaphor for neurobiological processes like abductive reasoning.