Bayesian model reduction
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This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a special but ubiquitous case of Bayesian model comparison that, in the setting of variational Bayes, furnishes an analytic solution for (a lower bound on) model evidence induced by a change in priors. This analytic solution finesses the problem of scoring large model spaces in model comparison or structure learning. This is because each new model can be cast in terms of an alternative set of priors over model parameters. Furthermore, the reduced free energy (i.e. evidence bound on the reduced model) finds an expedient application in hierarchical models, where it plays the role of a summary statistic. In other words, it contains all the necessary information contained in the posterior distributions over parameters of lower levels. In this technical note, we review Bayesian model reduction - in terms of common forms of reduced free energy - and illustrate recent applications in structure learning, hierarchical or empirical Bayes and as a metaphor for neurobiological processes like abductive reasoning and sleep.
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