{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:10:48Z","timestamp":1758269448608},"reference-count":0,"publisher":"MIT Press - Journals","issue":"4","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,3,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Under the Bayesian brain hypothesis, behavioral variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioral preferences when confronted with similar choices. For example, greedy preferences are a consequence of confident (or precise) beliefs over certain outcomes. Here, we offer an alternative account of behavioral variability using R\u00e9nyi divergences and their associated variational bounds. R\u00e9nyi bounds are analogous to the variational free energy (or evidence lower bound) and can be derived under the same assumptions. Importantly, these bounds provide a formal way to establish behavioral differences through an \u03b1 parameter, given fixed priors. This rests on changes in \u03b1 that alter the bound (on a continuous scale), inducing different posterior estimates and consequent variations in behavior. Thus, it looks as if individuals have different priors and have reached different conclusions. More specifically, \u03b1\u21920+ optimization constrains the variational posterior to be positive whenever the true posterior is positive. This leads to mass-covering variational estimates and increased variability in choice behavior. Furthermore, \u03b1\u2192+\u221e optimization constrains the variational posterior to be zero whenever the true posterior is zero. This leads to mass-seeking variational posteriors and greedy preferences. We exemplify this formulation through simulations of the multiarmed bandit task. We note that these \u03b1 parameterizations may be especially relevant (i.e., shape preferences) when the true posterior is not in the same family of distributions as the assumed (simpler) approximate density, which may be the case in many real-world scenarios. The ensuing departure from vanilla variational inference provides a potentially useful explanation for differences in behavioral preferences of biological (or artificial) agents under the assumption that the brain performs variational Bayesian inference.<\/jats:p>","DOI":"10.1162\/neco_a_01484","type":"journal-article","created":{"date-parts":[[2022,3,2]],"date-time":"2022-03-02T00:51:17Z","timestamp":1646182277000},"page":"829-855","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":7,"title":["Bayesian Brains and the R\u00e9nyi Divergence"],"prefix":"10.1162","volume":"34","author":[{"given":"Noor","family":"Sajid","sequence":"first","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, U.K. noor.sajid.18@ucl.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesco","family":"Faccio","sequence":"additional","affiliation":[{"name":"The Swiss AI Lab IDSIA, USI, SUPSI, 6962, Viganello, Lugano, Switzerland francesco@idsia.ch"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lancelot","family":"Da Costa","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, U.K."},{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, U.K. l.da-costa@imperial.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Parr","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, U.K. thomas.parr.12@ucl.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Schmidhuber","sequence":"additional","affiliation":[{"name":"The Swiss AI Lab IDSIA, USI, SUPSI, 6962, Viganello, Lugano, Switzerland juergen@idsia.ch"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl","family":"Friston","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, U.K. k.friston@ucl.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","published-online":{"date-parts":[[2022,3,23]]},"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/direct.mit.edu\/neco\/article-pdf\/34\/4\/829\/2003077\/neco_a_01484.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/direct.mit.edu\/neco\/article-pdf\/34\/4\/829\/2003077\/neco_a_01484.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T17:11:15Z","timestamp":1648487475000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/34\/4\/829\/109665\/Bayesian-Brains-and-the-Renyi-Divergence"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,23]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,3,23]]},"published-print":{"date-parts":[[2022,3,23]]}},"URL":"https:\/\/doi.org\/10.1162\/neco_a_01484","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,4]]},"published":{"date-parts":[[2022,3,23]]}}}