The Safe Bayesian - Learning the Learning Rate via the Mixability Gap

By Peter D. Grünwald. 2012

118 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

PAC-Bayesian Theory Meets Bayesian Inference (2016, neutral): “Grünwald (2012) [16] .”
Follow the leader if you can, hedge if you must (2013, background): “…know whether this is the case, we note that, in the stochastic setting, being able to compete with the best η ∈ B2 is already satisfactory: it implies that one can achieve minimax optimal risk convergence rates in a variety of settings, e.g. if a Tsybakov margin condition holds (Grünwald, 2012).”
Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors (2017, background): “Similar connections have been made by Zhang (2006a;b); Grünwald (2012); Grünwald & Mehta (2016).”
Bayesian Differential Privacy through Posterior Sampling (2013, background): “Other future directions include investigating the links between posterior sampling and the exponential mechanism, as well as with the safe Bayesian approach (Grünwald, 2012) to inference.”
Entropy-SGD optimizes the prior of a PAC-Bayes bound: Data-dependent PAC-Bayes priors via differential privacy (2017, background): “Similar connections have been made by Zhang (2006a), Zhang (2006b), Grünwald (2012), and Grünwald and Mehta (2016).”
Fast Rates with Unbounded Losses (2016, methodology): “In previous works (Audibert (2009) and many others) it is suggested to do this using e.g. crossvalidation, but recent works such as Grünwald (2011) and Grünwald (2012) present ‘safe Bayesian’ methods for doing this which provably select the right η under Bernstein conditions and bounded losses.”
Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It (2014, methodology): “…1990, McAllester, 2003, Barron and Cover, 1991, Walker and Hjort, 2002, Zhang, 2006a) and suggested as a tool for dealing with misspecification by Grünwald (2011, 2012). η trades off the relative weight of the prior and the likelihood in determining the η-generalized posterior, where η = 1…”