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I was looking at the Fiducial Inference page on wikipedia, which is an alternative to the traditional Frequentist and Bayesian standpoints. Although it was out of favour in mainstream statistics for many years, there seems to have been a resurgence in interest in recent years (see for example Jan Hannig's recent publications on the subject). Does anyone know of anyone in the ML community looking at these ideas from a theoretical point of view, or who has successfully created an algorithm based on them?

kjetil b halvorsen
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    Well, as Hannig himself mentions, "fiducial inference" is now called "generalized inference" and a search for the latter brings up quite a lot of results. Not that I can suggest anything though! – andreister Feb 15 '12 at 13:08

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I do not know of anybody in ML looking at this problem. (It's probably not in people's mind as a problem per se). ML folks are more interested in predictive problems, where the quality of the "learning" or "inference" is determined by how well it does on a test set.