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I've recently came across topic known as PAC-Bayesian, but I cannot find a source to read about it. Any article that I came across are talking about its application in a specific area but there is no introduction to what it exactly is.

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Here are a few quick Google hits...

From this last one, a quote:

A more refined, Bayesian extension of the PAC model is explored in [26]. Using the Bayesian approach involves assuming a prior distribution over possible target concepts as well as training instances. Given these distributions, the average error of the hypothesis as a function of training sample size, and even as a function of the particular training sample, can be defined. Also, $1 - \delta$ confidence intervals like those in the PAC model can be defined as well.

[26] $=$ W. Buntine, A Theory of Learning Classification Rules. PhD thesis, University of Technology, Sydney, 1990.

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I'm lately interested in this topic myself, and have been looking for some good sources as well. The most interesting one I found so far is the overview/tutorial paper by David McAllester titled A PAC-Bayesian Tutorial with A Dropout Bound.

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