While Bayesian inference pairs unique prior and posterior, PAC bayes is completely model free
PAC-Bayes is a generic framework to efficiently rethink generalization for numerous machine learning algorithms. It leverages the flexibility of Bayesian learning and allows to derive new learning algorithms. An important component in the PAC-Bayes analysis is the choice of the prior distribution.
When using a probabilistic classifier, it mathematically proves the necessity of keeping the prior and posterior distributions as similar as possible.
This is based on the KL Divergence between the distributions of expected empirical error and expected generalization error. KL Divergence is a measure of closeness, and as seen in VC dimension, the Generalization Error follows the curse of dimensionality (proportional to data dimension and inversely proportional to confidence)
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