To address this issue, various approximate Bayesian inference methods have been proposed, such as Markov Chain Monte Carlo [MCMC, see e.g.

"one-shot" formulation of the Knowledge Gradient, enabled by a combination of

Efficient approximation and sampling methods of intractable distributions plays a key role in probabilistic machine learning, especially Bayesian inference.

Suppose that we observe i.i.d.

This framework has the flexibility of deriving distribution-and algorithm-dependent bounds, which are often tighter than VC-related uniform convergence bounds.