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Machine Learning: What is the difference between MLE and MAP estimation? When are they the same thing?

Machine Learning: Why is resampling important when using sequential Monte Carlo methods?

Machine Learning: Are undirected graphical models a richer class of distributions than directed graphical models? Or is it the other way around?

Machine Learning: What are alternative sampling methods to the ones based on the Metropolis-Hastings algorithm? One example is SMC samplers, but perhaps there are more.

Machine Learning: Is there a principled way to drop points from a Gaussian process, so that computation doesn't slow down too much, without completely ruining accuracy?

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