I'd like to ask why `BayesianRidge` and `ARDRegression` do not use
marginal log likelihood (MLL) but learned coefficients to check
convergence when fitting.
I know that most iterative algorithms must have some objective
function by which the convergence is checked.
In Bayesian inference, like variational learning, the objective function is MLL.
Are there any reason not to use  MLL?

And also, is the learning algorithm of `BayesianRidge` and
`ARDRegression` a kind of variational learning?
If so, the MLL is ensured to increase upon learning.
However, the MLL of ARDRegression
(http://scikit-learn.org/stable/_images/plot_ard_3.png) did decrease.
Is this a bug or did I misunderstand something?

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杜 世橋 (Shiqiao Du)
E-mail [email protected]
Twitter http://twitter.com/lucidfrontier45

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