Hi,
Minorization-maximization is a simple optimization method, and I agree
that it is likely that more efficient algorithms can be applied.
Newton's method implies estimating the inverse of the Hessian matrix.
Really computing the inverse has a cost cubic in the size of the matrix,
so it is not practical with tens of thousands of parameters.
Nevertheless, Newton's method can be applied to each parameter one by
one. If I understand correctly, this is what Jason proposed. One step of
Newton's method on just one parameter has a computational cost very
similar to MM, and is much more efficient (it should converge in just
one or two iterations).
Still, MM has the advantage that it can be applied in batch mode, thus
saving a lot of computation.
I cannot say for sure which approach would be more efficient.
Rémi
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