Note that LM is very sensitive to the initial guess, as stated in wikipedia, and it could not deal with outliers. If the data contains a lot of outliers, LM is not able to converge.
A simpler version of LM, without using lambda is ![\mathbf{(J^{T}J)\boldsymbol \delta = J^{T} [y - f(\boldsymbol \beta)]} \!](https://upload.wikimedia.org/math/d/3/a/d3a53790a98a976ea5419852596ac10f.png)
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.Sunday, 17 January 2016
Levenberg-Marquardt algorithm
I find one implementation of Levenberg-Marquardt that solves Ax = b using least square, which does not seem to make sense. To learn more about Levenberg-Marquardt algorithm, I find one fascinating blog here.
In cases with only one minimum, an uninformed standard guess likeβT=(1,1,...,1) will work fine; in cases with multiple minima, the algorithm converges to the global minimum only if the initial guess is already somewhat close to the final solution.
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If the problem is convex then there are plenty of other methods right...?
ReplyDeleteCan you use SGD on this kind of problems?