Gaussian Mixture Model as prior over parameters

[Moos Hueting]

Hi,

I love Ceres and have used it for many previous projects, but now I am a bit stumped.

I am trying to solve a NNLS problem for a small number of parameters. I know that these parameters are distributed according to a Gaussian Multivariate Mixture Model, and I would like to incorporate this as a prior cost function.

The expected behaviour would be that without data terms the optimization would converge to the nearest component mean.

I know of the existence of ceres::NormalPrior. I am looking for something similar for a mixture model, but I am a bit confused as to where to look/how to go about this. I am happy to implement it myself but I am confused as to what to implement, exactly.

As far as I understand I cannot just use the NormalPrior k times, once for each mixture: the further away the current parameter vector is from a component mean, the higher the gradient will be w.r.t. that component, so instead of converging to the closest component mean, the optimization would converge to a weighted mean of the component means.

Could someone point me in the right direction?

[Alex Stewart]

I would have a look at the max mixture model from Ed Olson developed for robust SLAM, Cyrill Stachniss has some nice notes on it here:

http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/slam18-robust.pdf

-Alex

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[John]

Did you ever get anywhere with this, Moos? I'm facing a similar problem - I am regularising my cost function with the probability the params exist in the gmm - however struggling to get it to converge!

Cheers

John