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I have a set of points which I can fit a Gaussian model on them using Maximum likelihood estimation. but this estimation is weak and I want to improve it.

I want to fit a mixture of Gaussian on these points so I get better results but I don't know how ! I searched the internet for several days and I only found out that if I have multiple Gaussian distribution, adding them together with some weights will result in mixture of Gaussian. But in my example I only have a single distribution and I don't have any other Gaussian to get the mixture model.

How can I fit a mixture of Gaussians on my observed data ?

my data are in 2D space but for simplicity you can solve it for 1D.

Danica
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Parsa
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  • Use EM: https://www.google.com/search?q=em+algorithm+for+fitting+the+gaussian+mixture+model&oq=em+algorithm+for+f&aqs=chrome.2.69i57j0l5.5174j0j7&sourceid=chrome&es_sm=91&ie=UTF-8 – Neil G Sep 05 '15 at 20:32
  • Why do you want to fit a "mixture" of Gaussians if you know that your data consists in only one Gaussian? You have only to estimate its parameters $\mu, \Sigma$. – mic Sep 05 '15 at 20:32
  • thanks for your replies, no I am sure that my data doesn't consist in only one Gaussian so I want to estimate it using mixture of gaussians – Parsa Sep 05 '15 at 20:35
  • @NeilG is there any other way except EM ? – Parsa Sep 05 '15 at 20:39
  • what's wrong with em? – Neil G Sep 05 '15 at 21:04
  • Yes, there are certainly other ways; e.g. you could write the entire likelihood for all the unknowns and maximize that directly, or you could use some other criterion than maximum likelihood. But there's a reason why people tend to use E-M -- it's relatively simple. – Glen_b Sep 06 '15 at 01:28
  • yeah I tried and wrote the EM one... thanks Glen_b :) – Parsa Sep 07 '15 at 13:57

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