Correct number of samples, based on new mean and variance

Question

I have a set of sample, sampled from a specific gaussian mixture. Then I update the mixture parameters (mean, variance, weights). Now, I want to correct (move) these samples by the new parameters. I don't want to randomly sample from the new mixture, just move the old samples to match the new parameters. How can I do that

Answer 1

Use Expectation Maximization

After updating mixture parameters (M-Step), you want to compute the expected membership values for every sample. An example can look like this

Where A, B are the mixture memberships (there can be more components, of course) and Pa, Pb are their relative frequencies with constraint Pa + Pb = 1. Those 2 steps can be repeated until the change of mixture converges to any small enough epsilon.