I have a set of discrete data points {xi}, sampled from a specific gaussian mixture. Then I update the mixture parameters $mean^{old}, covariance^{old}, weights^{old}$ using Optimal transport algorithm. Now, I want to correct (move) these samples by the new mixture parameters $mean^{new}, covariance^{new}, weights^{new}$. I don't want to randomly sample from the new mixture, I need to update the old samples to match the new mixture model. How can I do that?
My trial is: $$X_i^{new} = mean + weights * covariance * X_i^{old}$$
What is your motivation behind altering the original data points. So after the algorithm converges you used your data points to determine the most likely mixture parameters. Since they were sampled from the unknown distribution there is no need to alter them.