gaussian mixture model probability matlab

Question

I have a data of dimension 50x100000. (100000 features, each has a dimension of 50).

I would like to fit a gaussian mixture model using this data. I used the following code.

               obj = gmdistribution.fit(X',3);

What I need is when I give a new data Y I should be able to get the likelihood probabilities $p(Y|\theta)$, where $\theta$ are the gaussing mixture model parameters.

I used the following code to get the probability values.

               P = pdf(obj,X');

But I am getting very low values all are about 0. Whay it is happning? How can i get the appropreate probability values?

Answer 1

In one dimension, the maximum value of the pdf of the Gaussian distribution is 1/sqrt(2*PI). So in 50 dimensions, the maximum value is going to be 1/(sqrt(2*PI)^50) which is around 1E-20. So the values of the pdf are all going to be of that order of magnitude, or smaller.