I've implemented a GMM for one class of the data. Then I performed ROC analysis and the diagram is not bad. I achieved 83% accuracy with a threshold but the problem is that the threshold is pretty small. It's 0.36*E-25. The probabilities of the test data are pretty small too. They are all near zero. Do you think it's unreasonable or is it an immense problem?
It's typical that the probabilities are very small - this is due to the exponential function's fast decay.
This *can* cause numerical issues. Therefore, it is typically a good idea to compute log(p(x|c)) rather than p(x|c).
The Gaussian function also makes a logarithmic probability computation very easy, so this solution not only helps numerically but also eases implementation.
Very small density values can occur in GMMs. Usually, the higher the dimensionality of the data, the smaller your probability density values will be. Theoretically, this should be just fine. However, numerical problems can occur if your data is too high-dimensional and you have to do some tricks or even invoke a feature reduction step prior to density estimation.
So, if your ROC analysis looks reasonable, there is a priori no reason to assume that your GMM might work erroneously.
It is normaly if your data have a hight dimension, to solve this problem try to use log(p(x|y)). The log function don't affect the performance of your system and it just simplify your calcule
Hello
Thank you all. I am pretty happy for such friends.
Yes you are right I also talked to my adviser professor Yesterday and he think so.
My dataset is 30D and it causes that small probability.
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