I have a follow-up question to the one asked here: Mallet topic modeling - topic keys output parameter
I hope I can still get a more detailed explanation of this subject because I have trouble understanding these numbers in the output files.
What can the summation of the output numbers tell us? For example, with 20 topics and an optimization value 20 on 2000 iterations, the summation of the output is approximately 2. With the same corpus, but with 15 topics/1000 iterations/optimization 10 the result is 0,77 and with 10 topics/1000 iterations/optimization 10 it's 0,72. What does this mean? Does it even mean anything?
Also, these people are referring to these results as parameters, but for my understanding, the parameter is the optimization interval and not the result in the output. So what is the correct way to refer to the result in the output? Frequency of the topic? Is it a procentage of something? What part did I get wrong?
You're correct that parameter is being used to mean two different things here.
Parameters of the statistical model are values that determine the properties of that model. In this case they determine which topics we expect to occur more often, and how confident we are of that. In some cases these are set by the user, in other cases they are set by the inference algorithm.
Parameters of the inference algorithm are settings that determine the procedure by which we set the parameters of the statistical model.
An additional confusion is that when model parameters are explicitly set by the user, Mallet uses the same interface as for algorithm settings.
The numbers you see are the parameters of a Dirichlet distribution that describes our prior expectation of the mix of topics in a document. You can think of it as having two parts: proportions and magnitude. If you rescale the numbers to add up to 1.0, the resulting proportions would tell you the model's guess at which topics occur most frequently. The actual sum of the numbers (the magnitude) tells you how confident the model is that this is the actual proportion you will see in a document. Smaller values indicate more variability.
A possible explanation for the numbers you're seeing (and please treat this as raw speculation) is that the 20 topic model has more flexibility to fit consistent topics, and so it is about three times more confident that there are topics that consistently occur more often in documents. As the number of topics decreases, the specificity of topics drops, so it is more likely that any particular topic could be large in any given document.