How could we know the Dirichlet allocation is describing the topic rather than something else?

Question

Dirichlet distribution is widely used in document modelling and document clustering.

I tried to understand its rational. I read from this article that:

Different Dirichlet distributions can be used to model documents by different authors or documents on different topics.

So how could we tell whether it is modelling about different authors or about different topics? This is important because in a document clustering task, it directly dictates the semantic of the clustering result.

And I found it too subjective to limit the possible aspects of modelling to only author or topic. Since there seems to be no strong evidence to favor a specific aspect, it could be any other potential/latent aspect.

Could anyone shed some light on this?

Answer 1

We do not know in general. Usually more context is required.

A topic is just a distribution over words. It can be referring to topics as interpreted by humans (those that we see on the news like business, politics, entertainment...) or if you look at those words generated, it is possible to assign them to authors as well as the words generated could reflect who produces the word and in this context, the authors are the topics.

From the LDA paper by David Blei, Andrew Ng, and Michael Jordan, in the first footnote, it is mentioned that

"We refer to the latent multinomial variables in the LDA model as topics, so as to exploit text-oriented intuitions, but we make no epistemological claims regarding these latent variables beyond their utility in representing probability distributions on sets of word".

They are just the latent variables.

In the example section of the paper:

The top words from some of the resulting multinomial distributions p(w|z) are illustrated in Figure 8 (top). As we have hoped, these distributions seem to capture some of the underlying topics in the corpus (and we have named them according to these topics).

Notice the choice of words of "seem to capture" and they name them according to how they interpreted the collection of words. If you manage to get a list of words that reflect a particular person (including authors), you can name the topic after the person.

Answer 2

(Maybe it should be thought this way...)

Mathematics is not meant to explain things. But rather to describe things. And make predictions if necessary.

Maybe we cannot find direct evidence that Dirichlet allocation IS about topic. But it can be taken as a statistical description of topic as long as the result meets the expectation well. And until a better mathematical model is found.