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I have a more theoretical question about LDA (Latent Dirichet Allocation).

When doing LDA we provide number of topics ourselves. As far as I understand it tries to build topic-word-document distributions to minimize perplexity (which is why we are doing it in iterative manner).

So the question - can we fit the LDA several times with different number of topics, check the perplexity of each result and choose the number of topics which yielded minimal perplexity? Or am I misunderstanding the perplexity meaning and the algorithm itself - so the perplexity is actually not a 'fit measure' for LDA?

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Yes, in fact this is the cross validation method of finding the number of topics. But note that you should minimize the perplexity of a held-out dataset to avoid overfitting.

It's worth noting that a non-parametric extension of LDA can derive the number of topics from the data without cross validation. Implementations exist at David Blei's lab github, but at the time of this writing I haven't see HDP LDA implemented in any mainstream, open-source ML libraries.

Caveat: Hierarchal LDA is different. It finds a hierarchy of topics, whereas hierarchal Dirichlet processes let you fit a potentially infinite number of flat topics. (The dual use of "hierarchy" can be confusing.)

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  • $\begingroup$ Thank you! Any advice which library has good H-LDA implementation? I do know sklearn has nothing like it, but I am not sure which one has a good implementation $\endgroup$ – Maksim Khaitovich Aug 11 '17 at 17:04
  • $\begingroup$ Sorry, I haven't seen an implementation in any of the widely used libraries. David Blei's lab has two implementations, but I haven't used them. Also, keep in mind that H-LDA is different: It finds a hierarchy of topics. Hierarchal Dirichlet processes lets you fit a potentially infinite number of flat topics. (The dual use of "hierarchy" can be confusing.) $\endgroup$ – Sean Easter Aug 11 '17 at 17:18
  • $\begingroup$ Now I get it. In such case any advice on where I could read a bit more about the CV method you mentioned - just want to understand if there is anything I need to keep in mind and was there any research which demonstrates potential value of performing such topics number optimization based on perplexity? $\endgroup$ – Maksim Khaitovich Aug 11 '17 at 18:47
  • $\begingroup$ Sure, but clarify for me: Are you asking why we use perplexity, or why cross validate to find the number of clusters? $\endgroup$ – Sean Easter Aug 11 '17 at 18:48
  • $\begingroup$ I understand why, but I am more interested in why perplexity and what are the potential benefits from business standpoint. Right now I just try to play around with number of topics manually until I get a list of topics which seem meaningful to me. But I want try and come up with the more systematic way of doing this instead of just relying on 'gut feeling' $\endgroup$ – Maksim Khaitovich Aug 11 '17 at 19:02

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