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Add a better implementation of Latent Dirichlet Allocation #31925

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Describe the workflow you want to enable

While this remains to be rigorously tested, the scikit-learn implementation of Latent Dirichlet Allocation is, in the unanimous experience of topic modelling scholars, outperformed by Gibbs-Sampling implementations, such as the ones in MALLET and tomotopy when it comes to topic quality. I have personally been criticised for using the scikit-learn implementation of LDA in my publications as a baseline, since other scholars do not think this implementation does justice to how well LDA can actually work in practice.
This is quite sad, since scikit-learn otherwise has a very authoritative position when it comes to machine learning, and many research and industry workflows build on your well-thought out and convenient API.

It would be of immense value for both industry and academia if Latent Dirichlet Allocation had multiple implementations, and preferably another one were the default.

Describe your proposed solution

Include the implementation of LDA from the following publication:
Distributed Algorithms for Topic Models

This implementation has been around for a while, is used both in tomotopy and MALLET, is published in a reputable journal and has been cited more than 600 times according to Google Scholar.

Describe alternatives you've considered, if relevant

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