A Principled Approach to Expectation Maximisation and Latent Dirichlet Allocation Using Jeffrey’s Update Rule

In Helle Hvid Hansen, Andre Scedrov & Ruy J. G. B. de Queiroz (eds.), Logic, Language, Information, and Computation: 29th International Workshop, WoLLIC 2023, Halifax, NS, Canada, July 11–14, 2023, Proceedings. Springer Nature Switzerland. pp. 256-273 (2023)
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Expectation Maximisation (EM) and Latent Dirichlet Allocation (LDA) are two frequently used inference algorithms, for finding an appropriate mixture of latent variables, and for finding an allocation of topics for a collection of documents. A recent insight in probabilistic learning is that Jeffrey’s update rule gives a decrease of Kullback-Leibler divergence. Its logic is error correction. It is shown that this same rule and divergence decrease logic is at the heart of EM and LDA, ensuring that successive iterations are decreasingly wrong.



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