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Abstract:
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Modeling data distributions and transformations in simplexes and performing Bayesian inference can be challenging due to simplicial constraints and the behavior near boundaries. However, as demonstrated by the popularity of topic modeling, being able to do so can prove useful in a vast array of applications. In this work we propose several approaches to accomplish these goals. The first is to apply a parsimonious, simplex-preserving transformation and to induce different noise distributions on the transformed data. The second is organize the simplicial elements into a hierarchy of subsets, an approach inspired by the nested Chinese Restaurant Process. We proceed to show how to perform inference and apply it to simulations and real world data sets.
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