Dirichlet Simplex Nest and Geometric Inference

Mikhail Yurochkin; Aritra Guha; Yuekai Sun; XuanLong Nguyen

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arXiv · 1905.11009

Dirichlet Simplex Nest and Geometric Inference

Mikhail Yurochkin·Aritra Guha·Yuekai Sun·XuanLong Nguyen

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Abstract

We propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the model's convex geometry and low dimensional simplicial structure. By exploiting the connection to Voronoi tessellation and properties of Dirichlet distribution, the proposed inference algorithm is shown to achieve consistency and strong error bound guarantees on a range of model settings and data distributions. The effectiveness of our model and the learning algorithm is demonstrated by simulations and by analyses of text and financial data.

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Mikhail Yurochkin, Aritra Guha, Yuekai Sun, XuanLong Nguyen. 2019-05-27. Dirichlet Simplex Nest and Geometric Inference. https://arxiv.org/abs/1905.11009

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