  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.
