Dirichlet Simplex Nest and Geometric Inference
This work addresses the need for efficient and reliable inference in probabilistic models for researchers and practitioners in fields like text and financial analysis, though it appears incremental as it builds on existing geometric and Dirichlet-based methods.
The authors tackled the problem of probabilistic modeling for diverse data types by proposing Dirichlet Simplex Nest, a model with fast and provably accurate inference algorithms, achieving consistency and strong error bounds across various settings and data distributions, as demonstrated through simulations and analyses of text and financial data.
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.