Dirichlet Simplex Nest and Geometric Inference

TL;DR

This paper introduces Dirichlet Simplex Nest, a probabilistic model with efficient inference algorithms that leverage convex geometry and Dirichlet distribution properties, demonstrating strong theoretical guarantees and practical effectiveness.

Contribution

It presents a novel probabilistic model and inference method that exploit geometric and low-dimensional structures, with proven consistency and error bounds.

Findings

Inference algorithms achieve strong error bounds.

Model demonstrates effectiveness on text and financial data.

Theoretical guarantees ensure reliable inference.

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.