Consistency Analysis for the Doubly Stochastic Dirichlet Process

TL;DR

This paper proves the consistency of the Doubly Stochastic Dirichlet Process, demonstrating exponential convergence of posterior probability, and supports these findings with simulations and real-world experiments.

Contribution

It establishes the components consistency and exponential convergence of the DSDP, providing foundational properties and inference algorithms.

Findings

Proves components consistency of DSDP

Demonstrates exponential convergence of posterior

Validates results with simulations and real data

Abstract

This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi-cluster also support the consistency proof. This report is also a support document for the paper "Computationally Efficient Hyperspectral Data Learning Based on the Doubly Stochastic Dirichlet Process".