Consistency Analysis for the Doubly Stochastic Dirichlet Process

This technical report proves components consistency for the Doubly Stochastic Dirichlet Process [1] with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. This report is also a support document for the paper "Computationally Efficient Hyperspectral Data Learning Based on the Doubly Stochastic Dirichlet Process" [1]. The probability of data partitions is important in mixture modeling [2]. LetM be the unordered partition ofn observations, then the probability mass function [3] ofM follows.