Adaptive Low-Complexity Sequential Inference for Dirichlet Process Mixture Models
This work addresses the challenge of efficient online inference for Dirichlet process mixtures, which is incremental as it builds on existing methods with adaptive parameter design.
The paper tackled the problem of online clustering and parameter estimation for Dirichlet process mixture models with unknown cluster numbers by developing a sequential low-complexity inference procedure, demonstrating superior performance to other state-of-the-art methods in experiments on synthetic and real datasets.
We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyperparameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a novel adaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and data predictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to other online state-of-the-art methods.