Dirichlet Process Mixture Models

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Dirichlet Process Mixtures of Trees with Gaussian Process Splits: A Bayesian Nonparametric Framework with Posterior Contraction Rate
Aug 22, 2026Subhasish Basak, Anik Roy, Sourabh BhattacharyaDirichlet Process Mixture Models Posterior Contraction
Indian Statistical Institute
DP-BOA: Dirichlet-Process Birth-or-Assign for On-the-Fly Category Discovery
Jul 15, 2026Peiyan Gu, Zixin Teng, Xuming HeDirichlet Process Mixture Models Bayesian Mixture Models
ShanghaiTech University, Shanghai, China · Shanghai Engineering Research Center of Intelligent Vision and Imaging
DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting
Jul 12, 2026Aqi DongBayesian Mixture Models Dirichlet Process Mixture Models
Embry-Riddle Aeronautical University
BPDA-GMM: Bayesian Probabilistic Data Association via Gaussian Mixture Models for Semantic SLAM
Jun 3, 2026Thanh Nguyen Canh, Haolan Zhang, Xiem HoangVan +2Simultaneous Localization and Mapping Dirichlet Process Mixture Models
School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, 923-1211, Japan · University of Engineering and Technology, Vietnam National University, Hanoi, 10000, Vietnam
Courtroom Analogy: New Perspective on Uncertainty-Aware Classification
May 25, 2026Taeseong Yoon, Heeyoung KimDirichlet Process Mixture Models Uncertainty Quantification
Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.
Enhancing Multi-Robot Exploration Using Probabilistic Frontier Prioritization with Dirichlet Process Gaussian Mixtures
Apr 3, 2026John Lewis Devassy, Meysam Basiri, Mário A. T. Figueiredo +1Dirichlet Process Mixture Models Multi-Robot Exploration
Institute for Systems and Robotics / LARSyS and Instituto Superior Técnico, Universidade de Lisboa, Lisbon 1049-001, Portugal · Instituto de Telecomunicações and Instituto Superior Técnico, Universidade de Lisboa, Lisbon 1049-001, Portugal
Deconfounded Lifelong Learning for Autonomous Driving via Dynamic Knowledge Spaces
Mar 15, 2026Jiayuan Du, Yuebing Song, Yiming Zhao +6Dirichlet Process Mixture Models End-to-End Autonomous Driving
Tongji University, Shanghai, China
Prognostics of Multisensor Systems with Unknown and Unlabeled Failure Modes via Bayesian Nonparametric Process Mixtures
Feb 22, 2026Kani Fu, Sanduni S Disanayaka Mudiyanselage, Chunli Dai +1Dirichlet Process Mixture Models Predictive Maintenance
Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA · School of Forest, Fisheries, and Geomatics Sciences, University of Florida, Gainesville, USA

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Dirichlet Process Mixtures of Trees with Gaussian Process Splits: A Bayesian Nonparametric Framework with Posterior Contraction Rate

Subhasish Basak, Anik Roy, Sourabh Bhattacharya

Indian Statistical Institute

Dirichlet Process Mixture Models Posterior Contraction Bayesian Inference Regression Prediction Intervals

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We propose a Bayesian nonparametric mixture of regression trees with a Dirichlet process prior over tree-parameter pairs, enabling data-driven selection of ensemble size and unifying CART, BART, random forests, and boosting. A novel splitting rule driven by the posterior predictive of a Gaussian process within each terminal node generates flexible, smooth decision boundaries; remarkably, the GP density cancels exactly in the Metropolis--Hastings ratio for GROW/PRUNE moves, ensuring computational feasibility. An exact Gibbs sampler for posterior predictive inference propagates uncertainty through random tree traversal. A parallel MPI implementation distributes independent tree updates across processors, achieving adequate speedups. We prove posterior consistency at rate

n^{-1/4}

in Hellinger distance under only continuity of the true regression function, allowing misspecification, via the identity

h(Θ)=0

. Simulations on Friedman benchmark show near-nominal coverage (0.94 Gaussian, 0.92 Cauchy), robust to high-dimensional noise and heavy tails, outperforming BART and bagged CART. Applications to QSAR toxicity, crime, riboflavin, wheat genomics, and air quality confirm reliable credible intervals and automatic sparsity. The DP mixture offers a principled, robust, theoretically justified alternative for challenging regression with honest uncertainty quantification.