{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/summarizing-bayesian-nonparametric-mixture","title":"Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures","arxiv_id":"2411.14674","date":"2024-11-22","proceeding":null,"authors":["Khai Nguyen","Peter Mueller"],"abstract":"Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al., 2022). We propose a novel approach for summarizing posterior inference in nonparametric Bayesian mixture models, prioritizing estimation of the mixing measure (or mixture) as an inference target. One of the key features is the model-agnostic nature of the approach, which remains valid under arbitrarily complex dependence structures in the underlying sampling model. Using a decision-theoretic framework, our method identifies a point estimate by minimizing posterior expected loss. A loss function is defined as a discrepancy between mixing measures. Estimating the mixing measure implies inference on the mixture density and the random partition. Exploiting the discrete nature of the mixing measure, we use a version of sliced Wasserstein distance. We introduce two specific variants for Gaussian mixtures. The first, mixed sliced Wasserstein, applies generalized geodesic projections on the product of the Euclidean space and the manifold of symmetric positive definite matrices. The second, sliced mixture Wasserstein, leverages the linearity of Gaussian mixture measures for efficient projection","url_abs":"https://arxiv.org/abs/2411.14674v5","url_pdf":"https://arxiv.org/pdf/2411.14674v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"summarizing-bayesian-nonparametric-mixture","repo_url":"https://github.com/khainb/sbnpm-sot","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":null,"task_name":"valid"}],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2411.14674","atlas_url":"https://app.syntology.ai/?focus=2411.14674","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2411.14674"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/khainb/sbnpm-sot","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"dcb558cb662e2601","entry":"sample_from_mixture","repo":"khainb/sbnpm-sot","repo_kind":"official","path":"simulation/run_truncated_dpgmm.py","file_url":"https://github.com/khainb/sbnpm-sot/blob/HEAD/simulation/run_truncated_dpgmm.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"dcb558cb662e2601"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}