{"paper":{"title":"Matching Observations to Distributions: Efficient Estimation via Sparsified Hungarian Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"cs.DS","authors_text":"Abhay Parekh, Avishek Ghosh, Forest Yang, Kannan Ramchandran, Sinho Chewi","submitted_at":"2018-06-18T15:19:05Z","abstract_excerpt":"Suppose we are given observations, where each observation is drawn independently from one of $k$ known distributions. The goal is to match each observation to the distribution from which it was drawn. We observe that the maximum likelihood estimator (MLE) for this problem can be computed using weighted bipartite matching, even when $n$, the number of observations per distribution, exceeds one. This is achieved by instantiating $n$ duplicates of each distribution node. However, in the regime where the number of observations per distribution is much larger than the number of distributions, the H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06766","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.06766/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}