{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-8504491","patent":{"patent_number":"US-8504491","title":"Variational EM algorithm for mixture modeling with component-dependent partitions","assignee":null,"inventors":[],"filing_date":"2010-05-25T00:00:00.000Z","publication_date":"2013-08-06T00:00:00.000Z","cpc_codes":["G06F"],"num_claims":9,"abstract":"Described are variational Expectation Maximization (EM) embodiments for learning a mixture model using component-dependent data partitions, where the E-step is sub-linear in sample size while the algorithm still maintains provable convergence guarantees. Component-dependent data partitions into blocks of data items are constructed according to a hierarchical data structure comprised of nodes, where each node corresponds to one of the blocks and stores statistics computed from the data items in the corresponding block. A modified variational EM algorithm computes the mixture model from initial component-dependent data partitions and a variational R-step updates the partitions. This process is repeated until convergence. Component membership probabilities computed in the E-step are constrained such that all data items belonging to a particular block in a particular component-dependent partition behave in the same way. The E-step can therefore consider the blocks or chunks of data items via their representative statistics, rather than considering individual data items."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Variational EM algorithm for mixture modeling with component-dependent partitions","description":"Described are variational Expectation Maximization (EM) embodiments for learning a mixture model using component-dependent data partitions, where the E-step is sub-linear in sample size while the algo","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-8504491","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-8504491","citation_suggestion":"Patentable. \"Variational EM algorithm for mixture modeling with component-dependent partitions\" (US-8504491). https://patentable.app/patents/US-8504491","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-8504491","json":"https://patentable.app/api/llm-context/US-8504491","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-05-31T07:44:25.526Z"}