{"doi":"10.1214/23-aos2292","title":"Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM","abstract":"Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the function domain. We describe a stratification of the Fisher information eigenvalues according to transcendence degrees of graded pieces of the algebra of group invariants, and we relate critical points of the log-likelihood landscape to a sequence of moment optimization problems, extending previous results for a discrete rotation group without projections. We then compute the transcendence degrees and forms of these optimization problems for several examples of function estimation under SO(2) and SO(3) rotations, including a simplified model of cryo-EM as introduced by Bandeira, Blum-Smith, Kileel, Niles-Weed, Perry and Wein. We affirmatively resolve conjectures that third-order moments are sufficient to locally identify a generic signal up to its rotational orbit in these examples. For low-dimensional approximations of the electric potential maps of two small protein molecules, we empirically verify that the noise scalings of the Fisher information eigenvalues conform with our theoretical predictions over a range of SNR, in a model of SO(3) rotations without projections.","journal":"The Annals of Statistics","year":2024,"id":457304,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":5,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9576,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":717127,"name":"Roy R. Lederman","orcid":"0000-0002-5080-4483","position":1,"is_corresponding":false},{"id":1282621,"name":"Yi Sun","orcid":"0000-0002-6124-4127","position":2,"is_corresponding":false},{"id":966870,"name":"Tianhao Wang","orcid":"0000-0002-2126-6110","position":3,"is_corresponding":false},{"id":577527,"name":"Sheng Xu","orcid":"0000-0002-3120-4992","position":4,"is_corresponding":false},{"id":1025201,"name":"Zhou Fan","orcid":"0000-0002-5940-4697","position":0,"is_corresponding":true}],"reference_count":45,"raw_metadata":null,"created_at":"2026-07-19T02:03:37.136946Z","pmid":"40881772","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}