{"id":"https://openalex.org/W2975601855","doi":"https://doi.org/10.1109/isit.2019.8849681","title":"High-Dimensional Linear Regression and Phase Retrieval via PSLQ Integer Relation Algorithm","display_name":"High-Dimensional Linear Regression and Phase Retrieval via PSLQ Integer Relation Algorithm","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2975601855","doi":"https://doi.org/10.1109/isit.2019.8849681","mag":"2975601855"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849681","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031648070","display_name":"David Gamarnik","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"David Gamarnik","raw_affiliation_strings":["MIT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT","institution_ids":["https://openalex.org/I4210109586"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029207194","display_name":"Eren C. K\u0131z\u0131lda\u011f","orcid":"https://orcid.org/0000-0003-0411-7161"},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Eren C. Kizilda\u011f","raw_affiliation_strings":["MIT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT","institution_ids":["https://openalex.org/I4210109586"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210109586"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1437","last_page":"1441"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6441664695739746},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6296278238296509},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.547530472278595},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.5061642527580261},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4623182415962219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43419349193573},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43364417552948},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37619537115097046},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3342277407646179},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12677672505378723},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1253218948841095}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6441664695739746},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6296278238296509},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.547530472278595},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.5061642527580261},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4623182415962219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43419349193573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43364417552948},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37619537115097046},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3342277407646179},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12677672505378723},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1253218948841095},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2019.8849681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849681","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W2019045525","https://openalex.org/W2049502219","https://openalex.org/W2070268091","https://openalex.org/W2073085121","https://openalex.org/W2101675075","https://openalex.org/W2103236565","https://openalex.org/W2115275122","https://openalex.org/W2122548617","https://openalex.org/W2127300249","https://openalex.org/W2135780853","https://openalex.org/W2140122025","https://openalex.org/W2141040012","https://openalex.org/W2150780437","https://openalex.org/W2164452299","https://openalex.org/W2171681164","https://openalex.org/W2595294663","https://openalex.org/W2770963231","https://openalex.org/W2790145796","https://openalex.org/W2963048782","https://openalex.org/W4301028776","https://openalex.org/W6735307612","https://openalex.org/W6746454450","https://openalex.org/W6748395944"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2042331445","https://openalex.org/W2134230263","https://openalex.org/W2129251126","https://openalex.org/W2950467063","https://openalex.org/W2079759874","https://openalex.org/W2806730547","https://openalex.org/W2143471372","https://openalex.org/W2348527119","https://openalex.org/W2016712352"],"abstract_inverted_index":{"We":[0,20,77,95],"study":[1],"high-dimensional":[2],"linear":[3,35],"regression":[4],"problem":[5],"without":[6],"sparsity,":[7],"and":[8,85],"address":[9],"the":[10,107],"question":[11],"of":[12,18,58,67,81],"efficient":[13],"recovery":[14],"with":[15,44,52],"small":[16],"number":[17],"measurements.":[19],"propose":[21],"an":[22,27,102],"algorithm":[23,105],"which":[24],"efficiently":[25],"recovers":[26],"unknown":[28],"feature":[29],"vector":[30],"\u03b2*":[31,59,112],"\u2208":[32,113],"\u211dpfrom":[33],"its":[34],"measurements":[36],"Y":[37,122],"=":[38,123],"X\u03b2*":[39],"in":[40,71],"polynomially":[41],"many":[42],"steps,":[43],"high":[45],"probability":[46],"(as":[47],"p":[48,72],"\u2192":[49],"\u221e),":[50],"even":[51],"a":[53,63,79],"single":[54],"measurement,":[55],"provided":[56],"elements":[57],"are":[60],"supported":[61],"on":[62],"rationally":[64],"independent":[65],"set":[66],"at":[68],"most":[69],"polynomial":[70],"size":[73],"known":[74],"to":[75,91,100,115,116],"learner.":[76],"use":[78],"combination":[80],"PSLQ":[82],"integer":[83],"relation":[84],"LLL":[86],"lattice":[87],"basis":[88],"reduction":[89],"algorithms":[90],"achieve":[92],"our":[93,98],"goal.":[94],"then":[96],"apply":[97],"ideas":[99],"develop":[101],"efficient,":[103],"single-sample":[104],"for":[106],"phase":[108],"retrieval":[109],"problem,":[110],"where":[111],"Cpis":[114],"be":[117],"recovered":[118],"from":[119],"magnitude-only":[120],"observations":[121],"|\u3008X,":[124],"\u03b2*\u3009|.":[125]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}