Minimax density estimation in the adversarial framework under local differential privacy
We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with t...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2024-03 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Mélisande Albert Chevallier, Juliette Laurent, Béatrice Sacko, Ousmane |
| description | We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates. |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_3014225129</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3014225129</sourcerecordid><originalsourceid>FETCH-proquest_journals_30142251293</originalsourceid><addsrcrecordid>eNqNjs0KwjAQhIMgWLTvsOC50CbWn7MoXrx58FaC2WBqm9RNWu3bG8EH8DTMzAczE5ZwIYpsu-J8xlLv6zzP-XrDy1Ik7Ho21rTyDQqtN2EE9CH6YJwFYyHcEaQakLwkIxvQJFt8OXpAbxUSNO4WU2W0RkIbvkhHZpC3ccGmWjYe05_O2fJ4uOxPWUfu2ceVqnY92VhVIi_it7LgO_Ef9QErxELv</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3014225129</pqid></control><display><type>article</type><title>Minimax density estimation in the adversarial framework under local differential privacy</title><source>Free E- Journals</source><creator>Mélisande Albert ; Chevallier, Juliette ; Laurent, Béatrice ; Sacko, Ousmane</creator><creatorcontrib>Mélisande Albert ; Chevallier, Juliette ; Laurent, Béatrice ; Sacko, Ousmane</creatorcontrib><description>We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Density ; Lower bounds ; Minimax technique ; Privacy ; Sobolev space</subject><ispartof>arXiv.org, 2024-03</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780</link.rule.ids></links><search><creatorcontrib>Mélisande Albert</creatorcontrib><creatorcontrib>Chevallier, Juliette</creatorcontrib><creatorcontrib>Laurent, Béatrice</creatorcontrib><creatorcontrib>Sacko, Ousmane</creatorcontrib><title>Minimax density estimation in the adversarial framework under local differential privacy</title><title>arXiv.org</title><description>We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates.</description><subject>Density</subject><subject>Lower bounds</subject><subject>Minimax technique</subject><subject>Privacy</subject><subject>Sobolev space</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNqNjs0KwjAQhIMgWLTvsOC50CbWn7MoXrx58FaC2WBqm9RNWu3bG8EH8DTMzAczE5ZwIYpsu-J8xlLv6zzP-XrDy1Ik7Ho21rTyDQqtN2EE9CH6YJwFYyHcEaQakLwkIxvQJFt8OXpAbxUSNO4WU2W0RkIbvkhHZpC3ccGmWjYe05_O2fJ4uOxPWUfu2ceVqnY92VhVIi_it7LgO_Ef9QErxELv</recordid><startdate>20240327</startdate><enddate>20240327</enddate><creator>Mélisande Albert</creator><creator>Chevallier, Juliette</creator><creator>Laurent, Béatrice</creator><creator>Sacko, Ousmane</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240327</creationdate><title>Minimax density estimation in the adversarial framework under local differential privacy</title><author>Mélisande Albert ; Chevallier, Juliette ; Laurent, Béatrice ; Sacko, Ousmane</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_30142251293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Density</topic><topic>Lower bounds</topic><topic>Minimax technique</topic><topic>Privacy</topic><topic>Sobolev space</topic><toplevel>online_resources</toplevel><creatorcontrib>Mélisande Albert</creatorcontrib><creatorcontrib>Chevallier, Juliette</creatorcontrib><creatorcontrib>Laurent, Béatrice</creatorcontrib><creatorcontrib>Sacko, Ousmane</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mélisande Albert</au><au>Chevallier, Juliette</au><au>Laurent, Béatrice</au><au>Sacko, Ousmane</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Minimax density estimation in the adversarial framework under local differential privacy</atitle><jtitle>arXiv.org</jtitle><date>2024-03-27</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2024-03 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_3014225129 |
| source | Free E- Journals |
| subjects | Density Lower bounds Minimax technique Privacy Sobolev space |
| title | Minimax density estimation in the adversarial framework under local differential privacy |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-07T17%3A42%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Minimax%20density%20estimation%20in%20the%20adversarial%20framework%20under%20local%20differential%20privacy&rft.jtitle=arXiv.org&rft.au=M%C3%A9lisande%20Albert&rft.date=2024-03-27&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E3014225129%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3014225129&rft_id=info:pmid/&rfr_iscdi=true |