Critical scaling in hidden state inference for linear Langevin dynamics
We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and study analytically the average prediction error and the typical relaxation time of correlations between errors. We focus on a stochastic linear dynamics of continuous degrees of f...
Gespeichert in:
| Veröffentlicht in: | arXiv.org |
|---|---|
| Hauptverfasser: | , |
| Format: | Paper |
| Sprache: | Englisch |
| Veröffentlicht: |
Ithaca
Cornell University Library, arXiv.org
25.04.2017
|
| Schlagworte: | |
| ISSN: | 2331-8422 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and study analytically the average prediction error and the typical relaxation time of correlations between errors. We focus on a stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings in the infinite network size limit. The expected error on the hidden time courses can be found as the equal-time hidden-to-hidden covariance of the probability distribution conditioned on observations. In the stationary regime, we analyze the phase diagram in the space of relevant parameters, namely the ratio between the numbers of observed and hidden nodes, the degree of symmetry of the interactions and the amplitudes of the hidden-to-hidden and hidden-to-observed couplings relative to the decay constant of the internal hidden dynamics. In particular, we identify critical regions in parameter space where the relaxation time and the inference error diverge, and determine the corresponding scaling behaviour. |
|---|---|
| AbstractList | We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and study analytically the average prediction error and the typical relaxation time of correlations between errors. We focus on a stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings in the infinite network size limit. The expected error on the hidden time courses can be found as the equal-time hidden-to-hidden covariance of the probability distribution conditioned on observations. In the stationary regime, we analyze the phase diagram in the space of relevant parameters, namely the ratio between the numbers of observed and hidden nodes, the degree of symmetry of the interactions and the amplitudes of the hidden-to-hidden and hidden-to-observed couplings relative to the decay constant of the internal hidden dynamics. In particular, we identify critical regions in parameter space where the relaxation time and the inference error diverge, and determine the corresponding scaling behaviour. |
| Author | Sollich, Peter Bravi, Barbara |
| Author_xml | – sequence: 1 givenname: Barbara surname: Bravi fullname: Bravi, Barbara – sequence: 2 givenname: Peter surname: Sollich fullname: Sollich, Peter |
| BookMark | eNotjcFKAzEURYMoWGs_wF3A9dTkZZJMljJoFQbcdF_eZF5qSs1oMi369w7o5h4uHO69YZdpTMTYnRTrutFaPGD-jue1NBLWQjprLtgClJJVUwNcs1UpByEEGAtaqwXbtDlO0eORlzli2vOY-HscBkq8TDjR3ANlSp54GDOfFcLMO0x7Os_q8JPwI_pyy64CHgut_rlk2-enbftSdW-b1_axq1CDrsCAl07UWgarBqkDOmEdofPKDy4oi7XzPngYXAMaqXdO9gKNChSM6pVasvu_2c88fp2oTLvDeMppftyBsEYaYxutfgGzek9g |
| ContentType | Paper |
| Copyright | 2017. 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. |
| Copyright_xml | – notice: 2017. 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. |
| DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.48550/arxiv.1612.01976 |
| DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic ProQuest Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) Engineering Collection |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2331-8422 |
| Genre | Working Paper/Pre-Print |
| GroupedDBID | 8FE 8FG ABJCF ABUWG AFKRA ALMA_UNASSIGNED_HOLDINGS AZQEC BENPR BGLVJ CCPQU DWQXO FRJ HCIFZ L6V M7S M~E PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| ID | FETCH-LOGICAL-a525-262c190451f73d15fa9079ea9c3cd9f37a49ccfc2d9825aeb991b0a63fef63b33 |
| IEDL.DBID | M7S |
| IngestDate | Mon Jun 30 09:30:27 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a525-262c190451f73d15fa9079ea9c3cd9f37a49ccfc2d9825aeb991b0a63fef63b33 |
| Notes | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| OpenAccessLink | https://www.proquest.com/docview/2076166785?pq-origsite=%requestingapplication% |
| PQID | 2076166785 |
| PQPubID | 2050157 |
| ParticipantIDs | proquest_journals_2076166785 |
| PublicationCentury | 2000 |
| PublicationDate | 20170425 |
| PublicationDateYYYYMMDD | 2017-04-25 |
| PublicationDate_xml | – month: 04 year: 2017 text: 20170425 day: 25 |
| PublicationDecade | 2010 |
| PublicationPlace | Ithaca |
| PublicationPlace_xml | – name: Ithaca |
| PublicationTitle | arXiv.org |
| PublicationYear | 2017 |
| Publisher | Cornell University Library, arXiv.org |
| Publisher_xml | – name: Cornell University Library, arXiv.org |
| SSID | ssj0002672553 |
| Score | 1.6213577 |
| SecondaryResourceType | preprint |
| Snippet | We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and study analytically the average... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| SubjectTerms | Conditioning Couplings Covariance Dynamics Error analysis Inference Mathematical analysis Nodes Parameter identification Phase diagrams Relaxation time Scaling Trajectory analysis |
| Title | Critical scaling in hidden state inference for linear Langevin dynamics |
| URI | https://www.proquest.com/docview/2076166785 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELagBYmJt3iUygNrSmI7dj0hgcpDKlUEHcpUOX6ILmlJSsXP5-wmMCCxsESKkiFyrO--O393H0KXAHgOUM_Pw0tpxLyRu-JeOSWoVaxvY23DnNmhGI36k4nM6oJbVcsqG0wMQG3m2tfIfSWEJxygNb1evEfeNcqfrtYWGpuo7ackJEG69_JdYyFcAGOm68PMMLrrSpWfs1UPaA7pAbkR_BcEh7hyt_vfL9pD7UwtbLmPNmxxgLaDnlNXh-i-sTDAFVwgPOFZgd_8uJAChx4iPGs6_TDQVuzJpirx0LcarOBVszaqr47Q-G4wvn2Ias-ESKXE69WIhhDP0sQJapLUKUh-pVVSU22ko0IxqbXTxEhIDZXNgR7mseLUWcdpTukxahXzwp4gTEzsuCU8BxRghmklc62FFBRyJMpMfIo6zbJM631fTX_W5Ozvx-doh_gAGbOIpB3UWpYf9gJt6dVyVpVd1L4ZjLLnbvidcJc9PmWvX6pfqlA |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V09T8MwELWqFgQT3-KjgAcYU1I7sesBMQClVUNViQ7dIsexRQbSkpRCfxT_kXPawIDE1oElS6Ioytnv3p3f3SF0AYBnAPVsPzyfOp4d5C6ZVU5xqqXX0q7SRZ_ZgPf7rdFIDCros6yFsbLKEhMLoI7HyubIbSaENRlAq38zeXXs1Ch7ulqO0Fgsi56ev0PIll9378C-l4S074e3HWc5VcCRPrGKLqLACXp-03AaN30jITwUWgpFVSwM5dITShlFYgHBk9QREKjIlYwabRiNbP4TEL8GLIKIQin49J3SIYwDQaeLs9OiU9iVzD6SWQNYFWkAl-LsF-IXbqy99c9-wDaqDeREZzuootNdtF6oVVW-hx7KAQ04hws4X5yk-Nk2Q0lxUSGFk7KOEQMpx5ZKywwHtpBiBo_G81S-wJv20XAVn36Aquk41YcIk9g1TBMWAcZ5saekiJTiglOIAKkXu0eoXlohXO7qPPwxwfHft8_RRmf4GIRBt987QZvEUgHXc4hfR9Vp9qZP0ZqaTZM8OytWEEbhig32Bfx4A5U |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Critical+scaling+in+hidden+state+inference+for+linear+Langevin+dynamics&rft.jtitle=arXiv.org&rft.au=Bravi%2C+Barbara&rft.au=Sollich%2C+Peter&rft.date=2017-04-25&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.1612.01976 |