Title: BIology Genetics and Statistics

Samy Tindel

Description

• dissertation

Project Proposal Title: BIology, Genetics and Statistics Acronym: BIGS Scientific leader: Samy Tindel Permanent responsible: Pierre Vallois Proposed INRIA theme: Biological Systems Keywords: Data Analysis, Support Vector Machines, Nonparametric Statis- tics, Regression models, Stochastic differential equations, Likelihood estima- tion.

• convergence obtained


• mechanistic models


• research direction


• complex situations


• biological systems


• noisy differential


• based approach


• monte carlo methods


• local regression techniques


• team

Sujets

• Dissertation
• Centre de recherche en automatique de Nancy
• Bastogne
• Müller
• Vallois
• Lou Ferrigno
• Barcelona

Informations

• Publié par: pefav
• Nombre de lectures: 10
• Langue: English

Extrait

ProjectProposal Title:BIology,GeneticsandStatistics Acronym: BIGS Scientificleader: SamyTindel Permanentresponsible: PierreVallois ProposedINRIAtheme: BiologicalSystems Keywords: DataAnalysis,SupportVectorMachines,NonparametricStatis- tics,Regressionmodels,Stochasticdifferentialequations,Likelihoodestima- .noit

2 Contents 1.Project-teamcomposition 2.Overallobjectives 3.Applicationdomains 3.1.Statisticalanalysisofhighdimensionaldata 3.2.EstimationforComplexandBiologicalSystems 3.3.Natureofthedata 4.Stateoftheart 4.1.Statisticalanalysisofhighdimensionaldata 4.2.EstimationforComplexandBiologicalSystems 5.Scientificfoundations 5.1.Statisticalanalysisofhighdimensionaldata 5.2.EstimationforComplexandBiologicalSystems 6.Researchdirections 6.1.Statisticalanalysisofhighdimensionaldata 6.2.EstimationforComplexandBiologicalSystems 7.Software 8.Expectedresultsandcriteriaofsuccess 9.Project-teampositioning 9.1.PositioningwithrespecttootherINRIAgroups 9.2.Researchgroupsinrelatedareas 10.Collaborations 10.1.CollaborationswithotherINRIAprojectteams 10.2.CollaborationswithotherFrenchresearchgroups 10.3.Collaborationswithforeignresearchgroups 10.4.IndustrialCollaborations Project-teambibliography Books,Monographs,andbookchapters Doctoraldissertationsand“Habilitation”theses Articlesininternationaljournals Publicationsininternationalconferencesandworkshops Articlesinnationaljournals Publicationsinnationalconferencesandworkshops InternalReports AnnexA.Permanentmemberrésumé References 3 3 6 6 7 8 9 9 01 11 21 41 51 61 81 02 02 22 22 32 52 25 52 62 62 62 62 72 72 13 23 33 33 33 93

1. Project-teamcomposition Listthemembersoftheproposedteam,includingthecurrentPhDstudents. StaffMembers • ThierryBastogne(AssistantProfessor,UniversityofNancy1andCRAN,50%) • SandieFerrigno(AssistantProfessor,INPLandIECN) • CélineLacaux(AssistantProfessor,INPLandIECN,50%) • Jean-MarieMonnez(Professor,UniversityofNancy2andIECN) • AurélieMuller(AssistantProfessor,INPLandIECN) • SamyTindel(Professor,UniversityofNancy1andIECN) • PierreVallois(Professor,UniversityofNancy1andIECN) • SophieWantz(AssistantProfessor,UniversityofNancy2andIECN,50%) PhDstudents • AurélienDeya(IECN) • RoukayaKeinj(CRANandIECN) • RémiBonidal(IECNandLORIA) 3 2. Overallobjectives Describetheoverallobjectivesandthemainresearchdirectionsoftheproject.This sectionshouldallowthereadertohaveafairideaoftheprojectatoneglance. TheBiostatisticsactivitiesattheInstitutElieCartan(IECN)beganfouryearsago, whensomecontactsbetweenourProbabilityteamandsomespecialistsofotherareas, suchasMedicine,Biophysics,AutomaticsorAgronomy,wereestablished.Thesecontacts, supportedbysomeconcreteappliedprojects,gaveraisequicklytoamaindrivingdirection inourinvestigations,whichconsistsinanalyzinghighdimensionaldata,withaspecial viewtowardsmodelingandsimulatingbiologicalphenomenon. Interestinglyenough,thiskindofanalysisrequiressomenewmathematicaltechniques, comingfromawiderangeofdomains,likeMonte-Carlomethods,classicalandbayesian statistics,Markovmodels,orconvergenceandinferenceforstochasticprocesses.Itisthus importanttoemphasizethefactthatalargespectrumoftoolswillberequiredinorderto analyzehighdimensionaldatainourcontext.Thisismainlybecausethecurrentproject hastobeseenasaninitialimpulse,whichshouldlaunchanewdynamicsinbiostatistics atNancy,andhopefullyintheEastofFranceaswell.Wewishtoachievethisimpulse :yb (1)Federatingtheenergiesofmostoftheresearchersinpureandappliedstatisticsin Nancy. (2)Startingagoodnumberofinterestingprojects,goingfromaconsequenttheoretical backgroundtotherealworldapplicationsinBiology,GeneticsorMedicine. Thisapplicationorientedpointofview,alwaysfocusedonbiologicsystems,forcesusto haveagrasponmanydifferenttechniques.Weclaimhoweverthatthecompositionof ourteam,madeofcompetentprobabilistsandstatisticianscomingfromdifferentareas, allowsustofacethischallengingsituation. Weshalltrytosummarizenowthemaindirections,whichwillleadourresearchin Biostatisticsduringthenextyears.

4 (1)Statisticalanalysisofhighdimensionaldata:Cancerdetectionprogramsand otherapplicationsingeneticshaveimpliedagreatdemandinanalysisofsmallsamplesof highdimensionaldata(typically,adatacanbeavectorin R d ,withdoforder10 4 ,while thesizeofthesampleisn,withnoforder10 2 ).Ourteamwishestomakesomestepsin thisdirection,andweshallfocusmainlyonthefollowingtopics: • OnlineFactorialAnalysis:Highdimensionaldataareoftenobtainedonline,andcannot bestoredintegrallyinacomputermemory.Oneoftherecentchallengesindataanalysisis thentobeabletoperformanaccurateclassificationbytakingadvantageofthepossibility ofupdatingourinformation.Thisshouldbedone,ofcourse,inarathersimpleand efficientway,allowingrealtimeanalysis.Weplantousetechniquesbasedonsome sophisticatedtoolscomingfromstochasticapproximationinordertocompletethiskind ofprogram. • ProbabilisticAnalysisofSupportVectorMachines:Stillinthecontextofclassification, wealsowishtoanalyze,ataprobabilisticlevel,theconvergencerateofsomeestimated boundaryformulticlassSupportVectorMachinealgorithms.Thiskindofanalysishas alreadybeencarriedoutforthecaseoftwoclassestobeseparated,andreliesoncon- centrationinequalities,basicallydistributionfree.Thegeneralizationtothemulticlass caseisnon-trivial,andhasbeenalreadystudiedbyYannGuermeur(LORIA).Weshall introducesomeprobabilistictoolsinordertoimprovetheratesofconvergenceobtained forsuchalgorithms.WealsoplantoperformanextensivecomparisonofSVMtechniques withotherclassifiactionmethods,atleastinsomeparticularcasesofunderlyingdistribu- tions,likeGaussianmixtures.Thisverynaturalquestion,whicharisesinmanypractical studies,isstrangelyhardlyaddressedfromatheoreticalpointofview. • Localregressiontechniques:Ourpreviousitemoncomparisonbetweenclassification methodsiscloselylinked,ascanbeeasilyunderstoodfromthelectureof[31],tolocal regressiontechniques.Ourteamalsoplanstocontributeactivelytothisfield,whichis obviouslyinterestinginitsownright.Indeed,weshallstudyofaglobalgoodnessoffittest forstatisticalmodels:ourtestwillbeabletoassess,inquiteageneralframework,whether agivenmodelfitsadatasetregardingmostassumptionsmadeinelaboratingthemodel. ItwillbebasedonageneralizationoftheCramer-VonMisesstatisticandinvolvesanon parametricestimateoftheconditionaldistributionoftheresponsevariable.Thiskindof strategy,whichfitsintotheglobalpictureofstatisticalanalysisofhighdimensionaldata, willbeimplementedforastudyconcerningfetalbiometry. (2)EstimationforComplexandBiologicalSystems:Thankstoourcontactswith practitionersworkingonbiologicalsystems,ourteamhasbeguntogetfamiliarizedwith someestimationproblemsindifferentcomplexsituations.Asweshallsee,theseproblems willalsobeaninvitationtoanalyzedeeplysomegeneralclassesofnoisydifferential systemsdrivenbyBrownianmotionofmoregeneralfamiliesofstochasticprocesses,such asfractionalBrownianmotions.Thisleadsustoanimportantscientificaimofourproject, whichconsistsinathoroughstudyofasymptotic,numericalandstatisticalpropertiesof Brownianorfractionaldifferentialsystems. Tobemorespecific,hereisalistofsomeprojectsonwhichwewillpayaspecial attention: • Photodynamictherapy:Since1988,somecontrolsystemscientistsandbiologistsatthe CentredeRechercheenAutomatiquedeNancy(CRANinshort)haveworkedtogetherto