Title: BIology Genetics and Statistics
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- 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
ProjectProposalTitle:BIology,GeneticsandStatisticsAcronym:BIGSScientificleader:SamyTindelPermanentresponsible:PierreValloisProposedINRIAtheme:BiologicalSystemsKeywords:DataAnalysis,SupportVectorMachines,NonparametricStatis-tics,Regressionmodels,Stochasticdifferentialequations,Likelihoodestima-.noit
2Contents1.Project-teamcomposition2.Overallobjectives3.Applicationdomains3.1.Statisticalanalysisofhighdimensionaldata3.2.EstimationforComplexandBiologicalSystems3.3.Natureofthedata4.Stateoftheart4.1.Statisticalanalysisofhighdimensionaldata4.2.EstimationforComplexandBiologicalSystems5.Scientificfoundations5.1.Statisticalanalysisofhighdimensionaldata5.2.EstimationforComplexandBiologicalSystems6.Researchdirections6.1.Statisticalanalysisofhighdimensionaldata6.2.EstimationforComplexandBiologicalSystems7.Software8.Expectedresultsandcriteriaofsuccess9.Project-teampositioning9.1.PositioningwithrespecttootherINRIAgroups9.2.Researchgroupsinrelatedareas10.Collaborations10.1.CollaborationswithotherINRIAprojectteams10.2.CollaborationswithotherFrenchresearchgroups10.3.Collaborationswithforeignresearchgroups10.4.IndustrialCollaborationsProject-teambibliographyBooks,Monographs,andbookchaptersDoctoraldissertationsand“Habilitation”thesesArticlesininternationaljournalsPublicationsininternationalconferencesandworkshopsArticlesinnationaljournalsPublicationsinnationalconferencesandworkshopsInternalReportsAnnexA.PermanentmemberrésuméReferences33667899011121415161810202222232522552626262627272132333333393
1.Project-teamcompositionListthemembersoftheproposedteam,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)32.OverallobjectivesDescribetheoverallobjectivesandthemainresearchdirectionsoftheproject.Thissectionshouldallowthereadertohaveafairideaoftheprojectatoneglance.TheBiostatisticsactivitiesattheInstitutElieCartan(IECN)beganfouryearsago,whensomecontactsbetweenourProbabilityteamandsomespecialistsofotherareas,suchasMedicine,Biophysics,AutomaticsorAgronomy,wereestablished.Thesecontacts,supportedbysomeconcreteappliedprojects,gaveraisequicklytoamaindrivingdirectioninourinvestigations,whichconsistsinanalyzinghighdimensionaldata,withaspecialviewtowardsmodelingandsimulatingbiologicalphenomenon.Interestinglyenough,thiskindofanalysisrequiressomenewmathematicaltechniques,comingfromawiderangeofdomains,likeMonte-Carlomethods,classicalandbayesianstatistics,Markovmodels,orconvergenceandinferenceforstochasticprocesses.Itisthusimportanttoemphasizethefactthatalargespectrumoftoolswillberequiredinordertoanalyzehighdimensionaldatainourcontext.Thisismainlybecausethecurrentprojecthastobeseenasaninitialimpulse,whichshouldlaunchanewdynamicsinbiostatisticsatNancy,andhopefullyintheEastofFranceaswell.Wewishtoachievethisimpulse:yb(1)FederatingtheenergiesofmostoftheresearchersinpureandappliedstatisticsinNancy.(2)Startingagoodnumberofinterestingprojects,goingfromaconsequenttheoreticalbackgroundtotherealworldapplicationsinBiology,GeneticsorMedicine.Thisapplicationorientedpointofview,alwaysfocusedonbiologicsystems,forcesustohaveagrasponmanydifferenttechniques.Weclaimhoweverthatthecompositionofourteam,madeofcompetentprobabilistsandstatisticianscomingfromdifferentareas,allowsustofacethischallengingsituation.Weshalltrytosummarizenowthemaindirections,whichwillleadourresearchinBiostatisticsduringthenextyears.
4(1)Statisticalanalysisofhighdimensionaldata:Cancerdetectionprogramsandotherapplicationsingeneticshaveimpliedagreatdemandinanalysisofsmallsamplesofhighdimensionaldata(typically,adatacanbeavectorinRd,withdoforder104,whilethesizeofthesampleisn,withnoforder102).Ourteamwishestomakesomestepsinthisdirection,andweshallfocusmainlyonthefollowingtopics:•OnlineFactorialAnalysis:Highdimensionaldataareoftenobtainedonline,andcannotbestoredintegrallyinacomputermemory.Oneoftherecentchallengesindataanalysisisthentobeabletoperformanaccurateclassificationbytakingadvantageofthepossibilityofupdatingourinformation.Thisshouldbedone,ofcourse,inarathersimpleandefficientway,allowingrealtimeanalysis.Weplantousetechniquesbasedonsomesophisticatedtoolscomingfromstochasticapproximationinordertocompletethiskindofprogram.•ProbabilisticAnalysisofSupportVectorMachines:Stillinthecontextofclassification,wealsowishtoanalyze,ataprobabilisticlevel,theconvergencerateofsomeestimatedboundaryformulticlassSupportVectorMachinealgorithms.Thiskindofanalysishasalreadybeencarriedoutforthecaseoftwoclassestobeseparated,andreliesoncon-centrationinequalities,basicallydistributionfree.Thegeneralizationtothemulticlasscaseisnon-trivial,andhasbeenalreadystudiedbyYannGuermeur(LORIA).Weshallintroducesomeprobabilistictoolsinordertoimprovetheratesofconvergenceobtainedforsuchalgorithms.WealsoplantoperformanextensivecomparisonofSVMtechniqueswithotherclassifiactionmethods,atleastinsomeparticularcasesofunderlyingdistribu-tions,likeGaussianmixtures.Thisverynaturalquestion,whicharisesinmanypracticalstudies,isstrangelyhardlyaddressedfromatheoreticalpointofview.•Localregressiontechniques:Ourpreviousitemoncomparisonbetweenclassificationmethodsiscloselylinked,ascanbeeasilyunderstoodfromthelectureof[31],tolocalregressiontechniques.Ourteamalsoplanstocontributeactivelytothisfield,whichisobviouslyinterestinginitsownright.Indeed,weshallstudyofaglobalgoodnessoffittestforstatisticalmodels:ourtestwillbeabletoassess,inquiteageneralframework,whetheragivenmodelfitsadatasetregardingmostassumptionsmadeinelaboratingthemodel.ItwillbebasedonageneralizationoftheCramer-VonMisesstatisticandinvolvesanonparametricestimateoftheconditionaldistributionoftheresponsevariable.Thiskindofstrategy,whichfitsintotheglobalpictureofstatisticalanalysisofhighdimensionaldata,willbeimplementedforastudyconcerningfetalbiometry.(2)EstimationforComplexandBiologicalSystems:Thankstoourcontactswithpractitionersworkingonbiologicalsystems,ourteamhasbeguntogetfamiliarizedwithsomeestimationproblemsindifferentcomplexsituations.Asweshallsee,theseproblemswillalsobeaninvitationtoanalyzedeeplysomegeneralclassesofnoisydifferentialsystemsdrivenbyBrownianmotionofmoregeneralfamiliesofstochasticprocesses,suchasfractionalBrownianmotions.Thisleadsustoanimportantscientificaimofourproject,whichconsistsinathoroughstudyofasymptotic,numericalandstatisticalpropertiesofBrownianorfractionaldifferentialsystems.Tobemorespecific,hereisalistofsomeprojectsonwhichwewillpayaspecialattention:•Photodynamictherapy:Since1988,somecontrolsystemscientistsandbiologistsattheCentredeRechercheenAutomatiquedeNancy(CRANinshort)haveworkedtogetherto
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