2015
Intrinsic modeling of stochastic dynamical systems using empirical geometry
Talmon R, Coifman R. Intrinsic modeling of stochastic dynamical systems using empirical geometry. Applied And Computational Harmonic Analysis 2015, 39: 138-160. DOI: 10.1016/j.acha.2014.08.006.Peer-Reviewed Original ResearchLow-dimensional manifoldDynamical systemsEmpirical geometryReal-world dynamical systemsStochastic dynamical systemsNon-Gaussian tracking problemsNonlinear filtering applicationsNonlinear differential equationsIntrinsic Riemannian metricMarkov chain schemeEmpirical probability densityLocal tangent spaceIntrinsic modelDifferential equationsIntrinsic modelingKnowledge of modelsTangent spaceProbability densityMathematical calibrationTracking problemInverse problemRiemannian metricLaplace operatorRandom measurementsSmall perturbations
2013
Empirical intrinsic geometry for nonlinear modeling and time series filtering
Talmon R, Coifman RR. Empirical intrinsic geometry for nonlinear modeling and time series filtering. Proceedings Of The National Academy Of Sciences Of The United States Of America 2013, 110: 12535-12540. PMID: 23847205, PMCID: PMC3732962, DOI: 10.1073/pnas.1307298110.Peer-Reviewed Original ResearchIntrinsic geometryNon-Gaussian tracking problemsHigh-dimensional time seriesNonlinear filtering frameworkTime series filteringInformation geometryStochastic settingParametric manifoldTracking problemStatistical modelBayesian approachNonlinear modelingEmpirical distributionFiltering frameworkEmpirical dynamicsInstrumental modalitiesInferred modelGeometryTime seriesTime series analysisDifferent observationsReal signalsSeries analysisDynamicsAnalysis tools