6533b822fe1ef96bd127cee6

RESEARCH PRODUCT

Deep Importance Sampling based on Regression for Model Inversion and Emulation

Fernando LlorenteLuca MartinoGustavo Camps-vallsDavid Delgado-gómez

subject

FOS: Computer and information sciencesComputer Science - Machine LearningImportance samplingComputer scienceMonte Carlo methodPosterior probabilityBayesian inferenceInferenceContext (language use)Machine Learning (stat.ML)02 engineering and technologyEstadísticaStatistics - ComputationMachine Learning (cs.LG)symbols.namesakeSurrogate modelStatistics - Machine LearningArtificial Intelligence0202 electrical engineering electronic engineering information engineeringAdaptive regressionEmulationElectrical and Electronic EngineeringModel inversionGaussian processComputation (stat.CO)EmulationApplied Mathematics020206 networking & telecommunicationsRemote sensingComputational Theory and MathematicsSignal Processingsymbols020201 artificial intelligence & image processingComputer Vision and Pattern RecognitionStatistics Probability and UncertaintyAlgorithmImportance sampling

description

Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and optimization. They require the choice of a suitable proposal density that is crucial for their performance. For this reason, several adaptive importance sampling (AIS) schemes have been proposed in the literature. We here present an AIS framework called Regression-based Adaptive Deep Importance Sampling (RADIS). In RADIS, the key idea is the adaptive construction via regression of a non-parametric proposal density (i.e., an emulator), which mimics the posterior distribution and hence minimizes the mismatch between proposal and target densities. RADIS is based on a deep architecture of two (or more) nested IS schemes, in order to draw samples from the constructed emulator. The algorithm is highly efficient since employs the posterior approximation as proposal density, which can be improved adding more support points. As a consequence, RADIS asymptotically converges to an exact sampler under mild conditions. Additionally, the emulator produced by RADIS can be in turn used as a cheap surrogate model for further studies. We introduce two specific RADIS implementations that use Gaussian Processes (GPs) and Nearest Neighbors (NN) for constructing the emulator. Several numerical experiments and comparisons show the benefits of the proposed schemes. A real-world application in remote sensing model inversion and emulation confirms the validity of the approach. This work has been supported by Spanish government via grant FPU19/00815, by Agencia Estatal de Investigación AEI (project SPGRAPH, ref. num. PID2019-105032GB-I00), by the Found action by the Community of Madrid in the framework of the Multiannual Agreement with the Rey Juan Carlos University in line of action 1, “Encouragement of Young Phd students investigation”, Project Ref. F661 Acronym Mapping-UCI, and by the European Research Council (ERC) under the ERC Consolidator Grant 2014 project SEDAL (647423).

yearjournalcountryeditionlanguage
2021-09-01
https://dx.doi.org/10.48550/arxiv.2010.10346