Search results for " optimization."

showing 10 items of 2333 documents

Latin hypercube sampling with inequality constraints

2010

International audience; In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS), consists in doing permutations on an initial LHS to honor the desired monotonic constraints. The relevance of this approach is shown on a real example concerning the numerical w…

Statistics and ProbabilityFOS: Computer and information sciencesEconomics and EconometricsMathematical optimizationDesign of Experiments020209 energyMonotonic functionSample (statistics)Mathematics - Statistics Theory02 engineering and technologyStatistics Theory (math.ST)01 natural sciencesStatistics - Computation010104 statistics & probabilityRobustness (computer science)[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]Sampling design0202 electrical engineering electronic engineering information engineeringFOS: Mathematics[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematicsDependenceUncertainty analysisLatin hypercube samplingComputation (stat.CO)MathematicsApplied MathematicsComputer experimentFunction (mathematics)[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]Computer experiment[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]Latin hypercube samplingModeling and SimulationUncertainty analysisSocial Sciences (miscellaneous)Analysis
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dglars: An R Package to Estimate Sparse Generalized Linear Models

2014

dglars is a publicly available R package that implements the method proposed in Augugliaro, Mineo, and Wit (2013), developed to study the sparse structure of a generalized linear model. This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method proposed in Efron, Hastie, Johnstone, and Tibshirani (2004). The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve: a predictor-corrector algorithm, proposed in Augugliaro et al. (2013), and a cyclic coordinate descent algorithm, proposed in Augugliaro, Mineo, and Wit (2012). The latter algorithm, as shown here, is significan…

Statistics and ProbabilityGeneralized linear modelEXPRESSIONMathematical optimizationTISSUESFortrancyclic coordinate descent algorithmdgLARSFeature selectionDANTZIG SELECTORpredictor-corrector algorithmLIKELIHOODLEAST ANGLE REGRESSIONsparse modelsDifferential (infinitesimal)differential geometrylcsh:Statisticslcsh:HA1-4737computer.programming_languageMathematicsLeast-angle regressionExtension (predicate logic)Expression (computer science)generalized linear modelsBREAST-CANCER RISKVARIABLE SELECTIONDifferential geometrydifferential geometry generalized linear models dgLARS predictor-corrector algorithm cyclic coordinate descent algorithm sparse models variable selection.MARKERSHRINKAGEStatistics Probability and UncertaintyHAPLOTYPESSettore SECS-S/01 - StatisticacomputerAlgorithmSoftware
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Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter

2018

A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the $$\ell _1$$ or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this…

Statistics and ProbabilityGeneralized linear modelMathematical optimizationGeneralized linear modelsPredictor-€“corrector algorithmGeneralized linear model02 engineering and technologyPoisson distributionDANTZIG SELECTOR01 natural sciencesCross-validationHigh-dimensional inferenceTheoretical Computer Science010104 statistics & probabilitysymbols.namesakeExponential familyLEAST ANGLE REGRESSION0202 electrical engineering electronic engineering information engineeringApplied mathematicsStatistics::Methodology0101 mathematicsCROSS-VALIDATIONMathematicsLeast-angle regressionLinear model020206 networking & telecommunicationsProbability and statisticsVARIABLE SELECTIONEfficient estimatorPredictor-corrector algorithmComputational Theory and MathematicsDispersion paremeterLINEAR-MODELSsymbolsSHRINKAGEStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaStatistics and Computing
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Differential geometric least angle regression: a differential geometric approach to sparse generalized linear models

2013

Summary Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense that only a few of the measured variables are involved in the process. We propose an explicit method of monotonically decreasing sparsity for outcomes that can be modelled by an exponential family. In our approach we generalize the equiangular condition in a generalized linear model. Although the …

Statistics and ProbabilityGeneralized linear modelSparse modelMathematical optimizationGeneralized linear modelsVariable selectionPath following algorithmEquiangular polygonGeneralized linear modelLASSODANTZIG SELECTORsymbols.namesakeExponential familyLasso (statistics)Sparse modelsDifferential geometryInformation geometryCOORDINATE DESCENTFisher informationERRORMathematicsLeast-angle regressionLeast angle regressionGeneralized degrees of freedomsymbolsSHRINKAGEStatistics Probability and UncertaintySimple linear regressionInformation geometrySettore SECS-S/01 - StatisticaAlgorithmCovariance penalty theory
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A differential-geometric approach to generalized linear models with grouped predictors

2016

We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important properties that distinguish it from the group lasso. First, its solution curve is based on the invariance properties of a generalized linear model. Second, it adds groups of variables based on a group equiangularity condition, which is shown to be related to score statistics. An adaptive version, which includes weights based on the Kullback-Leibler divergence, improves its variable selection fea…

Statistics and ProbabilityGeneralized linear modelStatistics::TheoryMathematical optimizationProper linear modelGeneral MathematicsORACLE PROPERTIESGeneralized linear modelSPARSITYGeneralized linear array model01 natural sciencesGeneralized linear mixed modelCONSISTENCY010104 statistics & probabilityScore statistic.LEAST ANGLE REGRESSIONLinear regressionESTIMATORApplied mathematicsDifferential geometry0101 mathematicsDivergence (statistics)MathematicsVariance functionDifferential-geometric least angle regressionPATH ALGORITHMApplied MathematicsLeast-angle regressionScore statistic010102 general mathematicsAgricultural and Biological Sciences (miscellaneous)Group lassoGROUP SELECTIONStatistics Probability and UncertaintyGeneral Agricultural and Biological SciencesSettore SECS-S/01 - Statistica
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Efficient spatial designs using Hausdorff distances and Bayesian optimization

2021

An iterative Bayesian optimisation technique is presented to find spatial designs of data that carry much information. We use the decision theoretic notion of value of information as the design criterion. Gaussian process surrogate models enable fast calculations of expected improvement for a large number of designs, while the full-scale value of information evaluations are only done for the most promising designs. The Hausdorff distance is used to model the similarity between designs in the surrogate Gaussian process covariance representation, and this allows the suggested algorithm to learn across different designs. We study properties of the Bayesian optimisation design algorithm in a sy…

Statistics and ProbabilityHausdorff distancebayesilainen menetelmäBayesian optimizationHausdorff spacepäätöksentukijärjestelmätBayesian optimisationpaikkatietoanalyysivalue of informationValue of informationHausdorff distanceoptimointiStatistics Probability and UncertaintyAlgorithmMathematics
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PROBABILISTIC QUANTIFICATION OF HAZARDS: A METHODOLOGY USING SMALL ENSEMBLES OF PHYSICS-BASED SIMULATIONS AND STATISTICAL SURROGATES

2015

This paper presents a novel approach to assessing the hazard threat to a locale due to a large volcanic avalanche. The methodology combines: (i) mathematical modeling of volcanic mass flows; (ii) field data of avalanche frequency, volume, and runout; (iii) large-scale numerical simulations of flow events; (iv) use of statistical methods to minimize computational costs, and to capture unlikely events; (v) calculation of the probability of a catastrophic flow event over the next T years at a location of interest; and (vi) innovative computational methodology to implement these methods. This unified presentation collects elements that have been separately developed, and incorporates new contri…

Statistics and ProbabilityHazard (logic)Volcanic hazardsgeographyControl and Optimizationgeography.geographical_feature_categoryProcess (engineering)Probabilistic logicHazard analysiscomputer.software_genreFlow (mathematics)VolcanoModeling and SimulationEconometricsDiscrete Mathematics and CombinatoricsEnvironmental scienceData miningcomputerEvent (probability theory)International Journal for Uncertainty Quantification
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Updating input–output matrices: assessing alternatives through simulation

2009

A problem that frequently arises in economics, demography, statistics, transportation planning and stochastic modelling is how to adjust the entries of a matrix to fulfil row and column aggregation constraints. Biproportional methods in general and the so-called RAS algorithm in particular, have been used for decades to find solutions to this type of problem. Although alternatives exist, the RAS algorithm and its extensions are still the most popular. Apart from some interesting empirical and theoretical properties, tradition, simplicity and very low computational costs are among the reasons behind the great success of RAS. Nowadays computer hardware and software have made alternative proce…

Statistics and ProbabilityInput/outputTransportation planningMathematical optimizationIterative proportional fittingbusiness.industryStochastic modellingApplied Mathematicsmedia_common.quotation_subjectColumn (database)Matrix (mathematics)SoftwareModeling and SimulationSimplicityStatistics Probability and UncertaintybusinessMathematicsmedia_commonJournal of Statistical Computation and Simulation
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Componentwise adaptation for high dimensional MCMC

2005

We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.

Statistics and ProbabilityMathematical optimization010504 meteorology & atmospheric sciencesMonte Carlo methodMarkov processMarkov chain Monte Carlo01 natural sciencesStatistics::Computation010104 statistics & probabilityComputational Mathematicssymbols.namesakeMetropolis–Hastings algorithmTest caseChain (algebraic topology)Component (UML)symbolsStatistics::MethodologyErgodic theory0101 mathematicsStatistics Probability and Uncertainty0105 earth and related environmental sciencesMathematicsComputational Statistics
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Including covariates in a space-time point process with application to seismicity

2020

AbstractThe paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.

Statistics and ProbabilityMathematical optimization010504 meteorology & atmospheric sciencesSpacetimeComputer scienceSpace timeSpace-time point processes ETAS model R package for seismic datacovariatesProcess (computing)01 natural sciencesPoint process010104 statistics & probabilitySpecificationComponent (UML)Covariate0101 mathematicsStatistics Probability and Uncertainty0105 earth and related environmental sciencesBranching process
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