Search results for "DANTZIG SELECTOR"

showing 3 items of 3 documents

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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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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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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