Variable Selection Using Adaptive Nonlinear Interaction Structures in High Dimensions
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Summary
This work introduces a new approach, “Variable selection using Adaptive Nonlinear Interaction Structures in High dimensions” (VANISH), that is based on a penalized least squares criterion and is designed for high dimensional nonlinear problems and suggests that VANISH should outperform certain natural competitors when the true interaction structure is sufficiently sparse.
- Type
- article
- Published
- 2010-12-01
- Cited by
- 133
- References
- 36
- Access
- Open access
- OpenAlex
- https://openalex.org/W2076349866
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:16762770
Keywords
Nonlinear system, Variable (mathematics), Selection (genetic algorithm), Constraint (computer-aided design), Mathematics
References
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- The Dantzig selector: Statistical estimation when P is much larger than n
- Nonparametric and Semiparametric Models
- Journal of the Royal Statistical Society (B): Gary K. Grunwald, Adrian E. Raftery and Peter Guttorp, 1993, “Time series of continuous proportions”, 55, 103–116.☆
- Nonnegative Garrote Component Selection in Functional ANOVA models
- PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES W_p^α
- Addendum: Regularization and variable selection via the elastic net
- The composite absolute penalties family for grouped and hierarchical variable selection
- A generalized Dantzig selector with shrinkage tuning
- The Adaptive Lasso and Its Oracle Properties
- Regularized Multivariate Regression for Identifying Master Predictors with Application to Integrative Genomics Study of Breast Cancer
- Variable Inclusion and Shrinkage Algorithms
- Hedonic housing prices and the demand for clean air
- Coordinate descent algorithms for lasso penalized regression
- PATHWISE COORDINATE OPTIMIZATION
- Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models
- Persistence in high-dimensional linear predictor selection and the virtue of overparametrization
- Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
- Variable Selection With the Strong Heredity Constraint and Its Oracle Property
- A Statistical View of Some Chemometrics Regression Tools
Cited by
- Variable selection in semi-parametric models
- A Survey of L1 Regression
- Selection and Clustering for Disease Associated Genetic Variants
- Topics in Modern Bayesian Computation
- Statistical downscaling of monthly reservoir inflows for Kemer watershed in Turkey: use of machine learning methods, multiple GCMs and emission scenarios
- Discriminant Analysis with Adaptively Pooled Covariance
- Regularization for sparsity in statistical analysis and machine learning
- Bias-corrected inference for multivariate nonparametric regression: Model selection and oracle property
- Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models.
- Coordinate Descent Based Hierarchical Interactive Lasso Penalized Logistic Regression and Its Application to Classification Problems
- Penalized likelihood and Bayesian function selection in regression models
- An efficient algorithm for weak hierarchical lasso
- Semiparametric regression models with additive nonparametric components and high dimensional parametric components
- Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling
- A Modified Adaptive Lasso for Identifying Interactions in the Cox Model with the Heredity Constraint
- A LASSO FOR HIERARCHICAL INTERACTIONS
- High dimensional single index models
- Hierarchical Interactions Model for Predicting Mild Cognitive Impairment (MCI) to Alzheimer's Disease (AD) Conversion
- The EBIC and a sequential procedure for feature selection in interactive linear models with high-dimensional data
- Learning interactions via hierarchical group-lasso regularization
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