Related papers: Component Selection in the Additive Regression Mod…

We consider the problems of variable selection and estimation in nonparametric additive regression models for high-dimensional data. In recent years, several methods have been proposed to model nonlinear relationships when the number of…

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the…

Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…

Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an…

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The ``COSSO'' is a method of regularization with the penalty functional being the sum…

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…

This chapter describes componentwise Least Squares Support Vector Machines (LS-SVMs) for the estimation of additive models consisting of a sum of nonlinear components. The primal-dual derivations characterizing LS-SVMs for the estimation of…

This paper investigates the two-step estimation of a high dimensional additive regression model, in which the number of nonparametric additive components is potentially larger than the sample size but the number of significant additive…

The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended…

Partially linear additive models generalize linear ones since they model the relation between a response variable and covariates by assuming that some covariates have a linear relation with the response but each of the others enter through…

We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…

The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing each to have either a linear or nonlinear effect on the…

Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…

We present a new class of methods for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive…

Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…

We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…