Related papers: Generalized Sparse Additive Models
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…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own…
We introduce a method for aggregating many least squares estimator so that the resulting estimate has two properties: sparsity and structure. That is, only a few candidate covariates are used in the resulting model, and the selected…
Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…
Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved…
Generalized Additive Models (GAMs) balance predictive accuracy and interpretability, but manually configuring their structure is challenging. We propose using the multi-objective genetic algorithm NSGA-II to automatically optimize GAMs,…
Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…
Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…