Related papers: Structural Change in Sparsity
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
Homogeneity, low rank, and sparsity are three widely adopted assumptions in multi-response regression models to address the curse of dimensionality and improve estimation accuracy. However, there is limited literature that examines these…
Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although…
In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to…
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…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…
This paper derives identification, estimation, and inference results using spatial differencing in sample selection models with unobserved heterogeneity. We show that under the assumption of smooth changes across space of the unobserved…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error $\epsilon$.…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…
Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by…
An important problem in the analysis of high-dimensional omics data is to identify subsets of molecular variables that are associated with a phenotype of interest. This requires addressing the challenges of high dimensionality, strong…
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…