相关论文: Sparse-penalized deep neural networks estimator un…

We consider the segmentation problem of Poisson and negative binomial (i.e. overdispersed Poisson) rate distributions. In segmentation, an important issue remains the choice of the number of segments. To this end, we propose a penalized…

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…

We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…

Deep neural networks with lots of parameters are typically used for large-scale computer vision tasks such as image classification. This is a result of using dense matrix multiplications and convolutions. However, sparse computations are…

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…

Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…

We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We…

This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

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 paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

In this paper, we develop a general theory for adaptive nonparametric estimation of the mean function of a non-stationary and nonlinear time series model using deep neural networks (DNNs). We first consider two types of DNN estimators,…

Recent work on deep neural network pruning has shown there exist sparse subnetworks that achieve equal or improved accuracy, training time, and loss using fewer network parameters when compared to their dense counterparts. Orthogonal to…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…