Related papers: Iterative Reweighted Framework Based Algorithms fo…

In some supervised learning settings, the practitioner might have additional information on the features used for prediction. We propose a new method which leverages this additional information for better prediction. The method, which we…

We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter…

Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…

It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…

We address regularised versions of the Expectation-Maximisation (EM) algorithm for Generalised Linear Mixed Models (GLMM) in the context of panel data (measured on several individuals at different time-points). A random response y is…

In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to use $\ell_{12}$ block…

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing…

Various $\ell_1$-penalised estimation methods such as graphical lasso and CLIME are widely used for sparse precision matrix estimation. Many of these methods have been shown to be consistent under various quantitative assumptions about the…

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

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…

The mean-variance (MV) model is the core of modern portfolio theory. Nevertheless, it suffers from the over-fitting problem due to the estimation errors of model parameters. We consider the $\ell_{1}$ regularized MV model, which adds an…

Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…

We study the problem of estimating the parameters of a regression model from a set of observations, each consisting of a response and a predictor. The response is assumed to be related to the predictor via a regression model of unknown…

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…