Related papers: Beyond L1: Faster and Better Sparse Models with sk…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing.…
We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…
Scaling autoregressive large language models (LLMs) has driven unprecedented progress but comes with vast computational costs. In this work, we tackle these costs by leveraging unstructured sparsity within an LLM's feedforward layers, the…
Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method…
L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…
We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
In this paper, we propose a double iteratively reweighted algorithm to solve nonconvex and nonsmooth optimization problems, where both the objectives and constraint functions are formulated by concave compositions to promote group-sparse…
We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
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…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…