Related papers: Pathwise Coordinate Optimization for Sparse Learni…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
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 consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…
In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…
In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve…
Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational…
Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…
We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…
Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
We present an evaluation of several representative sampling-based and optimization-based motion planners, and then introduce an integrated motion planning system which incorporates recent advances in trajectory optimization into a sparse…