7 citations · 17 across the 9 of their papers we have counts for
9 papers
Sparsity-Guided Multi-Parameter Selection in -Regularized Models via a Fixed-Point Proximity Approach
Qianru Liu, Rui Wang, Yuesheng Xu
We study a regularization framework that combines a convex fidelity term with multiple -based regularizers, each linked to a distinct linear transform. This multi-penalty m…
Sparse Deep Learning Models with the Regularization
Lixin Shen, Rui Wang, Yuesheng Xu +1
Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the s…
Hypothesis Spaces for Deep Learning
Rui Wang, Yuesheng Xu, Mingsong Yan
This paper introduces a hypothesis space for deep learning based on deep neural networks (DNNs). By treating a DNN as a function of two variables - the input variable and the param…
A Duality Approach to Regularized Learning Problems in Banach Spaces
Raymond Cheng, Rui Wang, Yuesheng Xu
Learning methods in Banach spaces are often formulated as regularization problems which minimize the sum of a data fidelity term in a Banach norm and a regularization term in anoth…
Sparse Representer Theorems for Learning in Reproducing Kernel Banach Spaces
Rui Wang, Yuesheng Xu, Mingsong Yan
Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning m…
Parameter Choices for Sparse Regularization with the Norm
Qianru Liu, Rui Wang, Yuesheng Xu +1
We consider a regularization problem whose objective function consists of a convex fidelity term and a regularization term determined by the norm composed with a linear tr…
Representer Theorems in Banach Spaces: Minimum Norm Interpolation, Regularized Learning and Semi-Discrete Inverse Problems
Rui Wang, Yuesheng Xu
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a mi…
Operator Reproducing Kernel Hilbert Spaces
Rui Wang, Yuesheng Xu
Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS).…
Optimal Sampling Points in Reproducing Kernel Hilbert Spaces
Rui Wang, Haizhang Zhang
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is re…