59 citations · 117 across the 11 of their papers we have counts for
11 papers
Theory on variational high-dimensional tensor networks
Zidu Liu, Qi Ye, Li-Wei Yu +2
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tenso…
Composite Optimization Algorithms for Sigmoid Networks
Huixiong Chen, Qi Ye
In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the…
Splitting Method for Support Vector Machine in Reproducing Kernel Banach Space with Lower Semi-continuous Loss Function
Mingyu Mo, Yimin Wei, Qi Ye
In this paper, we use the splitting method to solve support vector machine in reproducing kernel Banach space with lower semi-continuous loss function. We equivalently transfer sup…
Splitting Method for Support Vector Machine with Lower Semi-continuous Loss
Mingyu Mo, Qi Ye
In this paper, we study the splitting method based on alternating direction method of multipliers for support vector machine in reproducing kernel Hilbert space with lower semi-con…
Positive Definite Multi-Kernels for Scattered Data Interpolations
Qi Ye
In this article, we use the knowledge of positive definite tensors to develop a concept of positive definite multi-kernels to construct the kernel-based interpolants of scattered d…
Kernel-based Approximation Methods for Generalized Interpolations: A Deterministic or Stochastic Problem?
Qi Ye
In this article, we solve a deterministically generalized interpolation problem by a stochastic approach. We introduce a kernel-based probability measure on a Banach space by a cov…
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Yuesheng Xu, Qi Ye
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is…
Kernel-based Methods for Stochastic Partial Differential Equations
Qi Ye
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of…
Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions
Gregory E. Fasshauer, Fred J. Hickernell, Qi Ye
In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in re…
Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Differential Operators
Qi Ye
In this paper we introduce a generalization of the classical $\Leb_2(\Rd)$-based Sobolev spaces with the help of a vector differential operator which consists of finit…
Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method
Igor Cialenco, Gregory E. Fasshauer, Qi Ye
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-d…