8 citations · 15 across the 7 of their papers we have counts for
8 papers
Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels
Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou
Operator learning is formulated on function spaces, but training data are typically available only through finite-dimensional representations. In encoder--decoder architectures, a…
Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
Guanhang Lei, Zhen Lei, Lei Shi +2
Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some r…
Classification with Deep Neural Networks and Logistic Loss
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
Deep neural networks (DNNs) trained with the logistic loss (i.e., the cross entropy loss) have made impressive advancements in various binary classification tasks. However, general…
Optimality of Robust Online Learning
Zheng-Chu Guo, Andreas Christmann, Lei Shi
In this paper, we study an online learning algorithm with a robust loss function for regression over a reproducing kernel Hilbert space (RKHS). The loss function $\…
Pairwise Ranking with Gaussian Kernels
Guanhang Lei, Lei Shi
Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. Despite a wide range of applications, a rigorous theoretical demonstration still…
Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression
Jiading Liu, Lei Shi
Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel spa…
Capacity dependent analysis for functional online learning algorithms
Xin Guo, Zheng-Chu Guo, Lei Shi
This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regul…
Solving parametric partial differential equations with deep rectified quadratic unit neural networks
Zhen Lei, Lei Shi, Chenyu Zeng
Implementing deep neural networks for learning the solution maps of parametric partial differential equations (PDEs) turns out to be more efficient than using many conventional num…