4 citations · 10 across the 7 of their papers we have counts for
12 papers
Fourier Features for Identifying Differential Equations (FourierIdent)
Mengyi Tang, Hao Liu, Wenjing Liao +1
We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are c…
Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories
Zixuan Zhang, Minshuo Chen, Mengdi Wang +2
Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data struc…
Group projected Subspace Pursuit for Identification of variable coefficient differential equations (GP-IDENT)
Yuchen He, Sung-Ha Kang, Wenjing Liao +2
We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observatio…
Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness
Hao Liu, Alex Havrilla, Rongjie Lai +1
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled n…
High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization
Jiahui Cheng, Minshuo Chen, Hao Liu +2
Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of…
Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks
Hao Liu, Minshuo Chen, Tuo Zhao +1
Most of existing statistical theories on deep neural networks have sample complexities cursed by the data dimension and therefore cannot well explain the empirical success of deep…