Publications (by Years)

2022

• Ensemble Dynamics Guided Weak Formulation for Identifying Differential Equations.
  Jiahui Cheng, Sungha Kang, Haomin Zhou, Wenjing Liao.
  Preprint, 2023
  

• High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization. [arxiv] [Summary]
  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 the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. To bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong. Jiahui Cheng, Minshuo Chen, Hao Liu, Tuo Zhao, Wenjing Liao.
  Sampling Theory, Signal Processing, and Data Analysis, 2022
  

2021

• Estimate the spectrum of affine dynamical systems from partial observations of a single trajectory data [arxiv] [Summary]
  In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we prove an annihilating polynomial of the system matrix, whose roots are a subset of the spectrum, can be uniquely determined from data. We then study which eigenvalues of the system matrix can be recovered and derive various sufficient and necessary conditions to characterize the relationship between the recoverability of each eigenvalue and the observation locations. We propose various reconstruction algorithms, with theoretical guarantees, generalizing the classical Prony method, ESPIRIT, and matrix pencil method. We test the algorithms over a variety of examples with applications to graph signal processing, disease modeling and a real-human motion dataset. The numerical results validate our theoretical results and demonstrate the effectiveness of the proposed algorithms, even when the data did not follow an exact linear dynamical system. Jiahui Cheng, Sui Tang
  Inverse Problem, 2021
  

2020

• Continuum simulation based on Material Point Method [Summary]
  In this thesis, we study the hybrid Eulerian/ Lagrangian Material Point Method (MPM) and propose a new discretization for the weak form of MPM based on the weak form of force balance and alleviated the energy dissipation. We improve the stability and energy dissipation compared with MPM and Affine Particle in Cell method. We implemented a Java Graphical User Interface (GUI) for visualization of our algorithm for snow simulation. Jiahui Cheng, Weihua Tong
  Bachelor's thesis, 2020