Xiuyuan Cheng

Journal article Communications biology · July 2025 Identifying accurate cell markers in single-cell RNA-seq data is crucial for understanding cellular diversity and function. Localized Marker Detector (LMD) is a novel tool to identify "localized genes"-genes exclusively expressed in groups of highly simila ... Full text Cite

Gene trajectory inference for single-cell data by optimal transport metrics.

Journal article Nature biotechnology · February 2025 Single-cell RNA sequencing has been widely used to investigate cell state transitions and gene dynamics of biological processes. Current strategies to infer the sequential dynamics of genes in a process typically rely on constructing cell pseudotime throug ... Full text Cite

Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise.

Journal article Information and inference : a journal of the IMA · December 2024 Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically normalized graph La ... Full text Cite

Kernel two-sample tests for manifold data

Journal article Bernoulli · November 1, 2024 We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize the test level a ... Full text Cite

The G -invariant graph Laplacian part II: Diffusion maps.

Journal article Applied and computational harmonic analysis · November 2024 The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider embedding data sets that were sampled from a manifold which is closed under ... Full text Cite

The G -invariant graph Laplacian Part I: Convergence rate and eigendecomposition.

Journal article Applied and computational harmonic analysis · July 2024 Graph Laplacian based algorithms for data lying on a manifold have been proven effective for tasks such as dimensionality reduction, clustering, and denoising. In this work, we consider data sets whose data points lie on a manifold that is closed under the ... Full text Cite

Flow-Based Distributionally Robust Optimization

Journal article IEEE Journal on Selected Areas in Information Theory · January 1, 2024 We present a computationally efficient framework, called FlowDRO, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case distribution (also called the Least Fa ... Full text Cite

Convergence of Flow-Based Generative Models via Proximal Gradient Descent in Wasserstein Space

Journal article IEEE Transactions on Information Theory · January 1, 2024 Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, ... Full text Cite

Neural Stein Critics with Staged L2-Regularization

Journal article IEEE Transactions on Information Theory · November 1, 2023 Learning to differentiate model distributions from observed data is a fundamental problem in statistics and machine learning, and high-dimensional data remains a challenging setting for such problems. Metrics that quantify the disparity in probability dist ... Full text Cite

Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling

Journal article SIAM Journal on Mathematics of Data Science · January 1, 2023 The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude varies consider ... Full text Cite

Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation

Journal article Applied and Computational Harmonic Analysis · November 1, 2022 We study the spectral convergence of graph Laplacians to the Laplace-Beltrami operator when the kernelized graph affinity matrix is constructed from N random samples on a d-dimensional manifold in an ambient Euclidean space. By analyzing Dirichlet form con ... Full text Cite

Classification logit two-sample testing by neural networks for differentiating near manifold densities.

Journal article IEEE transactions on information theory · October 2022 The recent success of generative adversarial networks and variational learning suggests that training a classification network may work well in addressing the classical two-sample problem, which asks to differentiate two densities given finite samples from ... Full text Cite

Statistical inference using GLEaM model with spatial heterogeneity and correlation between regions.

Journal article Scientific reports · October 2022 A better understanding of various patterns in the coronavirus disease 2019 (COVID-19) spread in different parts of the world is crucial to its prevention and control. Motivated by the previously developed Global Epidemic and Mobility (GLEaM) model, this pa ... Full text Cite

Convergence of graph Laplacian with kNN self-tuned kernels

Journal article Information and Inference: A Journal of the IMA · September 8, 2022 AbstractKernelized Gram matrix $W$ constructed from data points $\{x_i\}_{i=1}^N$ as $W_{ij}= k_0( \frac{ \| x_i - x_j \|^2} {\sigma ^2} ) $ is widely used in graph-based geometric data analysis and unsupervised learning. A ... Full text Cite

Invertible Neural Networks for Graph Prediction

Journal article IEEE Journal on Selected Areas in Information Theory · September 1, 2022 Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop invertible graph neural ... Full text Cite

Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters

Journal article Journal of Machine Learning Research · January 1, 2022 Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-eq ... Cite

Detection of differentially abundant cell subpopulations in scRNA-seq data.

Journal article Proceedings of the National Academy of Sciences of the United States of America · June 2021 Comprehensive and accurate comparisons of transcriptomic distributions of cells from samples taken from two different biological states, such as healthy versus diseased individuals, are an emerging challenge in single-cell RNA sequencing (scRNA-seq) analys ... Full text Cite

Butterfly-net: Optimal function representation based on convolutional neural networks

Journal article Communications in Computational Physics · November 1, 2020 Deep networks, especially convolutional neural networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. This paper introduces Butterfly-net, a low-co ... Full text Open Access Cite

A Witness Function Based Construction of Discriminative Models Using Hermite Polynomials

Journal article Frontiers in Applied Mathematics and Statistics · August 18, 2020 In machine learning, we are given a dataset of the form (Formula presented.), drawn as i.i.d. samples from an unknown probability distribution μ; the marginal distribution for the xj's being μ*, and the marginals of the kth ... Full text Cite

On matrix rearrangement inequalities

Journal article Proceedings of the American Mathematical Society · January 1, 2020 Given two symmetric and positive semidefinite square matrices A,B, is it true that any matrix given as the product of m copies of A and n copies of B in a particular sequence must be dominated in the spectral norm by the ordered matrix product AmBn? For ex ... Full text Cite

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian.

Journal article SIAM journal on imaging sciences · January 2020 The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The tra ... Full text Cite

Two-sample statistics based on anisotropic kernels

Journal article Information and Inference: A Journal of the IMA · December 10, 2019 AbstractThe paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely many multivariate samples. When the distributions ... Full text Link to item Cite

Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters

Journal article · September 24, 2019 Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-eq ... Link to item Cite

On the diffusion geometry of graph Laplacians and applications

Journal article Applied and Computational Harmonic Analysis · May 2019 Full text Cite

The geometry of nodal sets and outlier detection

Journal article Journal of Number Theory · April 2018 Full text Cite

Prevalence, awareness, treatment, and control of hypertension in China: data from 1·7 million adults in a population-based screening study (China PEACE Million Persons Project)

Journal article The Lancet · December 2017 Full text Cite

Xiuyuan Cheng

Scholarly Works - Journal articles

PDEs for machine learning

Cluster-independent multiscale marker identification in single-cell RNA-seq data using localized marker detector (LMD).

Gene trajectory inference for single-cell data by optimal transport metrics.

Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise.

Kernel two-sample tests for manifold data

The G -invariant graph Laplacian part II: Diffusion maps.

The G -invariant graph Laplacian Part I: Convergence rate and eigendecomposition.

Flow-Based Distributionally Robust Optimization

Convergence of Flow-Based Generative Models via Proximal Gradient Descent in Wasserstein Space

Neural Stein Critics with Staged L2-Regularization

Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling

Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation

Classification logit two-sample testing by neural networks for differentiating near manifold densities.

Statistical inference using GLEaM model with spatial heterogeneity and correlation between regions.

Convergence of graph Laplacian with kNN self-tuned kernels

Invertible Neural Networks for Graph Prediction

Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters

Detection of differentially abundant cell subpopulations in scRNA-seq data.

Butterfly-net: Optimal function representation based on convolutional neural networks

A Witness Function Based Construction of Discriminative Models Using Hermite Polynomials

On matrix rearrangement inequalities

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian.

Two-sample statistics based on anisotropic kernels

Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters

On the diffusion geometry of graph Laplacians and applications

The geometry of nodal sets and outlier detection

Prevalence, awareness, treatment, and control of hypertension in China: data from 1·7 million adults in a population-based screening study (China PEACE Million Persons Project)

A Graph Partitioning Approach to Simultaneous Angular Reconstitution

Marčenko–Pastur law for Tyler’s M-estimator

Deep Haar scattering networks

Concentration of the Kirchhoff index for Erdős–Rényi graphs

The Spectrum of Random Inner-product Kernel Matrices

Subcritical bifurcation in spatially extended systems

Nucleation of Ordered Phases in Block Copolymers

A numerical method for the study of nucleation of ordered phases