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Xiuyuan Cheng

Associate Professor of Mathematics
Mathematics
120 Science Drive, P.O. Box 90320, Durham, NC 27708
120 Science Drive, 293 Physics Building, Durham, NC 27708

Selected Publications


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 · September 30, 2023 Full text Cite

Training Neural Networks for Sequential Change-Point Detection

Conference ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · January 1, 2023 Detecting an abrupt distributional shift of a data stream, known as change-point detection, is a fundamental problem in statistics and machine learning. We introduce a novel approach for online change-point detection using neural net-works. To be specific, ... 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 unsuperv ... 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

NEURAL SPECTRAL MARKED POINT PROCESSES

Conference ICLR 2022 - 10th International Conference on Learning Representations · January 1, 2022 Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric mo ... Cite

SpecNet2: Orthogonalization-free Spectral Embedding by Neural Networks

Conference Proceedings of Machine Learning Research · January 1, 2022 Spectral methods which represent data points by eigenvectors of kernel matrices or graph Laplacian matrices have been a primary tool in unsupervised data analysis. In many application scenarios, parametrizing the spectral embedding by a neural network that ... 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

Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples

Conference Proceedings of Machine Learning Research · January 1, 2021 The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for estimating the GOT ... Cite

Spatiotemporal Joint Filter Decomposition in 3D Convolutional Neural Networks

Conference Advances in Neural Information Processing Systems · January 1, 2021 In this paper, we introduce spatiotemporal joint filter decomposition to decouple spatial and temporal learning, while preserving spatiotemporal dependency in a video. A 3D convolutional filter is now jointly decomposed over a set of spatial and temporal f ... Cite

Neural Tangent Kernel Maximum Mean Discrepancy

Conference Advances in Neural Information Processing Systems · January 1, 2021 We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a new connection between neural tangent kernel (NTK) and MMD. This connection enables us to develop a computationally efficient and memory-efficient approach to compu ... Cite

Graph Convolution with Low-rank Learn-able Local Filters

Conference ICLR 2021 - 9th International Conference on Learning Representations · January 1, 2021 Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes non-trivial to b ... 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

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 · September 30, 2023 Full text Cite

Training Neural Networks for Sequential Change-Point Detection

Conference ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · January 1, 2023 Detecting an abrupt distributional shift of a data stream, known as change-point detection, is a fundamental problem in statistics and machine learning. We introduce a novel approach for online change-point detection using neural net-works. To be specific, ... 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 unsuperv ... 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

NEURAL SPECTRAL MARKED POINT PROCESSES

Conference ICLR 2022 - 10th International Conference on Learning Representations · January 1, 2022 Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric mo ... Cite

SpecNet2: Orthogonalization-free Spectral Embedding by Neural Networks

Conference Proceedings of Machine Learning Research · January 1, 2022 Spectral methods which represent data points by eigenvectors of kernel matrices or graph Laplacian matrices have been a primary tool in unsupervised data analysis. In many application scenarios, parametrizing the spectral embedding by a neural network that ... 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

Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples

Conference Proceedings of Machine Learning Research · January 1, 2021 The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for estimating the GOT ... Cite

Spatiotemporal Joint Filter Decomposition in 3D Convolutional Neural Networks

Conference Advances in Neural Information Processing Systems · January 1, 2021 In this paper, we introduce spatiotemporal joint filter decomposition to decouple spatial and temporal learning, while preserving spatiotemporal dependency in a video. A 3D convolutional filter is now jointly decomposed over a set of spatial and temporal f ... Cite

Neural Tangent Kernel Maximum Mean Discrepancy

Conference Advances in Neural Information Processing Systems · January 1, 2021 We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a new connection between neural tangent kernel (NTK) and MMD. This connection enables us to develop a computationally efficient and memory-efficient approach to compu ... Cite

Graph Convolution with Low-rank Learn-able Local Filters

Conference ICLR 2021 - 9th International Conference on Learning Representations · January 1, 2021 Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes non-trivial to b ... 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 class (Formula presented.) possi ... 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

STOCHASTIC CONDITIONAL GENERATIVE NETWORKS WITH BASIS DECOMPOSITION

Conference 8th International Conference on Learning Representations, ICLR 2020 · January 1, 2020 While generative adversarial networks (GANs) have revolutionized machine learning, a number of open questions remain to fully understand them and exploit their power. One of these questions is how to efficiently achieve proper diversity and sampling of the ... 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

Variational Diffusion Autoencoders with Random Walk Sampling

Conference Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) · January 1, 2020 Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and the sampling spac ... Full text Cite

Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization

Conference Proceedings of Machine Learning Research · January 1, 2020 Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and i ... 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

On the diffusion geometry of graph Laplacians and applications

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

Provable estimation of the number of blocks in block models

Conference Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS'18) · April 9, 2018 Link to item Cite

The geometry of nodal sets and outlier detection

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

A Graph Partitioning Approach to Simultaneous Angular Reconstitution

Journal Article IEEE Transactions on Computational Imaging · September 2016 Full text Cite

Marčenko–Pastur law for Tyler’s M-estimator

Journal Article Journal of Multivariate Analysis · July 2016 Full text Cite

Deep Haar scattering networks

Journal Article Information and Inference · June 2016 Full text Cite

A Deep Learning Approach to Unsupervised Ensemble Learning

Conference Proceedings of The 33rd International Conference on Machine Learning · June 2016 Cite

Concentration of the Kirchhoff index for Erdős–Rényi graphs

Journal Article Systems & Control Letters · December 2014 Full text Cite

Unsupervised Deep Haar Scattering on Graphs.

Conference Advances in Neural Information Processing Systems 27 · 2014 Cite

The Spectrum of Random Inner-product Kernel Matrices

Journal Article Random Matrices: Theory and Applications · October 2013 Full text Cite

Subcritical bifurcation in spatially extended systems

Journal Article Nonlinearity · March 1, 2012 Full text Cite

Nucleation of Ordered Phases in Block Copolymers

Journal Article Physical Review Letters · April 9, 2010 Full text Cite

A numerical method for the study of nucleation of ordered phases

Journal Article Journal of Computational Physics · March 2010 Full text Cite