Xiuyuan Cheng | Scholars@Duke

Xiuyuan Cheng
Assistant Professor of Mathematics

As an applied analyst, I develop theoretical and computational techniques to solve problems in high-dimensional statistics, signal processing and machine learning.

Current Research Interests

Theory and computation of spectral methods, geometrical data analysis, high dimensional statistics, mathematical analysis of deep neural networks.

Current Appointments & Affiliations

Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2018

Contact Information

120 Science Drive, 293 Physics Building, Durham, NC 27708
120 Science Drive, P.O. Box 90320, Durham, NC 27708
xiuyuan.cheng@duke.edu
Personal website

Background
Education, Training, & Certifications
- Ph.D., Princeton University 2013
Duke Appointment History
- Scholar In Residence of Mathematics, Mathematics, Trinity College of Arts & Sciences 2017
Academic Positions Outside Duke
- Gibbs Assistant Professor, Yale University. 2015 - 2017
Research
Selected Grants
- RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by National Science Foundation 2021 - 2026
- NSF-BSF: Group Invariant Graph Laplacians: Theory and Computations awarded by National Science Foundation 2020 - 2024
- Efficient Methods for Calibration, Clustering, Visualization and Imputation of Large scRNA-seq Data awarded by Yale University 2019 - 2023
- HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by National Science Foundation 2019 - 2022
- CDS&E: Structure-aware Representation Learning using Deep Networks awarded by National Science Foundation 2018 - 2022
- Collaborative Research: Geometric Analysis and Computation of Generative Models awarded by National Science Foundation 2018 - 2022
- Sloan Foundation Fellowship for Xiuyuan Cheng in Mathematics awarded by Alfred P. Sloan Foundation 2019 - 2021
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Cheng, Xiuyuan, Alexander Cloninger, and Ronald R. Coifman. “Two-sample statistics based on anisotropic kernels.” Information and Inference: A Journal of the Ima, December 10, 2019. https://doi.org/10.1093/imaiai/iaz018.
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  - Cheng, Xiuyuan, Manas Rachh, and Stefan Steinerberger. “On the diffusion geometry of graph Laplacians and applications.” Applied and Computational Harmonic Analysis 46, no. 3 (May 2019): 674–88. https://doi.org/10.1016/j.acha.2018.04.001.
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  - Cheng, Xiuyuan, Gal Mishne, and Stefan Steinerberger. “The geometry of nodal sets and outlier detection.” Journal of Number Theory 185 (April 2018): 48–64. https://doi.org/10.1016/j.jnt.2017.09.021.
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  - Lu, Jiapeng, Yuan Lu, Xiaochen Wang, Xinyue Li, George C. Linderman, Chaoqun Wu, Xiuyuan Cheng, et al. “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).” The Lancet 390, no. 10112 (December 2017): 2549–58. https://doi.org/10.1016/s0140-6736(17)32478-9.
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  - Pragier, Gabi, Ido Greenberg, Xiuyuan Cheng, and Yoel Shkolnisky. “A Graph Partitioning Approach to Simultaneous Angular Reconstitution.” Ieee Transactions on Computational Imaging 2, no. 3 (September 2016): 323–34. https://doi.org/10.1109/tci.2016.2557076.
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  - Zhang, Teng, Xiuyuan Cheng, and Amit Singer. “Marčenko–Pastur law for Tyler’s M-estimator.” Journal of Multivariate Analysis 149 (July 2016): 114–23. https://doi.org/10.1016/j.jmva.2016.03.010.
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  - Cheng, Xiuyuan, Xu Chen, and Stéphane Mallat. “Deep Haar scattering networks.” Information and Inference 5, no. 2 (June 2016): 105–33. https://doi.org/10.1093/imaiai/iaw007.
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  - Boumal, Nicolas, and Xiuyuan Cheng. “Concentration of the Kirchhoff index for Erdős–Rényi graphs.” Systems & Control Letters 74 (December 2014): 74–80. https://doi.org/10.1016/j.sysconle.2014.10.006.
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  - CHENG, X. I. U. Y. U. A. N., and A. M. I. T. SINGER. “The Spectrum of Random Inner-product Kernel Matrices.” Random Matrices: Theory and Applications 02, no. 04 (October 2013): 1350010–1350010. https://doi.org/10.1142/S201032631350010X.
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  - E, Weinan, Xiang Zhou, and Xiuyuan Cheng. “Subcritical bifurcation in spatially extended systems.” Nonlinearity 25, no. 3 (March 1, 2012): 761–79. https://doi.org/10.1088/0951-7715/25/3/761.
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  - Lin, Ling, Xiuyuan Cheng, Weinan E, An-Chang Shi, and Pingwen Zhang. “A numerical method for the study of nucleation of ordered phases.” Journal of Computational Physics 229, no. 5 (March 2010): 1797–1809. https://doi.org/10.1016/j.jcp.2009.11.009.
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  - Cheng, Xiuyuan, Ling Lin, Weinan E, Pingwen Zhang, and An-Chang Shi. “Nucleation of Ordered Phases in Block Copolymers.” Physical Review Letters 104, no. 14 (n.d.). https://doi.org/10.1103/physrevlett.104.148301.
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- Conference Papers
  - Cheng, X., Q. Qiu, R. Calderbank, and G. Sapiro. “RoTDCF: Decomposition of convolutional filters for rotation-equivariant deep networks.” In 7th International Conference on Learning Representations, Iclr 2019, 2019.
  - Qiu, Qiang, Xiuyuan Cheng, A Robert Calderbank, and Guillermo Sapiro. “DCFNet: Deep Neural Network with Decomposed Convolutional Filters.” In Icml, edited by Jennifer G. Dy and Andreas Krause, 80:4195–4204. PMLR, 2018.
  - Yan, B., P. Sarkar, and X. Cheng. “Provable estimation of the number of blocks in block models.” In International Conference on Artificial Intelligence and Statistics, Aistats 2018, 1185–94, 2018.
  - Cheng, X., U. Shaham, O. Dror, A. Jaffe, B. Nadler, J. Chang, and Y. Kluger. “A Deep Learning Approach to Unsupervised Ensemble Learning.” In Proceedings of the 33rd International Conference on Machine Learning, 48:30–39. PMLR, 2016.
  - Chen, Xu, Xiuyuan Cheng, and Stéphane Mallat. “Unsupervised Deep Haar Scattering on Graphs.” In Advances in Neural Information Processing Systems 27, edited by Zoubin Ghahramani, Max Welling, Corinna Cortes, Neil D. Lawrence, and Kilian Q. Weinberger, 1709–17, 2014.
Teaching & Mentoring
Recent Courses
Teaching Activities
- In Fall 2017, I am teaching the graduate-level course Math 690 Topics in Data Analysis and Computation. I am teaching Math 532 Basic Analysis II in Spring 2018.

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Education, Training, & Certifications

Duke Appointment History

Academic Positions Outside Duke

Selected Grants

Selected Publications

Academic Articles

Conference Papers

Recent Courses

Teaching Activities