Scholars@Duke

• Background
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  Education, Training, & Certifications

  • Ph.D., Princeton University 2013
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  Previous Appointments & Affiliations

  • Scholar In Residence of Mathematics, Mathematics, Trinity College of Arts & Sciences 2017
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  Academic Positions Outside Duke

  • Gibbs Assistant Professor, Yale University. 2015 - 2017
• Research
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  Selected Grants

  • RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by  National Science Foundation 2021 - 2026
  • Bridging Statistical Hypothesis Tests and Deep Learning for Reliability and Computational Efficiency awarded by Georgia Tech Research Corporation 2022 - 2024
  • NSF-BSF: Group Invariant Graph Laplacians: Theory and Computations awarded by  National Science Foundation 2020 - 2024
  • Sloan Foundation Fellowship for Xiuyuan Cheng in Mathematics awarded by Alfred P. Sloan Foundation 2019 - 2023
  • 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
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  External Relationships

  • Tel Aviv University
• Publications & Artistic Works
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  Selected Publications

  • Academic Articles

    • Zhao, Jun, Ariel Jaffe, Henry Li, Ofir Lindenbaum, Esen Sefik, Ruaidhrí Jackson, Xiuyuan Cheng, Richard A. Flavell, and Yuval Kluger. “Detection of differentially abundant cell subpopulations in scRNA-seq data.” Proceedings of the National Academy of Sciences of the United States of America 118, no. 22 (June 2021): e2100293118. https://doi.org/10.1073/pnas.2100293118.
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    • Li, Y., X. Cheng, and J. Lu. “Butterfly-net: Optimal function representation based on convolutional neural networks.” Communications in Computational Physics 28, no. 5 (November 1, 2020): 1838–85. https://doi.org/10.4208/CICP.OA-2020-0214.
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    • Mhaskar, H. N., X. Cheng, and A. Cloninger. “A Witness Function Based Construction of Discriminative Models Using Hermite Polynomials.” Frontiers in Applied Mathematics and Statistics 6 (August 18, 2020). https://doi.org/10.3389/fams.2020.00031.
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    • Cheng, Xiuyuan, Zichen Miao, and Qiang Qiu. “Graph Convolution with Low-rank Learnable Local Filters,” August 4, 2020.
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    • Wang, Z., X. Cheng, G. Sapiro, and Q. Qiu. “A dictionary approach to domain-invariant learning in deep networks.” Advances in Neural Information Processing Systems 2020-December (January 1, 2020).
    • Cheng, Xiuyuan, and Gal Mishne. “Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian.” Siam Journal on Imaging Sciences 13, no. 2 (January 2020): 1015–48. https://doi.org/10.1137/18m1283160.
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    • 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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    • Xu, Zhongshu, Yingzhou Li, and Xiuyuan Cheng. “Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization,” December 9, 2019.
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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 &Amp; 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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    • 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 (April 9, 2010). https://doi.org/10.1103/physrevlett.104.148301.
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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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  • Conference Papers

    • Zhang, Yixing, Xiuyuan Cheng, and Galen Reeves. “Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples.” In 24th International Conference on Artificial Intelligence and Statistics (Aistats), Vol. 130, 2021.
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    • Li, H., O. Lindenbaum, X. Cheng, and A. Cloninger. “Variational Diffusion Autoencoders with Random Walk Sampling.” In Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12368 LNCS:362–78, 2020. https://doi.org/10.1007/978-3-030-58592-1_22.
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    • Wang, Ze, Xiuyuan Cheng, Guillermo Sapiro, and Qiang Qiu. “Stochastic Conditional Generative Networks with Basis Decomposition.” In Iclr. OpenReview.net, 2020.
    • Cheng, Xiuyuan, Qiang Qiu, Robert Calderbank, and Guillermo Sapiro. “RotDCF: Decomposition of convolutional filters for rotation-equivariant deep networks,” 2019.
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    • Yan, Bowei, Purnamrita Sarkar, and Xiuyuan Cheng. “Provable estimation of the number of blocks in block models.” In Proceedings of the Twenty First International Conference on Artificial Intelligence and Statistics (Aistats’18), 84:1185–94. PMLR, 2018.
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    • 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.
    • 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
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  Recent Courses

  • MATH 532: Basic Analysis II 2022
  • K_MATH 302: Numerical Analysis 2021
  • K_MATH 405: Mathematics of Data Analysis and Machine Learning 2021
  • MATH 790-90: Minicourse in Advanced Topics 2021
  • MATH 393: Research Independent Study 2020
  • MATH 532: Basic Analysis II 2020
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  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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