Scholars@Duke

• Background
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  Education, Training, & Certifications

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

  • Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2018 - 2022
  • 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

  • CAREER: Learning of graph diffusion and transport from high dimensional data with low-dimensional structures awarded by  National Science Foundation 2023 - 2028
  • 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
  • HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by  National Science Foundation 2019 - 2023
  • 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
  • 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
• Publications & Artistic Works
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  Selected Publications

  • Academic Articles

    • Cheng, X., and N. Wu. “Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation.” Applied and Computational Harmonic Analysis 61 (November 1, 2022): 132–90. https://doi.org/10.1016/j.acha.2022.06.003.
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    • Cheng, X., and A. Cloninger. “Classification Logit Two-Sample Testing by Neural Networks for Differentiating Near Manifold Densities.” Ieee Transactions on Information Theory 68, no. 10 (October 1, 2022): 6631–62. https://doi.org/10.1109/TIT.2022.3175691.
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    • Tan, Yixuan, Yuan Zhang, Xiuyuan Cheng, and Xiao-Hua Zhou. “Statistical inference using GLEaM model with spatial heterogeneity and correlation between regions.” Scientific Reports 12, no. 1 (October 2022): 16630. https://doi.org/10.1038/s41598-022-18775-8.
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    • Cheng, Xiuyuan, and Hau-Tieng Wu. “Convergence of graph Laplacian with kNN self-tuned kernels.” Information and Inference: A Journal of the Ima 11, no. 3 (September 8, 2022): 889–957. https://doi.org/10.1093/imaiai/iaab019.
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    • Zhu, W., Q. Qiu, R. Calderbank, G. Sapiro, and X. Cheng. “Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters.” Journal of Machine Learning Research 23 (January 1, 2022).
    • 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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    • 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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    • 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

    • Zhu, S., H. Wang, Z. Dong, X. Cheng, and Y. Xie. “NEURAL SPECTRAL MARKED POINT PROCESSES.” In Iclr 2022  10th International Conference on Learning Representations, 2022.
    • Cheng, X., Z. Miao, and Q. Qiu. “Graph Convolution with Low-rank Learn-able Local Filters.” In Iclr 2021  9th International Conference on Learning Representations, 2021.
    • Cheng, X., and Y. Xie. “Neural Tangent Kernel Maximum Mean Discrepancy.” In Advances in Neural Information Processing Systems, 9:6658–70, 2021.
    • Miao, Z., Z. Wang, X. Cheng, and Q. Qiu. “Spatiotemporal Joint Filter Decomposition in 3D Convolutional Neural Networks.” In Advances in Neural Information Processing Systems, 5:3376–88, 2021.
    • 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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    • Cheng, Xiuyuan, Zichen Miao, and Qiang Qiu. “Graph Convolution with Low-rank Learnable Local Filters,” 2020.
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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, Z., X. Cheng, G. Sapiro, and Q. Qiu. “STOCHASTIC CONDITIONAL GENERATIVE NETWORKS WITH BASIS DECOMPOSITION.” In 8th International Conference on Learning Representations, Iclr 2020, 2020.
    • Xu, Zhongshu, Yingzhou Li, and Xiuyuan Cheng. “Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization,” 2019.
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    • 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

  • COMPSCI 445: Introduction to High Dimensional Data Analysis 2023
  • MATH 465: Introduction to High Dimensional Data Analysis 2023
  • MATH 765: Introduction to High Dimensional Data Analysis 2023
  • STA 465: Introduction to High Dimensional Data Analysis 2023
  • 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
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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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