As an applied analyst, I develop theoretical and computational techniques to solve problems in high-dimensional data analysis, signal processing, and machine learning. Here is my CV.

Selected publications

• X. Cheng and N. Wu. "Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation". Applied and Computational Harmonic Analysis, 61, 132-190 (2022). [Abstract] [arXiv: 2101.09875] [Code]
• X. Cheng and A. Cloninger. "Classification logit two-sample testing by neural networks for differentiating near manifold densities.'' IEEE Transactions on Information Theory (2022). [Abstract] [arXiv: 1909.11298] [Code]
• X. Cheng and Y. Xie. "Neural tangent kernel maximum mean discrepancy". The 35th Conference on Neural Information Processing Systems (NeurIPS 2021). [Abstract] [arXiv: 2106.03227] [Code]
• X. Cheng and G. Mishne. "Spectral embedding norm: looking deep into the spectrum of the graph Laplacian". SIAM Journal on Imaging Sciences (2020). [Abstract] [arXiv: 1810.10695] [Code]
• X. Cheng, Q. Qiu, R. Calderbank, and G. Sapiro. "RotDCF: Decomposition of convolutional filters for rotation-equivariant deep networks". International Conference on Learning Representations (ICLR 2019). [Abstract] [arXiv: 1805.06846] [Code]
• X. Cheng and A. Singer. "The spectrum of high-dimensional random inner-product matrices". Random Matrices: Theory and Applications, 02, 04 (2013). [Abstract] [PDF]

Recent teaching

Course materials are distributed via Duke system Sakai. May you have any question about class, send me an email!

• Spring 2024: Math 532 Basic Analysis II. [Syllabus] New site on Canvas!
• Fall 2023: Math 631 Measure and Integration [Syllabus]; Math 465 Introduction to High Dimensional Data Analysis [Syllabus] (co-taught with Dr. Jiajia Yu).