Department of Mathematics
University of California, Santa Barbara
552 University Rd, Isla Vista, CA 93117
I am an assistant professor at Department of Mathematics. Before joining UCSB, I was a member of Prof. Mauro Maggioni's research group and worked as assistant research professor at Johns Hopkins University. Here is my CV.
I am interested in solving problems in the mathematical foundations of Data Science. My cuurent research projects are motivated by the need to exploit dynamical data sets in complex physical systems to perform inference with provable performance and build generalizable and interpretable predictive models, where I used and developed techniques from Statistical/Machine Learning, Harmonic Analysis, Approximation Theory, and Probability. My research can be categorized to the following two areas:
- Mathematical foundation of learning theory: statistical learning theory, statistical inference for ODEs and SDEs from time-series data, high dimensional data analysis
- Applied and computational harmonic Analysis: functional analysis, Fourier analysis, approximation theory, sampling and frame theory, inverse problem in mathematical/statistical signal processing
- Current Quater: Math 104A Numerical Analysis I and Math 104B Numerical Analysis II
- 2020 Fall: Math 104A Numerical Analysis I
- Jason Miller (PHD in applied math@JHU). 2019 Fall to 2020 Fall
- Jiahui Cheng (Undergraduate@USTC). 2019 summer, Placement: PHD in CSE@Gatech
- Cassandra Lem (Undergraduate@UCSB) 2020 Fall to present
- Noa Nabeshima (Undergraduate@UCSB) 2020 Fall to present
- Data-driven discovery of interacting particle systems using Gaussian processes (with Jinchao Feng and Yunxiang Ren). 1-29, Submitted.
- Estimate the spectrum of affine dynamical systems from partial
observations of a single trajectory data (with Jiahui Cheng). ArXiv:2105.02945, 1-32, Submitted.
- Learning theory for inferring interaction kernels in second-order interacting agent Systems (with J. Miller, M. Zhong and M. Maggioni). ArXiv:2010.03729, 1-68, Submitted.
- Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories (with F. Lu and M. Maggioni). ArXiv:2007.15174. To appear at Foundations of Computational Mathematics, 1-52, 2021.
- Learning interaction kernels in heterogeneous systems of agents from multiple trajectories (with F. Lu and M. Maggioni). Journal of Machine Learning Research, 22 (32), 1-67, 2021. Code.
- On the identifiability of interaction functions in systems of interacting particles (with Z. Li, F. Lu, M. Maggioni and C. Zhang). Stochastic processes and their applications, Vol 132, 135 - 163, 2021.
- Sensor Calibration for Spectral Estimation Off the Grid (with Y. Eldar and W. Liao). Applied and Computational Harmonic Analysis,48(2), 570-598, 2020.
- Phaseless reconstruction from space-time samples (with A. Aldroubi and I. Krishtal). Applied and Computational Harmonic Analysis, 48(1), 395-414, 2020.
Nonparametric inference of interaction laws in systems of agents from trajectory data (with F. Lu, M. Zhong and M. Maggioni). Proceedings of the National Academy of Sciences of USA, 116(29): 14424-14433, 2019. Appendix: 27 pages.
- Analysis of simulated crowd flow exit data: visualization, panic detection, exit time convergence, attribution and estimation (with A. Grim, B. Iskra, N. Ju, A. Kryshchenko, F.P. Medina, L. Ness, M. Ngamini, M. Owen, R. Paffenroth), Research in Data Science, 17:239-281, 2019.
- Undersampled windowed exponentials, spectra of Toeplitz operators and its applications (with C. Lai). Acta Applicanda Mathematicae, 164(1), 65-81, 2019
- Universal spatial-temporal sampling sets for discrete spatially invariant evolution systems. IEEE Transactions on Information Theory, 63(9): 5518-5528, 2017.
- System Identification in Dynamical Sampling. Advance in Computational Mathematics, 43(3): 555-580, 2017.
- Dynamical Sampling (with A. Aldroubi, C. Cabrelli and U. Molter). Applied and Computational Harmonic Analysis, 42(3): 378-401, 2017.
- Phase retrieval of evolving signals from space-time samples (with A. Aldroubi and I. Krishtal). Proceeding of 12th international conference on Sampling Theory and Applications, 2017.
- Multidimensional Signal Recovery in Discrete Evolution Systems via Spatiotemporal Trade Off (with R. Aceska and A. Petrosyan). Sampling Theory in Signal and Image Processing, 14(2):153-169, 2015.
- Filter Recovery in Infinite Spatially Invariant Evolutionary Systems via Spatiotemporal Trade off. Proceeding of 11th international conference on Sampling Theory and Applications, 2015.
- Dynamical sampling of two-dimensional temporally-varying signals (with R. Aceska and A. Petrosyan). Proceeding of 11th international conference on Sampling Theory and Applications, 2015.
- Dynamical sampling in hybrid shift invariant spaces (with R. Aceska). Contemporary Mathematics, American Mathematics Society, Providence, 626:149-166, 2014.
Previous Teaching at JHU
- Summer 2019: Math 109 Calculus II
- Spring 2019: Math 109 Calculus II (179 Students)
- Fall 2018: Math 201 Linear Algebra (167 Students)
- Spring 2018: Math 212 Honors Linear Algebra
- Fall 2017: Math 443 Fourier Analysis