Department of Mathematics
University of California, Santa Barbara
552 University Rd, Isla Vista, CA 93117
I am interested in solving problems in the mathematical foundations of Data Science. My 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 techniques from Statistical/Machine Learning, Harmonic Analysis, Approximation Theory, and Probability. 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.
- 2020 Fall: Math 104A Numerical Analysis I
- Jason Miller (PHD in applied math@JHU).
- Jiahui Cheng (Undergraduate). Placement: PHD in CSE@Gatech
- Learning theory for inferring interaction kernels in second-order interacting agent Systems (with J. Miller, M. Zhong and M. Magigoni). ArXiv:2010.03729. Submitted.
- Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories (with F. Lu and M. Maggioni). ArXiv:2007.15174. Submitted
- Learning interaction kernels in heterogeneous systems of agents from multiple trajectories (with F. Lu and M. Maggioni). Arxiv:1910.04832.Submitted
- On the identifiability of interaction functions in systems of interacting particles (with Z. Li, F. Lu, M. Maggioni and C. Zhang). Arxiv:1912.11965. To appear in Stochastic processes and their applications.
- 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.
- 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