The CEDAR (ComplEx Data Analysis Research) Team works at the interface of harmonic analysis and machine learning. We develop tools that uncover complex, multiscale patterns in high dimensional data by considering the underlying data geometries, invariants, hierarchies and statistics. Our focus is on rigorous mathematical theory coupled with state of the art numerical results in application specific domains. Research areas include:

• Mathematical foundations of deep learning
• Geometric and topological methods for high dimensional data analysis, including geometric deep learning
• Smooth extension and interpolation of data, with efficient algorithms (Whitney-type extensions)
• Multi-reference alignment inverse problems
• Machine learning and quantum many body physics
• Biological data analysis
• Stochastic processes
• Quantum computing and quantum information science

Team members

Scientific leader

Matthew Hirn [CMSE, Mathematics, MSU-Q]

Postdocs

• None currently

Graduate students

• Nathan Brugnone [Community Sustainability, CMSE] (PhD advisors: Robert Richardson, Matthew Hirn)
• Albert Chua [Mathematics] (PhD advisor: Matthew Hirn)
• Ryan LaRose [CMSE, Physics] (PhD advisor: Matthew Hirn)
• Renming Liu [CMSE] (PhD advisors: Matthew Hirn, Arjun Krishnan)
• Sarah McGuire [CMSE] (PhD advisors: Matthew Hirn, Elizabeth Munch)
• Elena Wang [CMSE] (PhD advisors: Matthew Hirn, Elizabeth Munch)
• Liping Yin [Mathematics] (PhD advisor: Matthew Hirn)
• Xitong Zhang [CMSE] (PhD advisor: Matthew Hirn)

Alumni

Postdocs

• Paul Sinz [CMSE] (mentor: Matthew Hirn)
  Now at Lucido Group LLC
• Anna Little [CMSE] (mentors: Yuying Xie, Matthew Hirn)
  Now a tenure track Assistant Professor at the University of Utah
• Michael Perlmutter [CMSE, Mathematics] (mentors: Matthew Hirn, Mark Iwen)
  Now a fixed term Assistant Professor at UCLA

Graduate Students

• Xavier Brumwell [CMSE] (PhD advisor: Matthew Hirn)
  Now a researcher at Michigan Tech Research Institute
• Jieqian He [CMSE, Statistics] (PhD advisor: Matthew Hirn)
  Now a research scientist at Meta/Facebook
• Feng Gao [Plant, Soil and Microbial Sciences, CMSE] (PhD advisor: Stephen Boyd)
  Now a postdoc at Yale University in the Krishnaswamy Lab

Undergraduate students

• Muawiz Chaudhary [2018 ACRES REU] (mentors: Matthew Hirn, Yue Qi)
• Nikhil Shankar [2018 ACRES REU] (mentors: Matthew Hirn, Yue Qi)

Papers by the CEDAR Team

• Wavelet invariants for statistically robust multi-reference alignment.
  With Anna Little.
  Information and Inference: A Journal of the IMA, in press, 2020.
  pdf, arXiv, IMA. Software.
• Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties.
  With Paul Sinz, Michael Swift, Xavier Brumwell, Jialin Liu, Kwang Jin Kim and Yue Qi.
  The Journal of Chemical Physics, volume 153, issue 8, 084109, 2020.
  pdf, arXiv, AIP.
• Geometric scattering networks on compact Riemannian manifolds.
  With Michael Perlmutter, Feng Gao and Guy Wolf.
  Proceedings of The First Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research, volume 107, pages 570–604, 2020.
  pdf, arXiv, PMLR.
• Kymatio: Scattering Transforms in Python.
  With Mathieu Andreux, Tomás Angles, Georgios Exarchakis, Roberto Leonarduzzi, Gasper Rochette, Louis Thiry, John Zarka, Stéphane Mallat, Joakim Andén, Eugene Belilovsky, Joan Bruna, Vincent Lostanlen, Muawiz Chaudhary, Edouard Oyallon, Sixhin Zhang, Carmine Cella, Michael Eickenberg.
  Journal of Machine Learning Research, volume 21, number 60, pages 1-6, 2020.
  pdf, arXiv, JMLR. Software.
• Coarse Graining of Data via Inhomogeneous Diffusion Condensation.
  With Nathan Brugnone, Alex Gonopolskiy, Mark W. Moyle, Manik Kuchroo, David van Dijk, Kevin R. Moon, Daniel Colon-Ramos, Guy Wolf and Smita Krishnaswamy.
  In Proceedings of the 2019 IEEE International Conference on Big Data, pages 2624–2633, 2019.
  pdf, arXiv, IEEE Xplore. Software.
• Geometric wavelet scattering on graphs and manifolds.
  With Feng Gao, Michael Perlmutter and Guy Wolf.
  In Proceedings of SPIE 11138, Wavelets and Sparsity XVIII, 111380Q, 2019.
  pdf, SPIE.
• Geometric Scattering for Graph Data Analysis.
  With Feng Gao and Guy Wolf.
  In Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research (PMLR), volume 97, pages 2122-2131, 2019.
  pdf, ICML/PMLR, arXiv.
• Geometric Scattering on Manifolds (contributed spotlight talk).
  With Michael Perlmutter and Guy Wolf.
  In NeurIPS Workshop on Integration of Deep Learning Theories, Montreal, Canada, December 8, 2018.
  pdf, arXiv, NIPS DLTheory.
• Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction (contributed spotlight talk).
  With Xavier Brumwell, Paul Sinz, Kwang Jin Kim and Yue Qi.
  In NeurIPS Workshop on Machine Learning for Molecules and Materials, Montreal, Canada, December 8, 2018.
  pdf, arXiv, NIPS MLMM.

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