Joe Kileel's Home Page

I am an assistant professor at UT Austin in the Department of Mathematics , Oden Institute for Computational Engineering and Sciences and Machine Learning Laboratory .

I work in applied mathematics and computational algebra. Specifically I am interested in: higher-order tensor methods; 3D reconstruction in imaging; and nonconvex optimization landscapes. My research is supported by the NSF, DOE and Sloan Foundation.

Previously I was a postdoc at Princeton with Amit Singer , and a graduate student at Berkeley with Bernd Sturmfels. Here is my CV.

Papers

- Geometry and optimization of shallow polynomial networks
with Y. Arjevani, J. Bruna, E. Polak, M. Trager
available on arXiv

- Covering number of real algebraic varieties and beyond: Improved bounds and applications
with Y. Zhang
available on arXiv

- Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC
with H. Fan, B. Kimia
available on arXiv

- Tensor moments of Gaussian mixture models: theory and applications
with J. Pereira, T. Kolda
available on arXiv (code)

- Subspace power method for symmetric tensor decomposition
with J. Pereira
available on arXiv (code)

- Fast expansion into harmonics on the ball
with N. Marshall, O. Mickelin, A. Singer
SIAM Journal on Scientific Computing, to appear

- Snapshot of algebraic vision
with K. Kohn
AMS Proceedings of Symposia in Pure Mathematics, to appear

- Tensor-based synchronization and the low-rankness of the block trifocal tensor
with D. Miao, G. Lerman
Advances in Neural Information Processing Systems, 2024

- Scalable symmetric Tucker tensor decomposition
with R. Jin, T. Kolda, R. Ward
SIAM Journal on Matrix Analysis and Applications, 2024

- Algebraic constraints and algorithms for common lines in cryo-EM
with T. Muller, A. Duncan, E. Verbeke
Biological Imaging, 2024

- The G-invariant graph Laplacian Part I: Convergence rate and eigendecomposition
with E. Rosen, P. Hoyos, X. Cheng, Y. Shkolnisky
Applied and Computational Harmonic Analysis, 2024

- The effect of smooth parametrizations on nonconvex optimization landscapes
with E. Levin, N. Boumal
Mathematical Programming, 2024

- Moment-based metrics for molecules computable from cryo-EM images
with A. Zhang, O. Mickelin, E. Verbeke, N. Marshall, M. Gilles, A. Singer
Biological Imaging, 2024

- Moment estimation for nonparametric mixture models through implicit tensor decomposition
with Y. Zhang
SIAM Journal on Mathematics of Data Science, 2023

- Moment varieties for mixtures of products
with Y. Alexandr, B. Sturmfels
ACM International Symposium on Symbolic and Algebraic Computation, 2023

- Autocorrelation analysis for cryo-EM with sparsity constraints: improved sample complexity and projection-based algorithms
with T. Bendory, Y. Khoo, O. Mickelin, A. Singer
Proceedings of the National Academy of Sciences, 2023

- Estimation under group actions: recovering orbits from invariants
with A. Bandeira, B. Blum-Smith, A. Perry, J. Weed, A. Wein
Applied and Computational Harmonic Analysis, 2023
Charles Chui Young Researcher Best Paper Award

- On the instability of relative pose estimation and RANSAC's role
with H. Fan, B. Kimia
IEEE Conference on Computer Vision and Pattern Recognition, 2022

- Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy
with E. Levin, N. Boumal
Mathematical Programming, 2022

- Landscape analysis of an improved power method for tensor decomposition
with T. Klock, J. Pereira
Advances in Neural Information Processing Systems, 2021

- Manifold learning with arbitrary norms
with A. Moscovich, N. Zelesko, A. Singer
Journal of Fourier Analysis and Applications, 2021

- Earthmover-based manifold learning for analyzing molecular conformation spaces
with N. Zelesko, A. Moscovich, A. Singer
IEEE International Symposium on Biomedical Imaging, 2020 (code)

- Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles
with N. Sharon, Y. Khoo, B. Landa, A. Singer
Inverse Problems, 2020 (code)

- On the expressive power of deep polynomial neural networks
with M. Trager, J. Bruna
Advances in Neural Information Processing Systems, 2019 (code)

- Numerical implicitization
with J. Chen
Journal of Software for Algebra and Geometry, 2019 (code)

- 3D ab initio modeling in cryo-EM by autocorrelation analysis
with E. Levin, T. Bendory, N. Boumal, A. Singer
IEEE International Symposium on Biomedical Imaging, 2018 (code)

- Distortion varieties
with Z. Kukelova, T. Pajdla, B. Sturmfels
Foundations of Computational Mathematics, 2018

- The Chow form of the essential variety in computer vision
with G. Fløystad, G. Ottaviani
Journal of Symbolic Computation, 2018 (supplementary)

- Algebraic geometry for computer vision
University of California, Berkeley, Ph.D. thesis, May 2017
Bernard Friedman Memorial Prize for Best Thesis in Applied Mathematics

- Minimal problems for the calibrated trifocal variety
SIAM Journal on Applied Algebra and Geometry, 2017 (supplementary)

- A clever elimination strategy for efficient minimal solvers
with Z. Kukelova, B. Sturmfels, T. Pajdla
IEEE Conference on Computer Vision and Pattern Recognition, 2017

- Rigid multiview varieties
with M. Joswig, B. Sturmfels, A. Wagner
International Journal of Algebra and Computation, 2016

- Hadamard products of linear spaces
with C. Bocci, E. Carlini
Journal of Algebra, 2016

Teaching

Spring 2025: Calculus I
Fall 2024: Calculus I
Spring 2024: Foundational techniques of machine learning and data sciences
Fall 2023: Scientific computation in numerical analysis
Spring 2023: Foundational techniques of machine learning and data sciences
Spring 2022: Scientific computation in numerical analysis
Fall 2021: Geometric methods in data science
Spring 2021: Real analysis I

People

Julia Lindberg: Bing instructor, Math Dept, January 2023-present

Gabriel Brown: CSEM Ph.D. student, July 2023-present

Addie Duncan: Math Ph.D. student, November 2023-present

Paulina Hoyos: Math Ph.D. student, September 2022-present

Elzbieta Polak: Math Ph.D. student, July 2021-present

Yifan Zhang: CSEM Ph.D. student, January 2021-present

George D. Torres: Math Ph.D. student, June 2022-August 2023, co-advised with Ngoc Tran (subsequently: research scientist at Striveworks)

João M. Pereira: Postdoc, Oden Institute, January 2021-May 2022, co-mentored with Rachel Ward (subsequently: assistant professor at IMPA, Brazil)

Bronson Zhou: Math undergraduate researcher, 2021-2022 (subsequently: Ph.D. student at Yale)

Travel

Address

Department of Mathematics, PMA 12.154

Oden Institute for Computational Engineering and Sciences, POB 3.434

University of Texas at Austin

jkileel@math.utexas.edu