Joe Kileel's Home Page

I am an assistant professor at the University of Texas at Austin, and a member of the Department of Mathematics , Oden Institute for Computational Engineering and Sciences and Machine Learning Laboratory .

My research is in applied mathematics and computational algebra. Specific areas of focus are: higher-order tensor methods; 3D reconstruction in cryo-electron microscopy and computer vision; and nonconvex optimization.

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

Papers

- Diffusion maps for group-invariant manifolds
with P. Hoyos
Available on arXiv

- Moment estimation for nonparametric mixture models through implicit tensor decomposition
with Y. Zhang
Available on arXiv

- Snapshot of algebraic vision
with K. Kohn
Available on arXiv

- The effect of smooth parametrizations on nonconvex optimization landscapes
with E. Levin, N. Boumal
Available on arXiv

- Scalable symmetric Tucker tensor decomposition
with R. Jin, T. Kolda, R. Ward
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 and generalized PCA
with J. Pereira
Available on arXiv (code)

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

- 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 120 18 (2023), e2216507120

- 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, accepted

- 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 27 82 (2021), pp. 1-56

- Earthmover-based manifold learning for analyzing molecular conformation spaces
with N. Zelesko, A. Moscovich, A. Singer
IEEE International Symposium on Biomedical Imaging 2020, pp. 1715-1719 (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 36 044003 (2020), pp. 1-40 (code)

- On the expressive power of deep polynomial neural networks
with M. Trager, J. Bruna
Advances in Neural Information Processing Systems 2019, pp. 10310-10319 (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, pp. 1569-1573 (code)

- Algebraic geometry for computer vision
University of California, Berkeley, PhD thesis, 139 pages, May 2017
Bernard Friedman Memorial Prize for Best Thesis in Applied Mathematics

- Numerical implicitization
with J. Chen
Journal of Software for Algebra and Geometry 9 (2019), pp. 55-63 (code)

- Distortion varieties
with Z. Kukelova, T. Pajdla, B. Sturmfels
Foundations of Computational Mathematics 18 (2018), pp. 1043-1071

- The Chow form of the essential variety in computer vision
with G. Fløystad, G. Ottaviani
Journal of Symbolic Computation 86 (2018), pp. 97-119 (supplementary)

- Minimal problems for the calibrated trifocal variety
SIAM Journal on Applied Algebra and Geometry 1 (2017), pp. 575-598 (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, pp. 3605-3614

- Rigid multiview varieties
with M. Joswig, B. Sturmfels, A. Wagner
International Journal of Algebra and Computation 26 (2016), pp. 775-788

- Hadamard products of linear spaces
with C. Bocci, E. Carlini
Journal of Algebra 448 (2016), pp. 595-617

Teaching

Spring 2023: Foundational techniques of machine learning and data sciences, instructor
Spring 2022: Scientific computation in numerical analysis, instructor
Fall 2021: Geometric methods in data science, instructor
Spring 2021: Real analysis I, instructor
Spring 2017: Introduction to optimization, consultant
May 2016: Outstanding Graduate Student Instructor Award
Spring 2016: Tropical geometry, grader and guest lecturer
Spring 2016: Analytic geometry and calculus, TA
Fall 2015: Methods of mathematics: calculus, statistics and combinatorics, TA
Spring 2015: Methods of mathematics: calculus, statistics and combinatorics, TA
Fall 2014: Calculus, TA

People

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

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

Paulina Hoyos: Math PhD Student, September 2022-present

Elzbieta Polak: Math PhD Student, July 2021-present

George Torres: Math PhD Student, June 2022-present, co-advised with Ngoc Tran

Yifan Zhang: CSEM PhD Student, January 2021-present

Bronson Zhou: Math Undergraduate Researcher, 2021-2022 (next: 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