Moore-Sloan Research Fellow

60 5th Ave, New York, NY 1011

Office 621

soledad.villar at nyu edu

I am a Research Fellow at the Center for Data Science at New York University. I also have a Collaboration Scientist appointment at the Algorithms and Geometry Simons Collaboration.
My research is in mathematical data science and optimization. My papers can be found on my Google Scholar profile and my code can be found on my Github.

Before I was a Research Fellow at the Simons Institute, UC Berkeley. I got my PhD in Mathematics from the University of Texas at Austin, my PhD advisor is Rachel Ward. Here is my CV.

Optimization and learning techniques for clustering problems Statistical Physics and Machine Learning back together. Cargese, August 2018.

- SqueezeFit: Label-aware dimensionality reduction by semidefinite programming.
- With C. McWhirter and D. G. Mixon. In IEEE Transactions on Information Theory (to appear).
- On the equivalence between graph isomorphism testing and function approximation with GNNs.
- With Z. Chen , L. Chen and J. Bruna . In Advances in Neural Information Processing Systems (NeurIPS 2019) pp. 15868-15876.
- Clustering subgaussian mixtures by semidefinite programming.
- With D. G. Mixon and R. Ward. In Information and Inference: A Journal of the IMA 6 (4), pp. 389-415. [code]
- Probably certifiably correct k-means clustering.
- With T. Iguchi, D. G. Mixon and J. Peterson. In Mathematical Programming 2017 (165), pp. 605–642. [code]
- Relax, no need to round: integrality of clustering formulations.
- With P. Awasthi, A. S. Bandeira, M. Charikar, R. Krishnaswamy and R. Ward. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science. pp. 191-200.

- Fair redistricting is hard.
- With R. Kueng and D. G. Mixon. In Theoretical Computer Science 2019 (791), pp. 28-35.
- Experimental performance of graph neural networks on random instances of max-cut.
- With W. Yao and A. S. Bandeira In SPIE Wavelets and Sparsity 2019 XVIII 11138, 111380S.
- A note on learning algorithms for quadratic assignment with graph neural networks.
- With A. Nowak, A. S. Bandeira and J. Bruna. In IEEE Data Science Workshop, 2018 pp. 229-233. [code]
- Projected power iteration for network alignment.
- With E. Onaran In SPIE Wavelets and Sparsity 2017 XVII 10394, 103941C.
- Manifold optimization for k-means clustering.
- With T. Carson, D. G. Mixon and R. Ward In IEEE International Conference on Sampling Theory and Applications (SampTA 2017) pp. 73-77. [code]

- Optimal gene selection for cell type discrimination in single cell analyses.
- With B. Dumitrascu, D. G. Mixon and B. Engelhardt . [code]
- Can graph neural networks count substructures?
- With Z. Chen , L. Chen and J. Bruna .
- MREC: a fast and versatile framework for aligning and matching point clouds with applications to single cell molecular data .
- With A. J. Blumberg, M. Carriere, M. A. Mandell and R. Rabadan .
- Utility Ghost: Gamified redistricting with partisan symmetry.
- With D. G. Mixon.
- SUNLayer: stable denoising with generative networks.
- With D. G. Mixon.
- Monte Carlo approximation certificates for k-means clustering.
- With D. G. Mixon.
- A polynomial-time relaxation of the Gromov-Hausdorff distance.
- With A. S. Bandeira, A. J. Blumberg and R. Ward. [code]
- On the tightness of an SDP relaxation of kmeans clustering.
- With T. Iguchi, D. G. Mixon and J. Peterson.

- Gross formula on heights and special values of L-series.
- My master thesis on modular forms and quaternion algebras (in Spanish).
- Pell curves cryptography and generalizations.
- My undergraduate thesis (in Spanish).

- Differential equations
- From numbers to chaos
- Differential calculus
- Integral calculus
- Functions of a complex variable
- Introduction to mathematics

- Introduction to topology
- Programming (Python)
- Programming (Haskell)
- Linear algebra
- Mathematics for life sciences

- Complex analysis (teaching assistant)
- Linear algebra (lecturer)