I am interested in understanding machine learning and optimization from geometric and algebraic perspectives. My research generally involves using geometry and high-dimensional statistics to understand and develop machine learning concepts and algorithms. I tend to care about things such as the generalization and robustness of machine learning methods, and their susceptibility to altered or missing data. Previously, I worked on problems in computational algebra and number theory.


Approximate Gradient Coding via Sparse Random Graphs
Z. Charles, D. Papailiopoulos, J. Ellenberg

Stability and Generalization of Learning Algorithms that Converge to Global Optima
Z. Charles, D. Papailiopoulos

Exploiting Algebraic Structure in Global Optimization and the Belgian Chocolate Problem
Z. Charles, N. Boston

Subspace Clustering with Missing and Corrupted Data
Z. Charles, A. Jalali, R. Willett


Efficiently Finding All Power Flow Solutions to Tree Networks
Z. Charles, A. Zachariah
To appear in Allerton, 2017.

Generating Random Factored Ideals in Number Fields
Z. Charles
To appear in Mathematics of Computation, 2017. [arXiv:1612.06260]

Nonpositive Eigenvalues of Hollow, Symmetric, Nonnegative Matrices
Z. Charles, M. Farber, C. Johnson, L. Kennedy-Shaffer
SIAM Journal on Matrix Analysis and Applications, 2013.

Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues
Z. Charles, M. Farber, C. Johnson, L. Kennedy-Shaffer
Discrete Mathematics, 2013. [arXiv:1108.4810]

The Relation Between the Diagonal Entries and the Eigenvalues of a Symmetric Matrix, Based upon the Sign Pattern of its Off-Diagonal Entries
Z. Charles, M. Farber, C. Johnson, L. Kennedy-Shaffer
Linear Algebra and its Applications, 2013.