About Me
I am an Associate Professor in the Mathematics Department at Harvey Mudd College. My research focuses are in mathematical data science, optimization, and applied convex geometry. I leverage mathematical tools, such as those from probability, combinatorics, and convex geometry, on problems in data science and optimization. Areas in which I have been active recently include randomized numerical linear algebra, combinatorial methods for convex optimization, tensor decomposition for topic modeling, network consensus and ranking problems, and community detection on graphs and hypergraphs. My research is supported by NSF CAREER #2440040 “Randomized Iterative Methods for Corrupted Data, Constrained Problems, and Compressed Updates” and has been supported by NSF DMS #2211318 “Tensor Models, Methods, and Medicine”.
Before starting at HMC, I received my PhD in the Graduate Group in Applied Mathematics at the University of California, Davis where I was fortunate to be advised by Professor Jesús A. De Loera, and then was a CAM Assistant Professor (post-doc) in the University of California, Los Angeles (UCLA) Mathematics Department where my exceptional postdoctoral mentor was Professor Deanna Needell.
Recent News
October ‘26: We (with collaborators Jessie Chen, Ziyu Cheng, Yunhui He, Alona Kryshchenko, Jocelyn T. Chi, and Anna Ma) submitted our paper Weighted Randomized Kaczmarz for Sparsely Corrupted Linear Systems! In this paper, we propose and analyze a framework of Kaczmarz methods that utilize an input weighting function to solve overdetermined linear systems whose measurements are perturbed by sparse, additive corruptions. Our generalized weighted randomized Kaczmarz framework utilizes a user-defined function to decrease the probability of sampling equations that are suspected of being corrupted. We derive one-step expected squared error bounds that separate progress on uncorrupted equations from the contribution of corrupted equations. Our theoretical results and numerical experiments demonstrate the benefit of this generalized framework in its flexibility in developing approaches for settings in which information about the corruptions is known or unknown. This project stemmed from work done at the Research Collaboration Workshop in Science of Data and Mathematics (WiSDM) at the University of North Carolina, Chapel Hill, during August 4–8, 2025, in the group led by Jocelyn T. Chi and myself.
September ‘26: We (with collaborators Anna Ma and Elizaveta Rebrova) submitted our paper Quantile-based Loss Filtering for Outlier-Robust Stochastic Gradient Descent! In this paper, we propose and analyze a general loss-filtering framework for finite-sum optimization with a subset of corrupted component functions whose gradients may be highly unreliable. We prove linear convergence of this family of methods under standard convexity assumptions, requiring the sample size to scale with the number of corruptions and a subset strong-convexity threshold. For the cases when large enough sampling is impossible or undesirable, we give a complementary small-sample probabilistic analysis that covers any sample size k and the convergence behavior depends on the probability of selecting an outlier and on the curvature of the selected good step. Experiments on polynomial regression, regularized logistic regression, and regularized hinge loss show that intermediate quantiles often outperform both standard SGD and other corruption-robust variants of SGD.