3 papers
math.OC2023
Acceleration and Implicit Regularization in Gaussian Phase Retrieval
Tyler Maunu, Martin Molina-Fructuoso
We study accelerated optimization methods in the Gaussian phase retrieval problem. In this setting, we prove that gradient methods with Polyak or Nesterov momentum have similar imp…
math.ST2022
Eikonal depth: an optimal control approach to statistical depths
Martin Molina-Fructuoso, Ryan Murray
Statistical depths provide a fundamental generalization of quantiles and medians to data in higher dimensions. This paper proposes a new type of globally defined statistical depth,…
math.ST2021
Tukey Depths and Hamilton-Jacobi Differential Equations
Martin Molina-Fructuoso, Ryan Murray
The widespread application of modern machine learning has increased the need for robust statistical algorithms. This work studies one such fundamental statistical measure known as…