Showing math.STShow all
3 papers · 1 filter
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…
math.ST2016
A new analytical approach to consistency and overfitting in regularized empirical risk minimization
Nicolas Garcia Trillos, Ryan Murray
This work considers the problem of binary classification: given training data from a certain population, together with associated labels $y_1,\dots, y_n \in \left…