Updated: May 22nd, 2023 08:38

2023 article

The geometry of adversarial training in binary classification

Bungert, L., Trillos, N. G., & Murray, R. (2023, January 13). *INFORMATION AND INFERENCE-A JOURNAL OF THE IMA*, Vol. 1.

author keywords: adversarial training; nonlocal perimeter; nonlocal total variation; existence of solutions; regularity

Sources: Web Of Science, ORCID

Added: February 6, 2023

2022 journal article

Adversarial classification: Necessary conditions and geometric flows

*Journal of Machine Learning Research*, *23*(187), 1–38.

Source: ORCID

Added: November 10, 2022

2022 journal article

Distributed Gradient Flow: Nonsmoothness, Nonconvexity, and Saddle Point Evasion

*IEEE TRANSACTIONS ON AUTOMATIC CONTROL*, *67*(8), 3949–3964.

author keywords: Optimization; Convergence; Linear programming; Manifolds; Standards; Heuristic algorithms; Trajectory; Distributed optimization; gradient descent; gradient flow; nonconvex optimization; nonsmooth optimization; saddle point; stable manifold

Sources: ORCID, Web Of Science

Added: July 28, 2022

2022 article

From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds

Trillos, N. G., Murray, R., & Thorpe, M. (2022, April 8). *ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS*, Vol. 4.

Sources: Web Of Science, ORCID

Added: April 25, 2022

2022 journal article

Tukey Depths and Hamilton-Jacobi Differential Equations

*SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE*, *4*(2), 604–633.

author keywords: statistical depths; robust statistics; Hamilton-Jacobi equations; viscosity solutions

Sources: ORCID, Web Of Science

Added: May 12, 2022

2021 journal article

Dropout Fails to Regularize Nonparametric Learners

*JOURNAL OF STATISTICAL THEORY AND PRACTICE*, *15*(2).

author keywords: Dropout; Nonparametric statistics; Deep learning; Regularization

Sources: ORCID, Web Of Science

Added: January 21, 2021

2020 journal article

Neutral competition in a deterministically changing environment: Revisiting continuum approaches

*JOURNAL OF THEORETICAL BIOLOGY*, *486*.

Sources: Web Of Science, ORCID

Added: February 10, 2020

2020 journal article

On self-similar solutions to the incompressible Euler equations

*JOURNAL OF DIFFERENTIAL EQUATIONS*, *269*(6), 5142–5203.

Sources: Web Of Science, ORCID

Added: June 29, 2020

2020 journal article

Regular potential games

*Games and Economic Behavior*, *124*, 432–453.

author keywords: Game theory; Potential games; Generic games; Regular equilibria; Multi-agent systems

Source: ORCID

Added: October 2, 2020

2020 journal article

y A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors

*SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE*, *2*(3), 705–739.

author keywords: empirical risk minimization; graph Laplacian; discrete to continuum; nonparametric regression

Sources: ORCID, Web Of Science

Added: September 13, 2020

2019 journal article

Local minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions

*Proceedings of the American Mathematical Society*, *147*(12), 5167–5182.

author keywords: Second-order Gamma-convergence; rearrangement; Cahn-Hilliard functional; slow motion; Allen-Cahn equation; Cah-Hilliard equation

Source: ORCID

Added: December 6, 2019

2019 journal article

Revisiting Normalized Gradient Descent: Fast Evasion of Saddle Points

*IEEE Transactions on Automatic Control*, *64*(11), 4818–4824.

author keywords: Gradient methods; machine learning; nonconvex optimization; optimization

Source: ORCID

Added: December 6, 2019

2018 journal article

A model for system uncertainty in reinforcement learning

*Systems & Control Letters*, *122*, 24–31.

author keywords: Dynamic programming; Learning systems; Machine learning; Adaptive control

Source: ORCID

Added: December 6, 2019

2018 article

Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points

Swenson, B., Murray, R., Kar, S., & Poor, H. V. (2018, October). *2018 52nd Asilomar Conference on Signals, Systems, and Computers*.

Source: ORCID

Added: December 6, 2019

2018 journal article

On Best-Response Dynamics in Potential Games

*SIAM Journal on Control and Optimization*, *56*(4), 2734–2767.

author keywords: game theory; learning; best-response dynamics; fictitious play; potential games; convergence rate

Source: ORCID

Added: December 6, 2019

2017 journal article

A new analytical approach to consistency and overfitting in regularized empirical risk minimization

*European Journal of Applied Mathematics*, *28*(6), 886–921.

author keywords: Overfitting; empirical risk minimization; graph total variation; discrete to continuum; classification

Source: ORCID

Added: December 6, 2019

2017 journal article

Cutoff estimates for the linearized Becker–Döring equations

*Communications in Mathematical Sciences*, *15*(6), 1685–1702.

author keywords: coagulation-fragmentation equations; spectrum; cutoff estimates

Source: ORCID

Added: December 6, 2019

2016 journal article

Algebraic Decay to Equilibrium for the Becker--Döring Equations

*SIAM Journal on Mathematical Analysis*, *48*(4), 2819–2842.

author keywords: coagulation-fragmentation equations; rate of decay to equilibrium; interpolation inequalities

Source: ORCID

Added: December 6, 2019

2015 journal article

Second-Order Γ-limit for the Cahn–Hilliard Functional

*Archive for Rational Mechanics and Analysis*, *219*(3), 1383–1451.

Source: ORCID

Added: December 6, 2019