Updated: May 1st, 2024 05:32

2024 article

EIKONAL DEPTH: AN OPTIMAL CONTROL APPROACH TO STATISTICAL DEPTHS

Molina-Fructuoso, M., & Murray, R. (2024, April). *FOUNDATIONS OF DATA SCIENCE*, Vol. 4.

UN Sustainable Development Goal Categories

13. Climate Action
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: April 29, 2024

2024 article

NON-LINEAR SINGULARITY FORMATION FOR CIRCULAR VORTEX SHEETS (vol 82, pg 81, 2024)

Murray, R., & Wilcox, G. (2024, February 6). *QUARTERLY OF APPLIED MATHEMATICS*, Vol. 2.

Sources: Web Of Science, NC State University Libraries

Added: February 19, 2024

2023 article

NON-LINEAR SINGULARITY FORMATION FOR CIRCULAR VORTEX SHEETS

Murray, R., & Wilcox, G. (2023, May 3). *QUARTERLY OF APPLIED MATHEMATICS*, Vol. 5.

UN Sustainable Development Goal Categories

15. Life on Land
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: June 5, 2023

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.

Sources: Web Of Science, NC State University Libraries

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

TL;DR:
It is shown that if agents’ objective functions are assumed to be smooth and nonconvex, then DGF can only converge to a saddle point from a zero-measure set of initial conditions.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: ORCID, Web Of Science, NC State University Libraries

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, NC State University Libraries

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

TL;DR:
It is proved that this equation possesses a unique viscosity solution, and that this solution always bounds the Tukey depth from below.
(via Semantic Scholar)

Sources: ORCID, Web Of Science, NC State University Libraries

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

TL;DR:
This work studies the theory of dropout from a nonparametric viewpoint, which is considered a proxy for the deepest layers of a neural network.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

4. Quality Education
(OpenAlex)

Sources: ORCID, Web Of Science, NC State University Libraries

Added: January 21, 2021

2020 journal article

Neutral competition in a deterministically changing environment: Revisiting continuum approaches

*JOURNAL OF THEORETICAL BIOLOGY*, *486*.

MeSH headings : Population Dynamics; Probability

TL;DR:
A classical, competitive Moran model is extended to incorporate an environment that fluctuates periodically in time to investigate the effects of the magnitude and frequency of environmental fluctuations on two important population statistics: the probability of fixation and the mean time to fixation.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science; OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: February 10, 2020

2020 journal article

On self-similar solutions to the incompressible Euler equations

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

UN Sustainable Development Goal Categories

13. Climate Action
(Web of Science)

Sources: Web Of Science, NC State University Libraries

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

TL;DR:
It is shown that almost all potential games are regular, except for a closed subset with Lebesgue measure zero, which proves an oddness result for potential games: in almost all possible games, the number of Nash equilibrium strategies is finite and odd.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

10. Reduced Inequalities
(Web of Science)

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

TL;DR:
The argument relies on a simple, yet powerful, maximum principle for the graph Laplacian, which gives the explicit dependence of the rates in terms of the parameter $\varepsilon_n$, the strength of regularization $\beta_n$ and the number of data points $n$.
(via Semantic Scholar)

Sources: ORCID, Web Of Science, NC State University Libraries

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.

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

TL;DR:
A global convergence-time bound is established for NGD under mild assumptions because it is shown that NGD “almost never” converges to saddle points and the time required to escape from a ball of radius is small.
(via Semantic Scholar)

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

TL;DR:
This model provides one possible framework for studying the tradeoff between exploration and exploitation in reinforcement learning and can be seem as a variant of either Bayesian reinforcement learning or adaptive control.
(via Semantic Scholar)

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

TL;DR:
The paper studies the convergence properties of (continuous-time) best-response dynamics from game theory to find out if they are convergent or non-convergent.
(via Semantic Scholar)

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.

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

TL;DR:
Algebraic rates of decay are established when initial perturbations of equilibrium have polynomial moments, proved by using new dissipation estimates in polynomially weighted $\ell^1$ spaces, operator decomposition techniques from kinetic theory, and interpolation estimates from the study of traveling waves.
(via Semantic Scholar)

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

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