109 citations · 243 across the 25 of their papers we have counts for
4 papers · 1 filter
Nonparametric forecasting of low-dimensional dynamical systems
Tyrus Berry, Dimitrios Giannakis, John Harlim
This letter presents a non-parametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift m…
Nonparametric Uncertainty Quantification for Stochastic Gradient Flows
Tyrus Berry, John Harlim
This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply th…
Local Kernels and the Geometric Structure of Data
Tyrus Berry, Timothy Sauer
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local ke…
Variable Bandwidth Diffusion Kernels
Tyrus Berry, John Harlim
Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is o…