SMBp Group Meeting: Loucas Pillaud-Vivien

Tuesday Apr 18, 2023, 2:00 PM → 3:00 PM America/New_York

3rd Floor Classroom/3-Flatiron Institute (162 5th Avenue)

Speaker: Loucas Pillaud-Vivien Flatiron Research Fellow, CCM

Title: Reaction coordinates estimations through kernelized diffusion maps

 

Abstract: Diffusion maps is a celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a graph kernel approach, however this local average construction is known to be cursed by the high-dimension and is highly unstable. In this talk we will show how to build a different estimator of the Laplacian, via a reproducing kernel Hilbert space method, which adapts naturally to the regularity of the problem, circumventing the curse of dimensionality and that can be computationally built efficiently (via Nystrom subsampling, Fourier features). Finally, we show how we can estimate the reaction coordinates of a physical system via a neural network approach built on top of this kernel estimator.