13 citations · 22 across the 8 of their papers we have counts for
9 papers
The Signature Kernel
Darrick Lee, Harald Oberhauser
The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and s…
Convex Hulls of Curves: Volumes and Signatures
Carlos Améndola, Darrick Lee, Chiara Meroni
Taking the convex hull of a curve is a natural construction in computational geometry. On the other hand, path signatures, central in stochastic analysis, capture geometric propert…
Capturing Graphs with Hypo-Elliptic Diffusions
Csaba Toth, Darrick Lee, Celia Hacker +1
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through ra…
A Topological Approach to Mapping Space Signatures
Chad Giusti, Darrick Lee, Vidit Nanda +1
A common approach for describing classes of functions and probability measures on a topological space is to construct a suitable map from into a vec…
Signatures, Lipschitz-free spaces, and paths of persistence diagrams
Chad Giusti, Darrick Lee
Paths of persistence diagrams provide a summary of the dynamic topological structure of a one-parameter family of metric spaces. These summaries can be used to study and characteri…
Path Signatures on Lie Groups
Darrick Lee, Robert Ghrist
Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. We lift t…
Iterated Integrals and Population Time Series Analysis
Chad Giusti, Darrick Lee
One of the core advantages topological methods for data analysis provide is that the language of (co)chains can be mapped onto the semantics of the data, providing a natural avenue…
Structure of vortex-bound states in spin-singlet chiral superconductors
Darrick Lee, Andreas P. Schnyder
We investigate the structure of vortex-bound states in spin-singlet chiral superconductors with ()-wave and ()-wave pairing symmetries…
Localization for transversally periodic random potentials on binary trees
Richard Froese, Darrick Lee, Christian Sadel +2
We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, , and a random transversally pe…