8 papers
Generative Modeling on Metric Graphs via Neural Optimal Transport
Alessandro Micheli, Yueqi Cao, Anthea Monod +1
We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target…
Riemannian Neural Optimal Transport
Alessandro Micheli, Yueqi Cao, Anthea Monod +1
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data…
Metric Graph Kernels via the Tropical Torelli Map
Yueqi Cao, Anthea Monod
We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges,…
Approximating Persistent Homology for Large Datasets
Yueqi Cao, Anthea Monod
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces pe…
Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs
Yueqi Cao, Anthea Monod
Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological fe…
A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams
Yueqi Cao, Anthea Monod
The Fréchet mean is an important statistical summary and measure of centrality of data; it has been defined and studied for persistent homology captured by persistence diagrams. H…