1 code implementation • 6 Jul 2023 • Qiquan Wang, Inés García-Redondo, Pierre Faugère, Anthea Monod, Gregory Henselman-Petrusek
In this paper, we revisit the persistent homology rank function -- an invariant measure of ``shape" that was introduced before barcodes and persistence diagrams and captures the same information in a form that is more amenable to data and computation.
1 code implementation • 18 Oct 2022 • Yueqi Cao, Prudence Leung, Anthea Monod
Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful applications to many domains.
4 code implementations • 30 Sep 2022 • Inés García-Redondo, Anthea Monod, Anna Song
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications.
1 code implementation • 13 Aug 2022 • Daniele Tramontano, Anthea Monod, Mathias Drton
In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees.
no code implementations • 16 Jul 2022 • Jakub Bober, Anthea Monod, Emil Saucan, Kevin N. Webster
Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks.
1 code implementation • 19 Apr 2022 • Yueqi Cao, Anthea Monod
We show that the mean of the persistence diagrams of subsamples -- taken as a mean persistence measure computed from the subsamples -- is a valid approximation of the true persistent homology of the larger dataset.
no code implementations • 7 Oct 2021 • John Sigbeku, Emil Saucan, Anthea Monod
We present a geometrically enhanced Markov chain Monte Carlo sampler for networks based on a discrete curvature measure defined on graphs.
1 code implementation • 4 Apr 2021 • Yueqi Cao, Athanasios Vlontzos, Luca Schmidtke, Bernhard Kainz, Anthea Monod
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in a hierarchy-preserving manner using a variety of metrics.
1 code implementation • 13 Nov 2019 • Wonjun Lee, Wuchen Li, Bo Lin, Anthea Monod
We study the problem of optimal transport in tropical geometry and define the Wasserstein-$p$ distances in the continuous metric measure space setting of the tropical projective torus.
Optimization and Control Metric Geometry Statistics Theory Statistics Theory
2 code implementations • 21 Nov 2016 • Lorin Crawford, Anthea Monod, Andrew X. Chen, Sayan Mukherjee, Raúl Rabadán
We introduce a novel statistic, the smooth Euler characteristic transform (SECT), which is designed to integrate shape information into regression models by representing shapes and surfaces as a collection of curves.
Applications