Tropical Sufficient Statistics for Persistent Homology

DOI10.1137/17M1148037zbMath1443.62018arXiv1709.02647OpenAlexW2753130960MaRDI QIDQ5234530

Anthea Monod, Lorin Crawford, Juan Ángel Patiño-Galindo, Sara Kališnik Verovšek

Publication date: 27 September 2019

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02647

zbMATH Keywords

sufficient statisticstropical geometrypersistent homologyinfectious viral disease

Mathematics Subject Classification ID

Epidemiology (92D30) Applications of statistics to biology and medical sciences; meta analysis (62P10) Persistent homology and applications, topological data analysis (55N31) Sufficient statistics and fields (62B05) Applications of tropical geometry (14T90) Topological data analysis (62R40)

Related Items (5)

Bayesian topological signal processing ⋮ Unnamed Item ⋮ Functional summaries of persistence diagrams ⋮ ToFU: topology functional units for deep learning ⋮ Symmetric polynomials in upper-bound semirings

Uses Software

• ape
• MrBayes
• PAUP*
• MAFFT
• DEseq
• PhyML
• Cd-hit
• GitHub
• trimAl
• Ripser
• CliqueTop
• PersistenceImages

Cites Work

• Confidence sets for persistence diagrams
• Hypothesis testing for topological data analysis
• Symmetric and \(r\)-symmetric tropical polynomials and rational functions
• The ring of algebraic functions on persistence bar codes
• The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
• Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces
• Topological complexity of smooth random functions. École d'Été de Probabilités de Saint-Flour XXXIX-2009.
• Fréchet means for distributions of persistence diagrams
• Stability of persistence diagrams
• A Klein-bottle-based dictionary for texture representation
• Geometry of the space of phylogenetic trees
• Computing persistent homology
• Topological persistence and simplification
• Clique topology reveals intrinsic geometric structure in neural correlations
• Probability measures on the space of persistence diagrams
• Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
• Geometry Helps to Compare Persistence Diagrams
• Persistent homology transform for modeling shapes and surfaces
• Stochastic Convergence of Persistence Landscapes and Silhouettes
• Modeling and replicating statistical topology and evidence for CMB nonhomogeneity
• Topological pattern recognition for point cloud data
• Topology of viral evolution
• Sufficiency and Approximate Sufficiency
• Persistence Images: A Stable Vector Representation of Persistent Homology
• Statistical topological data analysis using persistence landscapes
• Barcodes: The persistent topology of data
• Algebraic Statistics for Computational Biology
• Properties of sufficiency and statistical tests
• Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics
• On Information and Sufficiency
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• Unnamed Item
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