4 papers
Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget
Pramita Bagchi, Edward Bae, Atish Mitra +3
Many two-sample tests for populations of persistence diagrams assess global differences without identifying the regions of the birth-death plane that contribute to them. We study s…
COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules
Sushovan Majhi, Atish Mitra, Žiga Virk +1
Every multiparameter persistence vectorization we know of carries a one-sided Lipschitz upper bound and nothing below it: without a lower gauge there is no sense in which the featu…
Statistical Inference for Persistence Diagrams via Landmark Embeddings: Minimax Theory and Finite Approximation
Pramita Bagchi, Sushovan Majhi, Atish Mitra +1
Hilbert-space embeddings enable inference for populations of persistence diagrams, but separation between individual diagrams need not survive population averaging. We develop a fr…
Geometric embeddings of spaces of persistence diagrams with explicit distortions
Atish Mitra, Ziga Virk
Let be a positive integer. We provide an explicit geometrically motivated -Lipschitz map from the space of persistence diagrams on points (equipped with the Bottleneck d…