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Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning

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arxiv 2407.16733 v1 pith:3R4CSOYD submitted 2024-07-23 cs.LG math.CV

Vladimir Jacimovic , Marijan Markovic This is my paper · ORCID
classification cs.LGmath.CV
keywords hyperbolicdeepdiscdistributionsfamilygeometriclearningprobability
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We introduce the novel family of probability distributions on hyperbolic disc. The distinctive property of the proposed family is invariance under the actions of the group of disc-preserving conformal mappings. The group-invariance property renders it a convenient and tractable model for encoding uncertainties in hyperbolic data. Potential applications in Geometric Deep Learning and bioinformatics are numerous, some of them are briefly discussed. We also emphasize analogies with hyperbolic coherent states in quantum physics.

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  1. A group-theoretic framework for machine learning in hyperbolic spaces

    cs.LG 2025-01 reject novelty 4.0 of 10

    Introduces conformal and holomorphic barycenters and Möbius-type probability families on hyperbolic balls, together with hyperbolic gradient and maximum likelihood estimation algorithms.

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