Multi-distribution Rényi divergences are positive integrals of coincidence divergences C_α over four strata (simplex interior, mixed-sign cones, tropical boundary, KL edges).
Advances in Mathematics370, 107239 (2020)
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Infinitesimal causality is defined via compatibility of categorical and geometric Frobenius structures in Markov categories, with interventions as tangent vectors deforming copy/discard operations and Lie brackets measuring preservation of information flow.
Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.
Causal density functions are Radon-Nikodym derivatives serving as local density ratios between do and obs distributions, allowing observational expectations reweighted by the ratio to reproduce interventional ones.
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Multi-distribution Rényi divergences are positive integrals of coincidence divergences C_α over four strata (simplex interior, mixed-sign cones, tropical boundary, KL edges).
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Infinitesimal Causality
Infinitesimal causality is defined via compatibility of categorical and geometric Frobenius structures in Markov categories, with interventions as tangent vectors deforming copy/discard operations and Lie brackets measuring preservation of information flow.
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Interpreting De Finetti's theorem in the Category of Integrable Cones (long version)
Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.
-
Causal Density Functions
Causal density functions are Radon-Nikodym derivatives serving as local density ratios between do and obs distributions, allowing observational expectations reweighted by the ratio to reproduce interventional ones.
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