A geometry on the space of probabilities. I: The finite dimensional case

DOI10.4171/RMI/465zbMath1121.46043MaRDI QIDQ879629

Henryk Gzyl, Lázaro Recht

Publication date: 14 May 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1161871347

zbMATH Keywords

exponential families\(C^*\)-algebramaximum entropy methodreductive homogeneous spacelifting of geodesics

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) General theory of (C^*)-algebras (46L05) Spaces of measures, convergence of measures (28A33) Measures of information, entropy (94A17)

Related Items (3)

A geometry on the space of probabilities. II: Projective spaces and exponential families ⋮ Positive projective space of a \(C^*\)-algebra with a tracial conditional expectation ⋮ Parametric models and information geometry on \(W^\star\)-algebras

Cites Work

• Exponential sets and their geometric motions
• Convex analysis and nonlinear optimization. Theory and examples
• Conditional expectations and operator decompositions
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• The geometry of the space of selfadjoint invertible elements in a \(C^*\)-algebra
• Information Theory and Statistical Mechanics
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