MU25012 Information Geometry

Mathematical Institute in Opava
Summer 2017
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives (in Czech)
Tato přednáška podává obecný pohled na statistické modely jako diferencovatelné variety uvnitř prostoru všech rozdělení pravděpodobnosti a vyšetřuje je diferenciálně geometrickými metodami. Získané výsledky jsou potom aplikovány na praktický problém inverze generativních modelů. Ty představují univerzální a zcela soudobý přístup k automatickému učení.
Syllabus
  • 1. Statistics as geometry of states. Fisher metric, Cramer-Rao estimate.
    2. Frequency and Bayesian interpretation of statistics.
    3. f-divergence and entropy.
    4. Generative models and their inversions.
    5. Statistical file learning. Principle of minimum free energy. EM-algorithm.
    6. Dialistic structures on varieties of statistical models.
    7. Laplace approximation.
    8. Hierarchical generative models for statistical data.
    9. Dynamical generative models for statistical data.
Literature
    recommended literature
  • Karl Friston, Jean Daunizeau, James Kilner, and Stefan J. Kiebel. Action and behavior: a free-energy formulation. Biological Cybernetics 102, 227-260, 2010. info
  • Shun-ichi Amari and Hiroshi Nagaoka. Methods of information geometry. AMS Translations of Mathematical Monographs, Oxf, 2007. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2013, Summer 2014, Summer 2015, Summer 2016.
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