Information geometry

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  1. One useful aspect of information geometry is that it gives a means to prove results about statistical models, simply by considering them as well-behaved geometrical objects.[1]
  2. Coverage includes original work and synthesis exploring the foundation and application of information geometry in both mathematical and computational aspects.[2]
  3. To this extent, I recently stumbled across information geometry.[3]
  4. Remarkably however, as we shall see, the statistical manifolds of information geometry turn out to have a uniquely appropriate metric.[4]
  5. We have now covered enough basic concepts of differential geometry to begin to discuss information geometry.[4]
  6. Abstract We begin a global study of information geometry.[5]
  7. We illustrate the result by working out the details of the information geometry of a physically relevant two-level system.[6]
  8. In brief, any (weakly mixing) random dynamical system that possesses a Markov blanket—i.e. a separation of internal and external states—is equipped with an information geometry.[7]
  9. The conditional dependencies this implies equip the internal states of the system with an information geometry for a space of (Bayesian) beliefs about the external states.[7]
  10. Consequently, the internal state-space has an inherent information geometry (technically, this space is a statistical manifold).[7]
  11. Equation (2.3) implies an information geometry that links the statistics of the two, in virtue of the boundary that separates them.[7]
  12. We propose a unified framework for quantifying any combination of causal relationships between elements in a hierarchical manner based on information geometry.[8]
  13. To resolve these difficulties, we propose a theoretical framework based on information geometry for the quantification of multiple causal influences with a holistic approach.[8]
  14. To overcome these problems, we propose a unified framework for quantifying causal influences based on information geometry (22).[8]
  15. In this paper, we proposed a unified framework based on information geometry, which enables us to quantify multiple influences without overestimation and confounds of noncausal influences.[8]
  16. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions.[9]
  17. One very nice thing about information geometry is that it gives us very strong tools for proving results about statistical models, simply by considering them as well-behaved geometrical objects.[10]
  18. Since differential geometry lets me do coordinate-free physics, information geometry seems like an appealing way to do this.[10]
  19. Here, the information geometry is studied for a number of solvable statistical–mechanical models.[11]
  20. It reached maturity through the work of Shun'ichi Amari in the 1980s, with what is currently the canonical reference book: Methods of information geometry.[12]
  21. This journal will publish original work in the emerging interdisciplinary field of information geometry, with both a theoretical and computational emphasis.[13]
  22. Information geometry connects various branches of mathematical science in dealing with uncertainty and information based on unifying geometric concepts.[13]
  23. The purpose of this international conference is to exchange recent developments in information geometry and to establish its theoretical foundations in related fields.[14]
  24. I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models.[15]
  25. Abstract: Using ideas from information geometry we seek to develop a quantitative measure of complexity.[16]
  26. The journal will publish papers on such research along with those on application of information geometry, broadly construed, emphasizing both theoretical and computational aspects.[17]
  27. This is the first comprehensive book on information geometry, written by the founder of the field.[18]
  28. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry.[18]
  29. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III.[18]
  30. Information geometry has emerged from studies of invariant geometrical structure involved in statistical inference.[19]

소스

  1. ↑ information geometry in nLab
  2. ↑ Information Geometry
  3. ↑ Applications of information geometry to the natural sciences
  4. ↑ 이동: 4.0 4.1 A gentle introduction to information geometry
  5. ↑ Information geometry in a global setting
  6. ↑ Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics
  7. ↑ 이동: 7.0 7.1 7.2 7.3 Markov blankets, information geometry and stochastic thermodynamics
  8. ↑ 이동: 8.0 8.1 8.2 8.3 Unified framework for information integration based on information geometry
  9. ↑ An Information Geometry of Statistical Manifold Learning
  10. ↑ 이동: 10.0 10.1 Information Geometry
  11. ↑ Information geometry and phase transitions
  12. ↑ Information geometry
  13. ↑ 이동: 13.0 13.1 Information Geometry
  14. ↑ AIG2020
  15. ↑ Information Geometry of Mean-Field Approximation
  16. ↑ Information Geometry Webinars
  17. ↑ SPRINGER launches the Journal "Information Geometry"
  18. ↑ 이동: 18.0 18.1 18.2 Information Geometry and Its Applications
  19. ↑ 2016 PKU Mini-Course: Information Geometry

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  • [{'LOWER': 'information'}, {'LEMMA': 'geometry'}]
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