Information geometry

노트

말뭉치

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.
2. Coverage includes original work and synthesis exploring the foundation and application of information geometry in both mathematical and computational aspects.
3. To this extent, I recently stumbled across information geometry.
4. Remarkably however, as we shall see, the statistical manifolds of information geometry turn out to have a uniquely appropriate metric.
5. We have now covered enough basic concepts of differential geometry to begin to discuss information geometry.
6. Abstract We begin a global study of information geometry.
7. We illustrate the result by working out the details of the information geometry of a physically relevant two-level system.
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.
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.
10. Consequently, the internal state-space has an inherent information geometry (technically, this space is a statistical manifold).
11. Equation (2.3) implies an information geometry that links the statistics of the two, in virtue of the boundary that separates them.
12. We propose a unified framework for quantifying any combination of causal relationships between elements in a hierarchical manner based on information geometry.
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.
14. To overcome these problems, we propose a unified framework for quantifying causal influences based on information geometry (22).
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.
16. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions.
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.
18. Since differential geometry lets me do coordinate-free physics, information geometry seems like an appealing way to do this.
19. Here, the information geometry is studied for a number of solvable statistical–mechanical models.
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.
21. This journal will publish original work in the emerging interdisciplinary field of information geometry, with both a theoretical and computational emphasis.
22. Information geometry connects various branches of mathematical science in dealing with uncertainty and information based on unifying geometric concepts.
23. The purpose of this international conference is to exchange recent developments in information geometry and to establish its theoretical foundations in related fields.
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.
25. Abstract: Using ideas from information geometry we seek to develop a quantitative measure of complexity.
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.
27. This is the first comprehensive book on information geometry, written by the founder of the field.
28. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry.
29. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III.
30. Information geometry has emerged from studies of invariant geometrical structure involved in statistical inference.