相关论文: Information Geometry of Random Matrix Models
We examine the sensitiveness of the free-energy landscape of a directed polymer in random media with respect to various kinds of infinitesimally weak perturbation including the intriguing case of temperature-chaos. To this end, we combine…
Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a…
Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested…
The Fisher-Rao (FR) information matrix is a central object in multiparameter quantum estimation theory. The geometry of a quantum state can be envisaged through the Riemannian manifold generated by the FR-metric corresponding to the quantum…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity". Specifically, we consider $m\times n$ random matrices…
Information geometry is an important tool to study statistical models. There are some important examples in statistical models which are regarded as warped products. In this paper, we study information geometry of warped products. We…
We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to…
For a fissured medium, we analyze the impact that the geometry of the cracks, has in the phenomenon of preferential fluid flow. Using finite volume meshes we analyze the mechanical energy dissipation due to gravity, curvature of the surface…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on…
In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
In location estimation, we are given $n$ samples from a known distribution $f$ shifted by an unknown translation $\lambda$, and want to estimate $\lambda$ as precisely as possible. Asymptotically, the maximum likelihood estimate achieves…
We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random lattices as well as the famous meander problem of enumerating…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure with information geometry on the manifold of generalized…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…