Related papers: Statistical Geometry and Information Dynamics on H…
Geometry of the rock joint is a governing factor for joint mechanical and hydraulic behavior. A new method of evaluating aperture distribution based on measurement of joint surfaces and three dimensional characteristics of each surface is…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
Curvature influences generalization, robustness, and how reliably neural networks respond to small input perturbations. Existing sharpness metrics are typically defined in parameter space (e.g., Hessian eigenvalues) and can be expensive,…
Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while…
Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M. In this paper, we show that the Frechet manifold D is equipped with a Riemannian metric g^{D} and an…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…
We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature…
Information distances like the Hellinger distance and the Jensen-Shannon divergence have deep roots in information theory and machine learning. They are used extensively in data analysis especially when the objects being compared are high…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the…
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability…