Related papers: Examples of Application of Nonparametric Informati…
The dually flat structure of statistical manifolds can be derived in a non-parametric way from a particular case of affine space defined on a qualified set of probability measures. The statistically natural displacement mapping of the…
We construct an infinite-dimensional information manifold based on exponential Orlicz spaces without using the notion of exponential convergence. We then show that convex mixtures of probability densities lie on the same connected component…
We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. This approach has the advantage that statistical mechanics is much better…
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 investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
A generalization of the Pistone-Sempi argument, demonstrating the utility of non-commutative Orlicz spaces, is presented. The question of lifting positive maps defined on von Neumann algebra to maps on corresponding noncommutative Orlicz…
We review the construction of a quantum version of the exponential statistical manifold over the set of all faithful normal positive functionals on a von Neumann algebra. The construction is based on the relative entropy approach to state…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…
We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite…
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…
Using the square-root map p-->\sqrt{p} a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters,…
This paper is concerned with non-parametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random…
Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
This letter presents a non-parametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion…
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fr\'echet means of distributions on metric spaces, such as manifolds and stratified…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…