Related papers: Extension of Information Geometry to Non-statistic…
Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states.…
Graph states are the backbone of measurement-based continuous-variable quantum computation. However, experimental realisations of these states induce Gaussian measurement statistics for the field quadratures, which poses a barrier to obtain…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
Non-equilibrium conditions give rise to classes of universally evolving configurations of quantum-many body systems at non-thermal fixed points. While the fixed point and thus full scaling in space and time is generically reached at very…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
This is a study of the information evolution of complex systems by geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
We study the thermodynamic properties of solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation. First we study the nonextensive grand canonical distribution function and the…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their…
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…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
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…