Related papers: Information geometry in cosmological inference pro…
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…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is…
A model-independent or non-parametric approach for modeling a database has been widely used in cosmology. In these scenarios, the data has been used directly to reconstruct an underlying function. In this work, we introduce a novel…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…
We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear…
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…
We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on…
Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
We develop a purely mathematical tool to recover some of the information lost in the non-linear collapse of large-scale structure. From a set of 141 simulations of dark matter density fields, we construct a non-linear Weiner filter in order…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
We study the problem of using i.i.d. samples from an unknown multivariate probability distribution $p$ to estimate the mutual information of $p$. This problem has recently received attention in two settings: (1) where $p$ is assumed to be…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
We address the nonGaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that nG of the…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…