Related papers: Information geometry in cosmological inference pro…
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…
A family of probability distributions parametrized by an open domain $\Lambda$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
Modern radio and multi-instrument astrophysical datasets are increasingly assembled from surveys with different sensitivities and selection effects. In such heterogeneous datasets, published measurement uncertainties are often incomplete,…
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach…
Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces…
Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework…
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,…
Results by van der Vaart (1991) from semi-parametric statistics about the existence of a non-zero Fisher information are reviewed in an infinite-dimensional non-linear Gaussian regression setting. Information-theoretically optimal inference…
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
In this brief paper we revisit the Fisher information content of cosmological power spectra or two-point functions of Gaussian fields in order to comment on the assumption of Gaussian estimators and the use of parameter-dependent covariance…
We derive bounds for the Orlicz norm of the deviation of a random variable defined on $\mathbb{R}^n$ from its Gaussian mean value. The random variables are assumed to be smooth and the bound itself depends on the Orlicz norm of the…
We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…