Related papers: Differential Entropy on Statistical Spaces

The notion of software entropy is often invoked to describe the tendency of software systems to become increasingly disordered as they evolve, yet existing approaches to quantify it are largely heuristic. In this work we introduce a formal…

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…

Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…

In modern settings of data analysis, we may be running our algorithms on datasets that are sensitive in nature. However, classical machine learning and statistical algorithms were not designed with these risks in mind, and it has been…

Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse…

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium…

We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous state spaces is ubiquitous since its…

Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…

We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different…

Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…

We consider a family of quantum conditional entropies based on the concept of quantum $f$-divergences. First, we explicitly formulate conditions under which the notion of quantum conditional entropy is well defined in this way. In…

Differential privacy is a widely used notion of security that enables the processing of sensitive information. In short, differentially private algorithms map "neighbouring" inputs to close output distributions. Prior work proposed several…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

In this work, we introduce a new approach for statistical quantification of differential privacy in a black box setting. We present estimators and confidence intervals for the optimal privacy parameter of a randomized algorithm $A$, as well…

A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and…

Differential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine learning. In this paradigm one assumes there is a…

It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann…

For statistical inference on an infinite-dimensional Hilbert space $\H $ with no moment conditions we introduce a new class of energy distances on the space of probability measures on $\H$. The proposed distances consist of the integrated…