相关论文: A categorical characterization of relative entropy…

We construct a 2-categorical extension of the relative entropy functor of Baez and Fritz, and show that our construction is functorial with respect to vertical morphisms. Moreover, we show such a `2-relative entropy' satisfies natural…

A Bayesian functorial characterization of the classical relative entropy (KL divergence) of finite probabilities was recently obtained by Baez and Fritz. This was then generalized to standard Borel spaces by Gagn\'e and Panangaden. Here, we…

We give a new characterization of relative entropy, also known as the Kullback-Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a…

We propose an intersubjective epistemic approach to foundations of probability theory and statistical inference, based on relative entropy and category theory, and aimed to bypass the mathematical and conceptual problems of existing…

We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike…

We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…

Using convex Grothendieck fibrations, we characterize the von Neumann entropy as a functor from finite-dimensional non-commutative probability spaces and state-preserving *-homomorphisms to real numbers. Our axioms reproduce those of Baez,…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness.…

We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…

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…

The basic concepts of category theory are developed and examples of them are presented to illustrate them using measurement theory and probability theory tools. Motivated by Perrone's workarXiv:1912.10642 where notes on category theory are…

It is well-known that a random variable, i.e., a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an…

We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…

We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…

We introduce a new class of (not necessarily convex) bodies and show, among other things, that these bodies provide yet another link between convex geometric analysis and information theory. Namely, they give geometric interpretations of…

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…

Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…