Related papers: A Third Information-Theoretic Approach to Finite d…
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
We introduce a relative variant of information loss to characterize the behavior of deterministic input-output systems. We show that the relative loss is closely related to Renyi's information dimension. We provide an upper bound for…
Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We introduce a general framework for de Finetti reduction results, applicable to various notions of partially exchangeable probability distributions. Explicit statements are derived for the cases of exchangeability, Markov exchangeability,…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
We survey known solutions to the infinite extendibility problem for (necessarily exchangeable) probability laws on $\mathbb{R}^d$, which is: Can a given random vector $\vec{X} = (X_1,\ldots,X_d)$ be represented in distribution as the first…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…
At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant fundamental advances in our understanding of the…
Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…
A sequence of random variables is called \textit{exchangeable} if its joint distribution is invariant under permutations of indices. The original formulation of de Finetti's theorem roughly says that any exchangeable sequence of…
The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots,X_K$ are processed separately so as to learn as much information as possible about some ground truth $Y$. We investigate this…
We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the…
Each compact manifold M of finite dimension k is differentiable and supports an intrinsic probability measure. There then exists a measurable transformation of M to the k-dimensional "surface" of the (k+1)-dimensional ball.