Related papers: On the robustness of q-expectation values and Reny…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
We show that the new quantum extension of Renyi's \alpha-relative entropies, introduced recently by Muller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, Commun. Math. Phys. 331,…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, (i) the sensitivity to initial…
This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…
The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…
Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.
Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective…
Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the…
A random vector ${\bf X}$ is weakly stable iff for all $a,b \in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X} + b {\bf X}' \stackrel{d}{=} {\bf X} \Theta$, where $X'$ is an independent copy of $X$ and $\Theta$ is…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
The Tukey-$\lambda$ distribution has interesting properties including (i) for some parameters values it has finite support, and for others infinite support, and (ii) it can mimic several other distributions such that parameter estimation…
Consider a measure-preserving transition kernel $T$ on an arbitrary probability space $(\mathbb X,\mathcal cA,\pi)$. In this level of generality, we prove that a one-step hyper-contractivity estimate of the form $\|T\|_{p\to q}\le 1$ with…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
Escort distributions have been shown to be very useful in a great variety of fields ranging from information theory, nonextensive statistical mechanics till coding theory, chaos and multifractals. In this work we give the notion and the…
We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty$, where $(q_n)_{n=1}^\infty$ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set…
The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches…
Distributional assumptions have been shown to be necessary for the robust learnability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019). In this paper, we study…