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Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator first proposed by Catoni and Giulini. While…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…
The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones.…
Doubly truncated data arise in many areas such as astronomy, econometrics, and medical studies. For the regression analysis with doubly truncated response variables, the existence of double truncation may bring bias for estimation as well…
Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…
We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic…