Related papers: Sequential Empirical Coordination Under an Output …
We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each…
The problem of multi-hypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal…
We investigate temporal correlations in the simplest measurement scenario, i.e., that of a physical system on which the same measurement is performed at different times, producing a sequence of dichotomic outcomes. The resource for…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
Experimental designs are tools which can dramatically reduce the number of simulations required by time-consuming computer codes. Because we don't know the true relation between the response and inputs, designs should allow one to fit a…
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees…
Using fluorescence spectroscopy we directly measure entropy production of a single two-level system realized experimentally as an optically driven defect center in diamond. We exploit a recent suggestion to define entropy on the level of a…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the…
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…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…
A method of estimating the joint probability mass function of a pair of discrete random variables is described. This estimator is used to construct the conditional Shannon-R\'eyni-Tsallis entropies estimates. From there almost sure rates of…