Related papers: Information Theory for Expectation Measures
We study trade-off relations in information extraction from quantum systems subject to null-result weak measurements, where the absence of a detected photon continuously updates the system state. We present a detailed analysis of qubit and…
Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open…
In communications, unknown variables are usually modelled as random variables, and concepts such as independence, entropy and information are defined in terms of the underlying probability distributions. In contrast, control theory often…
Turbulence theory is usually concerned with the statistical moments of the velocity or its fluctuations. One could also analyze the implicit probability distributions. This is the purview of information theory. Here we use information…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…
Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational power. In this chapter, we provide an introduction to these…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that characterize various operational tasks and are used to…
Feature selection is a key step when dealing with high dimensional data. In particular, these techniques simplify the process of knowledge discovery from the data by selecting the most relevant features out of the noisy, redundant and…
Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…
Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
Information based thermodynamic logic is revisited. It consists of two parts: Part A applies the modern theory of probability in which an arbitrary convex function \phi is employed as an analytic "device" to express information as…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…