Related papers: An algebraic framework for information theory: Cla…
Shannon's classical information theory uses probability theory to analyze channels as mechanisms for information flow. In this paper, we generalize results of Martin, Allwein and Moskowitz for binary channels to show how some more modern…
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…
Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles adopted for this scope have been expressed in terms of conditional probability…
What is information, physically, and why does it so reliably emerge in living, cultural, and technological systems? Existing theories quantify uncertainty, cost, or compressibility, but do not identify which physical structures count as…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
In this chapter, concepts related to information and computation are reviewed in the context of human computation. A brief introduction to information theory and different types of computation is given. Two examples of human computation…
Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They…
In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
Recently, several methods have leveraged deep generative modeling to produce example-based explanations of image classifiers. Despite producing visually stunning results, these methods are largely disconnected from classical explainability…
Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of…
Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed…
The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…
The authors discuss information-based complexity theory, which is a model of finite-precision computations with real numbers, and its applications to numerical analysis.