Related papers: Information, learning and falsification
A practical notation can convey valuable intuitions and concisely express new ideas. Information theory is of importance to machine learning, but the notation for information-theoretic quantities is sometimes opaque. We propose a practical…
In the setting where information cannot be verified, we propose a simple yet powerful information theoretical framework---the Mutual Information Paradigm---for information elicitation mechanisms. Our framework pays every agent a measure of…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
"Information Processing" is a recently launched buzzword whose meaning is vague and obscure even for the majority of its users. The reason for this is the lack of a suitable definition for the term "information". In my attempt to amend this…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic…
We introduce the informational power of a quantum measurement as the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We prove the additivity by showing that the informational…
A machine that learns a task from observations must encounter and process uncertainty and novelty, especially when it is to maintain performance when observing new information and to select the hypothesis that best fits the current…
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The…
This paper fills a gap in our understanding of the interaction between information and computation. It unifies other approaches to measuring information like Kolmogorov complexity and Shannon information. We define a theory about…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
We study approximation and integration problems and compare the quality of optimal information with the quality of random information. For some problems random information is almost optimal and for some other problems random information is…
We present a theory for modeling the structure of information and a language (Quanta) expressing the theory. Unlike Shannon's information theory, which focuses on the amount of information in an information system, we focus on the structure…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with…
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory.…