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Entropy (information theory), the Glossary

Index Entropy (information theory)

In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes.[1]

Table of Contents

  1. 165 relations: A Mathematical Theory of Communication, Absolute continuity, Approximate entropy, Arithmetic coding, Axiom, Base (exponentiation), Bayesian inference, Bell Labs Technical Journal, Bernoulli process, Binary logarithm, Bit, Boltzmann constant, Boltzmann's entropy formula, Broadcasting, Byte, Characterization (mathematics), Checksum, Claude Shannon, Combinatorics, Common logarithm, Communication channel, Computer program, Concave function, Conditional entropy, Conditional probability, Continuous function, Convex conjugate, Counting measure, Cross-entropy, Cryptanalysis, Data communication, Data compression, David Ellerman, David J. C. MacKay, Decision tree learning, Density matrix, Differential entropy, Differential equation, Diversity index, Dominance (ecology), Duality (mathematics), Dynamical system, E (mathematical constant), Edwin Thompson Jaynes, Entropy, Entropy (statistical thermodynamics), Entropy as an arrow of time, Entropy coding, Entropy estimation, Entropy power inequality, ... Expand index (115 more) »

  2. Entropy and information
  3. Statistical randomness

A Mathematical Theory of Communication

"A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in Bell System Technical Journal in 1948. Entropy (information theory) and a Mathematical Theory of Communication are information theory.

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Absolute continuity

In calculus and real analysis, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.

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Approximate entropy

In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data. Entropy (information theory) and approximate entropy are entropy and information.

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Arithmetic coding

Arithmetic coding (AC) is a form of entropy encoding used in lossless data compression. Entropy (information theory) and Arithmetic coding are data compression.

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Axiom

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

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Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

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Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

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Bell Labs Technical Journal

The Bell Labs Technical Journal was the in-house scientific journal for scientists of Nokia Bell Labs, published yearly by the IEEE society.

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Bernoulli process

In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1.

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Binary logarithm

In mathematics, the binary logarithm is the power to which the number must be raised to obtain the value.

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Bit

The bit is the most basic unit of information in computing and digital communication.

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Boltzmann constant

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas.

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Boltzmann's entropy formula

In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy S, also written as S_\mathrm, of an ideal gas to the multiplicity (commonly denoted as \Omega or W), the number of real microstates corresponding to the gas's macrostate: where k_\mathrm B is the Boltzmann constant (also written as simply k) and equal to 1.380649 × 10−23 J/K, and \ln is the natural logarithm function (or log base e, as in the image above).

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Broadcasting

Broadcasting is the distribution of audio or video content to a dispersed audience via any electronic mass communications medium, but typically one using the electromagnetic spectrum (radio waves), in a one-to-many model.

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Byte

The byte is a unit of digital information that most commonly consists of eight bits.

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Characterization (mathematics)

In mathematics, a characterization of an object is a set of conditions that, while different from the definition of the object, is logically equivalent to it.

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Checksum

A checksum is a small-sized block of data derived from another block of digital data for the purpose of detecting errors that may have been introduced during its transmission or storage.

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Claude Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist and cryptographer known as the "father of information theory" and as the "father of the Information Age". Entropy (information theory) and Claude Shannon are information theory.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with the counting, selecting and arranging of objects, both as a means and as an end in itself.

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Common logarithm

In mathematics, the common logarithm is the logarithm with base 10.

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Communication channel

A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. Entropy (information theory) and communication channel are information theory.

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Computer program

A computer program is a sequence or set of instructions in a programming language for a computer to execute.

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Concave function

In mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints.

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Conditional entropy

In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known. Entropy (information theory) and conditional entropy are entropy and information and information theory.

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Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred.

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Continuous function

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.

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Convex conjugate

In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions.

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Counting measure

In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity \infty if the subset is infinite.

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Cross-entropy

In information theory, the cross-entropy between two probability distributions p and q, over the same underlying set of events, measures the average number of bits needed to identify an event drawn from the set when the coding scheme used for the set is optimized for an estimated probability distribution q, rather than the true distribution p. Entropy (information theory) and cross-entropy are entropy and information.

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Cryptanalysis

Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems.

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Data communication

Data communication, including data transmission and data reception, is the transfer of data, transmitted and received over a point-to-point or point-to-multipoint communication channel.

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Data compression

In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Entropy (information theory) and data compression are information theory.

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David Ellerman

David Patterson Ellerman (born 14 March 1943) is a philosopher and author who works in the fields of economics and political economy, social theory and philosophy, quantum mechanics, and in mathematics.

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David J. C. MacKay

Sir David John Cameron MacKay (22 April 1967 – 14 April 2016) was a British physicist, mathematician, and academic.

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Decision tree learning

Decision tree learning is a supervised learning approach used in statistics, data mining and machine learning.

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Density matrix

In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble of physical systems as quantum states (even if the ensemble contains only one system).

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Differential entropy

Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy (a measure of average surprisal) of a random variable, to continuous probability distributions. Entropy (information theory) and Differential entropy are entropy and information, information theory and statistical randomness.

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Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

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Diversity index

A diversity index is a method of measuring how many different types (e.g. species) there are in a dataset (e.g. a community).

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Dominance (ecology)

Ecological dominance is the degree to which one or several species have a major influence controlling the other species in their ecological community (because of their large size, population, productivity, or related factors) or make up more of the biomass.

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Duality (mathematics)

In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is, then the dual of is.

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Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.

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E (mathematical constant)

The number is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways.

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Edwin Thompson Jaynes

Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis.

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Entropy

Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty.

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Entropy (statistical thermodynamics)

The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible.

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Entropy as an arrow of time

Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time.

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Entropy coding

In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have an expected code length greater than or equal to the entropy of the source. Entropy (information theory) and entropy coding are data compression and entropy and information.

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Entropy estimation

In various science/engineering applications, such as independent component analysis, image analysis, genetic analysis, speech recognition, manifold learning, and time delay estimation it is useful to estimate the differential entropy of a system or process, given some observations. Entropy (information theory) and entropy estimation are entropy and information, information theory and statistical randomness.

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Entropy power inequality

In information theory, the entropy power inequality (EPI) is a result that relates to so-called "entropy power" of random variables. Entropy (information theory) and entropy power inequality are information theory.

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Entropy rate

In the mathematical theory of probability, the entropy rate or source information rate is a function assigning an entropy to a stochastic process. Entropy (information theory) and entropy rate are information theory.

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Equiprobability

Equiprobability is a property for a collection of events that each have the same probability of occurring.

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Eta

Eta (uppercase, lowercase; ἦτα ē̂ta or ήτα ita) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel,.

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Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

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Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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Family of sets

In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class.

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Fisher information

In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. Entropy (information theory) and Fisher information are information theory.

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Graph entropy

In information theory, the graph entropy is a measure of the information rate achievable by communicating symbols over a channel in which certain pairs of values may be confused. Entropy (information theory) and graph entropy are information theory.

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H-theorem

In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity H (defined below) in a nearly-ideal gas of molecules.

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Hamming distance

In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different.

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Hartley (unit)

The hartley (symbol Hart), also called a ban, or a dit (short for "decimal digit"), is a logarithmic unit that measures information or entropy, based on base 10 logarithms and powers of 10.

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Hartley function

The Hartley function is a measure of uncertainty, introduced by Ralph Hartley in 1928. Entropy (information theory) and Hartley function are information theory.

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Histogram

A histogram is a visual representation of the distribution of quantitative data.

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History of entropy

The concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work.

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History of information theory

The decisive event which established the discipline of information theory, and brought it to immediate worldwide attention, was the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948. Entropy (information theory) and History of information theory are information theory.

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Huffman coding

In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. Entropy (information theory) and Huffman coding are data compression.

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Independence (probability theory)

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

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Information content

In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable. Entropy (information theory) and information content are entropy and information and information theory.

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Information dimension

In information theory, information dimension is an information measure for random vectors in Euclidean space, based on the normalized entropy of finely quantized versions of the random vectors. Entropy (information theory) and information dimension are information theory.

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Information fluctuation complexity

Information fluctuation complexity is an information-theoretic quantity defined as the fluctuation of information about entropy. Entropy (information theory) and information fluctuation complexity are complex systems theory, entropy and information, information theory and statistical randomness.

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Information gain (decision tree)

In information theory and machine learning, information gain is a synonym for Kullback–Leibler divergence; the amount of information gained about a random variable or signal from observing another random variable.

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Information geometry

Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. Entropy (information theory) and Information geometry are information theory.

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Information theory

Information theory is the mathematical study of the quantification, storage, and communication of information. Entropy (information theory) and information theory are data compression.

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ISBN

The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique.

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Σ-algebra

In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections.

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János Aczél (mathematician)

János Dezső Aczél (26 December 1924 – 1 January 2020), also known as John Aczel, was a Hungarian-Canadian mathematician, who specialized in functional equations and information theory.

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John von Neumann

John von Neumann (Neumann János Lajos; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist, engineer and polymath.

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Joint entropy

In information theory, joint entropy is a measure of the uncertainty associated with a set of variables. Entropy (information theory) and joint entropy are entropy and information.

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Josiah Willard Gibbs

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics.

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Joy A. Thomas

Joy Aloysius Thomas (1 January 1963 – 28 September 2020) was an Indian-born American information theorist, author and a senior data scientist at Google.

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Kolmogorov complexity

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. Entropy (information theory) and Kolmogorov complexity are data compression and information theory.

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Kullback–Leibler divergence

In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution is different from a second, reference probability distribution. Entropy (information theory) and Kullback–Leibler divergence are entropy and information.

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Landauer's principle

Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. Entropy (information theory) and Landauer's principle are entropy and information.

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Lebesgue measure

In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher dimensional Euclidean ''n''-spaces.

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Lempel–Ziv–Welch

Lempel–Ziv–Welch (LZW) is a universal lossless data compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. Entropy (information theory) and Lempel–Ziv–Welch are data compression.

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Level of measurement

Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables.

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Levenshtein distance

In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences.

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Limit of a function

Although the function is not defined at zero, as becomes closer and closer to zero, becomes arbitrarily close to 1.

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Limiting density of discrete points

In information theory, the limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy. Entropy (information theory) and limiting density of discrete points are information theory.

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Liouville function

The Liouville lambda function, denoted by and named after Joseph Liouville, is an important arithmetic function.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables.

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LogSumExp

The LogSumExp (LSE) (also called RealSoftMax or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms.

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Loomis–Whitney inequality

In mathematics, the Loomis–Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the "size" of a d-dimensional set by the sizes of its (d-1)-dimensional projections.

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Lossless compression

Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Entropy (information theory) and Lossless compression are data compression.

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Ludwig Boltzmann

Ludwig Eduard Boltzmann (20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher.

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Machine learning

Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data and thus perform tasks without explicit instructions.

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Markov information source

In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.

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Markov model

In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems.

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Maximum entropy thermodynamics

In physics, maximum entropy thermodynamics (colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes. Entropy (information theory) and maximum entropy thermodynamics are information theory.

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Maxwell's demon

Maxwell's demon is a thought experiment that appears to disprove the second law of thermodynamics.

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Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.

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Measure-preserving dynamical system

In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Entropy (information theory) and measure-preserving dynamical system are entropy and information and information theory.

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Microstate (statistical mechanics)

In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual particles or components that make up the system.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Mutual information

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. Entropy (information theory) and mutual information are entropy and information and information theory.

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Nat (unit)

The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information or information entropy, based on natural logarithms and powers of ''e'', rather than the powers of 2 and base 2 logarithms, which define the shannon.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to.

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Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.

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Negentropy

In information theory and statistics, negentropy is used as a measure of distance to normality. Entropy (information theory) and negentropy are entropy and information.

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Neural network (machine learning)

In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a model inspired by the structure and function of biological neural networks in animal brains.

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Noisy-channel coding theorem

In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel. Entropy (information theory) and noisy-channel coding theorem are information theory.

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One-time pad

In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is larger than or equal to the size of the message being sent.

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Partition of a set

In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.

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Permutation

In mathematics, a permutation of a set can mean one of two different things.

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Perplexity

In information theory, perplexity is a measure of uncertainty in the value of a sample from a discrete probability distribution. Entropy (information theory) and perplexity are entropy and information.

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Pigeonhole principle

In mathematics, the pigeonhole principle states that if items are put into containers, with, then at least one container must contain more than one item.

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Prediction by partial matching

Prediction by partial matching (PPM) is an adaptive statistical data compression technique based on context modeling and prediction. Entropy (information theory) and prediction by partial matching are data compression.

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Principle of maximum entropy

The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information). Entropy (information theory) and principle of maximum entropy are entropy and information.

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Prior probability

A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account.

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Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

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Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.

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Probability space

In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment".

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P.

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Proportionality (mathematics)

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.

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Qualitative variation

An index of qualitative variation (IQV) is a measure of statistical dispersion in nominal distributions.

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Quantities of information

The mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information. Entropy (information theory) and quantities of information are information theory.

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Quantum mechanics

Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.

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Quantum relative entropy

In quantum information theory, quantum relative entropy is a measure of distinguishability between two quantum states.

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Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. Entropy (information theory) and random variable are statistical randomness.

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Randomness

In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. Entropy (information theory) and randomness are statistical randomness.

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Rényi entropy

In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. Entropy (information theory) and Rényi entropy are entropy and information and information theory.

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Redundancy (information theory)

In information theory, redundancy measures the fractional difference between the entropy of an ensemble, and its maximum possible value \log(|\mathcal_X|). Entropy (information theory) and redundancy (information theory) are data compression and information theory.

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Rolf Landauer

Rolf William Landauer (February 4, 1927 – April 27, 1999) was a German-American physicist who made important contributions in diverse areas of the thermodynamics of information processing, condensed matter physics, and the conductivity of disordered media.

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Rosetta Code

Rosetta Code is a wiki-based programming chrestomathy website with implementations of common algorithms and solutions to various programming problems in many different programming languages.

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Sample entropy

Sample entropy (SampEn) is a modification of approximate entropy (ApEn), used for assessing the complexity of physiological time-series signals, diagnosing diseased states.

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Science (journal)

Science, also widely referred to as Science Magazine, is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals.

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Second law of thermodynamics

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions.

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Shannon (unit)

The shannon (symbol: Sh) is a unit of information named after Claude Shannon, the founder of information theory.

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Shannon's source coding theorem

In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy. Entropy (information theory) and Shannon's source coding theorem are data compression and information theory.

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Shearer's inequality

Shearer's inequality or also Shearer's lemma, in mathematics, is an inequality in information theory relating the entropy of a set of variables to the entropies of a collection of subsets. Entropy (information theory) and Shearer's inequality are information theory.

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Sign sequence

In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1.

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Signal processing

Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements.

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Species evenness

Species evenness describes the commonness or rarity of a species; it requires knowing the abundance of each species relative to those of the other species within the community.

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Species richness

Species richness is the number of different species represented in an ecological community, landscape or region.

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Stationary process

In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.

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Statistical classification

When classification is performed by a computer, statistical methods are normally used to develop the algorithm.

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Statistical dispersion

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

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Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities.

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Stochastic process

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time.

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Telecommunications

Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information with an immediacy comparable to face-to-face communication.

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Terence Tao

Terence Chi-Shen Tao (born 17 July 1975) is an Australian and American mathematician who is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences.

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Ternary numeral system

A ternary numeral system (also called base 3 or trinary) has three as its base.

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Theil index

The Theil index is a statistic primarily used to measure economic inequality and other economic phenomena, though it has also been used to measure racial segregation. Entropy (information theory) and Theil index are information theory.

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Thermodynamic system

A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics.

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Thomas M. Cover

Thomas M. Cover (August 7, 1938 – March 26, 2012) was an American information theorist and professor jointly in the Departments of Electrical Engineering and Statistics at Stanford University.

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Trace (linear algebra)

In linear algebra, the trace of a square matrix, denoted, is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of.

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Transposed letter effect

In psychology, the transposed letter effect is a test of how a word is processed when two letters within the word are switched.

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Turing machine

A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules.

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Typical set

In information theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution. Entropy (information theory) and typical set are information theory.

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Uncertainty principle

The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics.

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Units of information

In digital computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. Entropy (information theory) and units of information are information theory.

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Von Neumann entropy

In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics.

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Warren Weaver

Warren Weaver (July 17, 1894 – November 24, 1978) was an American scientist, mathematician, and science administrator.

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YouTube

YouTube is an American online video sharing platform owned by Google.

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See also

Entropy and information

Statistical randomness

References

[1] https://en.wikipedia.org/wiki/Entropy_(information_theory)

Also known as Average information, Data compression/entropy, Data entropy, Entropy (information), Entropy (statistics), Entropy function, Entropy of a probability distribution, Information Entropy, Information Theoretic Entropy, Informational entropy, Infotropy, Shannon Entropy, Shannon information entropy, Shannon's entropy, Weighted entropy.

, Entropy rate, Equiprobability, Eta, Event (probability theory), Expected value, Family of sets, Fisher information, Graph entropy, H-theorem, Hamming distance, Hartley (unit), Hartley function, Histogram, History of entropy, History of information theory, Huffman coding, Independence (probability theory), Information content, Information dimension, Information fluctuation complexity, Information gain (decision tree), Information geometry, Information theory, ISBN, Σ-algebra, János Aczél (mathematician), John von Neumann, Joint entropy, Josiah Willard Gibbs, Joy A. Thomas, Kolmogorov complexity, Kullback–Leibler divergence, Landauer's principle, Lebesgue measure, Lempel–Ziv–Welch, Level of measurement, Levenshtein distance, Limit of a function, Limiting density of discrete points, Liouville function, Logarithm, Logistic regression, LogSumExp, Loomis–Whitney inequality, Lossless compression, Ludwig Boltzmann, Machine learning, Markov information source, Markov model, Maximum entropy thermodynamics, Maxwell's demon, Measure (mathematics), Measure-preserving dynamical system, Microstate (statistical mechanics), Monotonic function, Mutual information, Nat (unit), Natural logarithm, Natural number, Negentropy, Neural network (machine learning), Noisy-channel coding theorem, One-time pad, Partition of a set, Permutation, Perplexity, Pigeonhole principle, Prediction by partial matching, Principle of maximum entropy, Prior probability, Probability density function, Probability distribution, Probability space, Projection (linear algebra), Proportionality (mathematics), Qualitative variation, Quantities of information, Quantum mechanics, Quantum relative entropy, Random variable, Randomness, Rényi entropy, Redundancy (information theory), Rolf Landauer, Rosetta Code, Sample entropy, Science (journal), Second law of thermodynamics, Shannon (unit), Shannon's source coding theorem, Shearer's inequality, Sign sequence, Signal processing, Species evenness, Species richness, Stationary process, Statistical classification, Statistical dispersion, Statistical mechanics, Stochastic process, Telecommunications, Terence Tao, Ternary numeral system, Theil index, Thermodynamic system, Thomas M. Cover, Trace (linear algebra), Transposed letter effect, Turing machine, Typical set, Uncertainty principle, Units of information, Von Neumann entropy, Warren Weaver, YouTube.