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Partial Information Decomposition
Partial Information Decomposition is an extension of information theory, that aims to generalize the pairwise relations described by information theory to the interaction of multiple variables. Motivation Information theory can quantify the amount of information a single source variable X_1 has about a target variable Y via the mutual information I(X_1;Y). If we now consider a second source variable X_2, classical information theory can only describe the mutual information of the joint variable \ with Y, given by I(X_1,X_2;Y). In general however, it would be interesting to know how exactly the individual variables X_1 and X_2 and their interactions relate to Y. Consider that we are given two source variables X_1, X_2 \in \ and a target variable Y=XOR(X_1,X_2). In this case the total mutual information I(X_1,X_2;Y)=1, while the individual mutual information I(X_1;Y)=I(X_2;Y)=0. That is, there is synergistic information arising from the interaction of X_1,X_2 about Y, which canno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, Neuroscience, neurobiology, physics, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a Fair coin, fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a dice, die (which has six equally likely outcomes). Some other important measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statistical dependence, dependence between the two variables. More specifically, it quantifies the "Information content, amount of information" (in Units of information, units such as shannon (unit), shannons (bits), Nat (unit), nats or Hartley (unit), hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of Entropy (information theory), entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable. Not limited to real-valued random variables and linear dependence like the Pearson correlation coefficient, correlation coefficient, MI is more general and determines how different the joint distribution of the pair (X,Y) is from the product of the marginal distributions of X and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synergistic
Synergy is an interaction or cooperation giving rise to a whole that is greater than the simple sum of its parts (i.e., a non-linear addition of force, energy, or effect). The term ''synergy'' comes from the Attic Greek word συνεργία ' from ', , meaning "working together". Synergy is similar in concept to emergence. History The words ''synergy'' and ''synergetic'' have been used in the field of physiology since at least the middle of the 19th century: SYN'ERGY, ''Synergi'a'', ''Synenergi'a'', (F.) ''Synergie''; from ''συν'', 'with', and ''εργον'', 'work'. A correlation or concourse of action between different organs in health; and, according to some, in disease. :—Dunglison, Roble''Medical Lexicon''Blanchard and Lea, 1853 In 1896, :fr:Henri Mazel, Henri Mazel applied the term "synergy" to social psychology by writing ''La synergie sociale'', in which he argued that Darwinian theory failed to account of "social synergy" or "social love", a collective evolutiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emergence
In philosophy, systems theory, science, and art, emergence occurs when a complex entity has properties or behaviors that its parts do not have on their own, and emerge only when they interact in a wider whole. Emergence plays a central role in theories of integrative levels and of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry and physics. In philosophy, theories that emphasize emergent properties have been called emergentism. In philosophy Philosophers often understand emergence as a claim about the etiology of a system's properties. An emergent property of a system, in this context, is one that is not a property of any component of that system, but is still a feature of the system as a whole. Nicolai Hartmann (1882–1950), one of the first modern philosophers to write on emergence, termed this a ''categorial novum'' (new category). Definitions This concept of emergence dates from at least the time of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statistical dependence, dependence between the two variables. More specifically, it quantifies the "Information content, amount of information" (in Units of information, units such as shannon (unit), shannons (bits), Nat (unit), nats or Hartley (unit), hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of Entropy (information theory), entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable. Not limited to real-valued random variables and linear dependence like the Pearson correlation coefficient, correlation coefficient, MI is more general and determines how different the joint distribution of the pair (X,Y) is from the product of the marginal distributions of X and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Correlation
In probability theory and in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information. It is also known as the ''multivariate constraint'' (Garner 1962) or ''multiinformation'' (Studený & Vejnarová 1999). It quantifies the redundancy or dependency among a set of ''n'' random variables. Definition For a given set of ''n'' random variables \, the total correlation C(X_1,X_2,\ldots,X_n) is defined as the Kullback–Leibler divergence from the joint distribution p(X_1, \ldots, X_n) to the independent distribution of p(X_1)p(X_2)\cdots p(X_n), :C(X_1, X_2, \ldots, X_n) \equiv \operatorname\left p(X_1)p(X_2)\cdots p(X_n)\right\; . This divergence reduces to the simpler difference of entropies, :C(X_1,X_2,\ldots,X_n) = \left sum_^n H(X_i)\right- H(X_1, X_2, \ldots, X_n) where H(X_) is the information entropy of variable X_i \,, and H(X_1,X_2,\ldots,X_n) is the joint entropy of the variable set \. In terms of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Total Correlation
In information theory, dual total correlation, information rate, excess entropy,Nihat Ay, E. Olbrich, N. Bertschinger (2001). A unifying framework for complexity measures of finite systems. European Conference on Complex Systemspdf or binding information is one of several known non-negative generalizations of mutual information. While total correlation is bounded by the sum entropies of the ''n'' elements, the dual total correlation is bounded by the joint-entropy of the ''n'' elements. Although well behaved, dual total correlation has received much less attention than the total correlation. A measure known as "TSE-complexity" defines a continuum between the total correlation and dual total correlation. Definition For a set of ''n'' random variables \, the dual total correlation D(X_1,\ldots, X_n) is given by : D(X_1,\ldots, X_n) = H\left( X_1, \ldots, X_n \right) - \sum_^n H\left( X_i \mid X_1, \ldots, X_, X_, \ldots, X_n \right) , where H(X_,\ldots, X_) is the joint entr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interaction Information
In probability theory and information theory, the interaction information is a generalization of the mutual information for more than two variables. There are many names for interaction information, including ''amount of information'', ''information correlation'', ''co-information'', and simply ''mutual information''. Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, ''beyond'' that which is present in any subset of those variables. Unlike the mutual information, the interaction information can be either positive or negative. These functions, their negativity and minima have a direct interpretation in algebraic topology. Definition The conditional mutual information can be used to inductively define the interaction information for any finite number of variables as follows: :I(X_1;\ldots;X_) = I(X_1;\ldots;X_n) - I(X_1;\ldots;X_n\mid X_), where :I(X_1;\ldots;X_n \mid X_) = \mathbb E_\big(I(X_1;\ldots;X_n) \mid X_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
