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In the view of Jaynes (1957), [20] thermodynamic entropy, as explained by statistical mechanics, should be seen as an application of Shannon's information theory: the thermodynamic entropy is interpreted as being proportional to the amount of further Shannon information needed to define the detailed microscopic state of the system, that remains ...
Mutual information is closely related to the log-likelihood ratio test in the context of contingency tables and the multinomial distribution and to Pearson's χ 2 test: mutual information can be considered a statistic for assessing independence between a pair of variables, and has a well-specified asymptotic distribution.
The Shannon information is closely related to entropy, which is the expected value of the self-information of a random variable, quantifying how surprising the random variable is "on average". This is the average amount of self-information an observer would expect to gain about a random variable when measuring it. [1]
More specifically, it quantifies the "amount of information" (in units such as shannons , nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the ...
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...
moving one input variable, keeping others at their baseline (nominal) values, then, returning the variable to its nominal value, then repeating for each of the other inputs in the same way. Sensitivity may then be measured by monitoring changes in the output, e.g. by partial derivatives or linear regression. This appears a logical approach as ...
The Fisher information is a way of measuring the amount of information that an observable random variable carries about an unknown parameter upon which the probability of depends. Let f ( X ; θ ) {\displaystyle f(X;\theta )} be the probability density function (or probability mass function ) for X {\displaystyle X} conditioned on the value of ...
The expected value of the information gain is the mutual information (;) of and – i.e. the reduction in the entropy of achieved by learning the state of the random variable . In machine learning, this concept can be used to define a preferred sequence of attributes to investigate to most rapidly narrow down the state of X .