The conditional entropy is an entropy measure used in information theory. The conditional entropy measures how much entropy a random variableY has remaining if we have already learned completely the value of a second random variable X. It is referred to as the entropy of Y conditional on X, and is written H(Y | X). Like other entropies, the conditional entropy is measured in bits. Entropy of a Bernoulli trial as a function of success probability. ... Information theory is a branch of the mathematical theory of probability and mathematical statistics that quantifies the concept of information. ... Entropy of a Bernoulli trial as a function of success probability. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ... A bit (abbreviated b) is the most basic information unit used in computing and information theory. ...
Given random variables X and Y with entropies H(X) and H(Y), and with a joint entropyH(X,Y), the conditional entropy of Y given X is defined as . Intuitively, the combined system contains H(X,Y) bits of information. If we learn the value of X, we have gained H(X) bits of information, and the system has H(Y | X) bits remaining. The joint entropy is an entropy measure used in information theory. ...
H(Y | X) = 0 if and only if the value of Y is completely determined by the value of X. Conversely, H(Y | X) = H(Y) if and only if Y and X are independent random variables. In probability theory, to say that two events are independent intuitively means that knowing whether or not one of them occurs makes it neither more probable nor less probable that the other occurs. ...
In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy. Quantum information science is a field of research at the interface of quantum mechanics and computer science. ... The conditional quantum entropy is an entropy measure used in quantum information theory. ...
The specific conditionalentropy formula computes the amount of uncertainty remaining after performing conditioning on one value of the signal distribution, whereas the conditionalentropy is the amount of uncertainty remaining after summing the products of specific signal probabilities and specific conditionalentropies.
The specific conditionalentropy column can be useful to examine in some detail, because low values are telling you that there is an uncertainty-reducing relationship between levels of your variables.
The specific entropy value in the fifth column is then multiplied by the corresponding probability in the second column to obtain the values in the sixth column.
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