![]() Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. The necessary conditional entropy CPC10 quantifies the amount of information that a random variable X X necessarily must carry above and beyond the mutual. In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy. condentropy takes two random vectors, X and Y, as input and returns the conditional entropy, H(XY), in nats (base e), according to the entropy estimator. Conversely, H( Y | X) = H( Y) if and only if Y and X are independent random variables. H( Y | X) = 0 if and only if the value of Y is completely determined by the value of X. If we learn the value of X, we have gained H( X) bits of information, and the system has H( Y | X) bits remaining of uncertainty. De nition 8.2 (Conditional entropy) The conditional entropy of a random variable is the entropy of one random variable conditioned on knowledge of another random variable, on average. In the discrete case (or bounded support) why the distribution maximising the entropy is uniform while it is the gaussian in the class of. There are a few ways to measure entropy for multiple variables we’ll use two, Xand Y. Theorem: Let X1, X2,Xn be random variables having the mass probability p(. Analytic expression for continuous-variable mutual information of uniform distributions. The entropy of a collection of random variables is the sum of conditional entropies. Multivariate discrete conditional entropy calculation. Intuitively, the combined system contains H( X, Y) bits of information: we need H( X, Y) bits of information to reconstruct its exact state. Conditional Entropy on a quantized random variable. Given discrete random variable X with support and Y with support, the conditional entropy of Y given X is defined as:įrom this definition and Bayes' theorem, the chain rule for conditional entropy is In Section 5 we define the conditional topological entropy of a quotient map and work out some natural results. Conditional entropy H (mif) defines the expected amount of information the set m carries with respect to feature f and movement mi. ![]()
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