Αποτελέσματα Αναζήτησης
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons, nats, or hartleys.
In this lecture we will discuss a few additional generalized entropy measures, namely the min-relative entropy, the conditional max-entropy, and the hypothesis-testing relative entropy. We will discuss various properties of these quantities, and relate them to the other entropic quantities we have previously discussed.
• Maximum entropy: We do not have a bound for general p.d.f functions f(x), but we do have a formula for power-limited functions. Consider a R.V. X ∼ f(x), such that E[x 2] = Z x f(x)dx ≤ P, (22) then maxh(X) = 1 2 log(2πeP), (23) and the maximum is achieved by X ∼ N(0,P).
In this lecture we will first define the max-relative entropy and observe some of its properties. We will then define the conditional min-entropy in terms of the quantum max-relative entropy, derive an alternative characterization of this quantity, and consider the conditional min-entropy of a few example classes of states.
Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy (discrimination, Kullback-Leibler information), along with the limiting normalized versions of these quantities
If \((X, Y) \sim p(x, y)\), the conditional entropy \(H(Y \mid X)\) is defined as \[\begin{split}H(Y \mid X) & = \sum_{x \in \mathcal{X}} p(x) H(Y \mid X = x) \\ & = - \sum_{x \in \mathcal{X}} p(x) \sum_{y \in \mathcal{Y}} p(y \mid x) \log p(y \mid x) \\ & = - \sum_{x \in \mathcal{X}}\sum_{y \in \mathcal{Y}} p(x, y) \log p(y \mid x) \\ & = - E ...
Conditional entropy refers to the uncertainty about a variable Y when another variable X is known. It can also be understood as the expected number of bits required to describe Y when both the encoder and decoder have knowledge of X. AI generated definition based on: Encyclopedia of Physical Science and Technology (Third Edition), 2003.
