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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 expected “amount of information” held in a random variable. Mutual Information is also known as information gain.
What is mutual information formula?
Mutual information is calculated between two variables and measures the reduction in uncertainty for one variable given a known value of the other variable. The mutual information between two random variables X and Y can be stated formally as follows: I(X ; Y) = H(X) – H(X | Y)
How uncertainty information and entropy are related?
Entropy, in other words, is a measure of uncertainty . In a way, saying that entropy is “a measure of uncertainty” is an understatement. Given certain assumptions (and foreshadowing an important result mentioned below), entropy is the measure of uncertainty.
Who is the winner of entropy mutual information?
The winner is: Eunsu Ryu, with number 6 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 9 10 A strategy to win the game? Dr. Yao Xie, ECE587, Information Theory, Duke University 1 Dr. Yao Xie, ECE587, Information Theory, Duke University 2 Uncertainty measure LetXbe a random variable taking on a \\fnite numberMof di\erent valuesx1; ;xM
Entropy is a functional ofp(x) Entropy is a lower bound on the number of bits need to represent a RV. E.g.: a RV that that has uniform distribution over 32 outcomes Dr. Yao Xie, ECE587, Information Theory, Duke University 7 Properties of entropy
How to write entropy as a function of uncertainty?
General de\\fnition of entropy H(X) = ∑ x2X p(x)log2p(x) bits 0log0 = 0 Dr. Yao Xie, ECE587, Information Theory, Duke University 6 Uncertainty in a single random variable Can also be written as: H(X) = E { log 1 p(X) } Intuition:H= log(#of outcomes/states) Entropy is a functional ofp(x)
When did Shannon write estimation of entropy and mutual information?
Estimation of Entropy and Mutual Information 1195 ducing anything particularly novel, but merely formalizing what statis-ticians have been doing naturally since well before Shannon wrote his papers. This strategy bears a striking resemblance to regularization methods em-ployed in abstract statistical inference (Grenander, 1981), generally known