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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables and .The area contained by both circles is the joint entropy (,).
A misleading [1] Venn diagram showing additive, and subtractive relationships between various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and violet) is the individual entropy H(X), with the red being the conditional entropy H(X|Y ...
The above expression makes clear that the uncertainty coefficient is a normalised mutual information I(X;Y). In particular, the uncertainty coefficient ranges in [0, 1] as I(X;Y) < H(X) and both I(X,Y) and H(X) are positive or null. Note that the value of U (but not H!) is independent of the base of the log since all logarithms are proportional.
where is the Kullback–Leibler divergence, and is the outer product distribution which assigns probability () to each (,).. Notice, as per property of the Kullback–Leibler divergence, that (;) is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when and are independent (and hence observing tells you nothing about ).
Venn diagram for various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and cyan) is the individual entropy H(X), with the red being the conditional entropy H(X|Y). The circle on the right (blue and cyan) is H(Y), with the blue being ...
Switzerland's Marco Odermatt celebrates at the finish area of an alpine ski, men's World Cup downhill, in Wengen, Switzerland, Saturday, Jan. 18, 2025 (AP Photo/Giovanni Maria Pizzato)
Entropy Η(X) (i.e. the expected surprisal) of a coin flip, measured in bits, graphed versus the bias of the coin Pr(X = 1), where X = 1 represents a result of heads. [ 10 ] : 14–15 Here, the entropy is at most 1 bit, and to communicate the outcome of a coin flip (2 possible values) will require an average of at most 1 bit (exactly 1 bit for ...
Ricardo Navarro Tolento, 29, was convicted by a Orange County Superior Court jury on Tuesday over his involvement in the 2020 death of 67-year-old Eugene Harbrecht.