joint entropy について

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joint entropy ：ウィキペディア英語版

joint entropy

In information theory, joint entropy is a measure of the uncertainty associated with a set of variables.
==Definition==
The joint Shannon entropy of two variables

X

and

Y

is defined as
:

H(X,Y) = -\sum_ \sum_ P(x,y) \log_2() \!

where

x

and

y

are particular values of

X

and

Y

, respectively,

P(x,y)

is the joint probability of these values occurring together, and

P(x,y) \log_2()

is defined to be 0 if

P(x,y)=0

.
For more than two variables

X_1, ..., X_n

this expands to
:

H(X_1, ..., X_n) = -\sum_ ... \sum_ P(x_1, ..., x_n) \log_2(..., x_n)) \!

where

x_1,...,x_n

are particular values of

X_1,...,X_n

, respectively,

P(x_1, ..., x_n)

is the probability of these values occurring together, and

P(x_1, ..., x_n) \log_2(..., x_n))

is defined to be 0 if

P(x_1, ..., x_n)=0

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