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Thread: conditional entropy of function

  1. May 3rd 2012, 03:08 PM #1
    alexandrabel90
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    conditional entropy of function

    how does one show that H(Y l f(X) ) greater than or equal to H(YlX) where f(X) is any function of X?
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  2. May 3rd 2012, 03:33 PM #2
    jens
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    Re: conditional entropy of function

    f(X) is a degraded observation of X, so we have that

    H(Y|f(X),X) = H(Y|X)

    Since conditioning reduces entropy,

    H(Y|f(X)) \geq H(Y|X)
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