Hands-On Learning Theory Fall 2016, Lecture 3
نویسنده
چکیده
A basic property of the entropy of a discrete random variable x is that: 0 ≤ H(x) ≤ log |X | In fact, the entropy is maximal for the discrete uniform distribution. That is, (∀x ∈ X ) p(x) = 1/|X |, in which case H(x) = log |X |. Definition 3.2 (Conditional entropy). The conditional entropy of y given x is defined as: H(y|x) = ∑ v∈X px(v)H(y|x = v) = − ∑ v∈X px(v) ∑ y∈Y py|x(y|v) log py|x(y|v) = − ∑ x∈X ,y∈Y pxy(x, y) log py|x(y|x)
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