Contents
Is the Kullback-Leibler divergence a symmetric quantity?
The Kullback-Leibler divergence is not symmetric, i.e., KL ( p || q )≠KL ( q || p) and it can be shown that it is a nonnegative quantity (the proof is similar to the proof that the mutual information is nonnegative; see Problem 12.16 of Chapter 12 ). Moreover, it is zero if and only if p = q.
How is Kullback Leibler divergence used in machine learning?
The relative entropy or Kullback-Leibler divergence is a quantity that has been developed within the context of information theory for measuring similarity between two pdfs. It is widely used in machine learning optimization tasks when pdfs are involved; see Chapter 12.
What’s the difference between KL divergence and cross entropy?
Both the cross-entropy and the KL divergence are tools to measure the distance between two probability distributions, but what is the difference between them? Moreover, it turns out that the minimization of KL divergence is equivalent to the minimization of cross-entropy.
When did Solomon Kullback and Richard Leibler create divergence?
The Kullback–Leibler divergence was introduced by Solomon Kullback and Richard Leibler in 1951 as the directed divergence between two distributions; Kullback preferred the term discrimination information. The divergence is discussed in Kullback’s 1959 book, Information Theory and Statistics.
When is DKL ( p, q ) equal to 0?
DKL is a positive quantity and is equal to 0 if and only if P = Q almost everywhere. DKL ( P, Q) is not symmetric because DKL ( P, Q )≠ DKL ( Q, P ).
Is the KL-divergence a distance or a distance?
The KL-divergence is not a distance, since it is not symmetric and does not satisfy the triangle inequality. It is nonlinear as well and varies in the range of zero to infinity. A zero KL-divergence indicates that the two probability density functions are strictly equal.