About convergence of KL divergence if the two probability distributions are type, does the law of large number work?

1. What is the KL divergence between two equal distributions?
2. What is a large KL divergence?
3. Which is true regarding Kullback-Leibler divergence?
4. Is the Kullback-Leibler divergence always positive?

What is the KL divergence between two equal distributions?

KL divergence can be calculated as the negative sum of probability of each event in P multiplied by the log of the probability of the event in Q over the probability of the event in P. The value within the sum is the divergence for a given event.

What is a large KL divergence?

Kullback-Leibler divergence is described as a measure of “suprise” of a distribution given an expected distribution. For example, when the distributions are the same, then the KL-divergence is zero. When the distributions are dramatically different, the KL-divergence is large.

Which is true regarding Kullback-Leibler divergence?

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.

Is the Kullback-Leibler divergence always positive?

Gibbs' inequality, also known as the Shannon-Kolmogorov Information inequality, states that the Kullback-Leibler divergence is always positive. KL ( F | G ) ≥ 0.