True or False:
\text {KL}(\mathbf{P}||\mathbf{Q})\geq 0 for all discrete distributions \mathbf{P} and \mathbf{Q}.
True
False
unanswered
If \text {KL}(\mathbf{P}||\mathbf{Q})= 0, then \mathbf{P}=\mathbf{Q} (\mathbf{P} and \mathbf{Q} are discrete).
True
False
True
True
True
To determine if the statement is true or false, we need to understand the concept of KL divergence. KL divergence is a measure of the difference between two probability distributions, denoted as KL(P || Q). It quantifies how one distribution, P, differs from another distribution, Q.
For discrete distributions P and Q, KL(P || Q) is always greater than or equal to 0. This means that the KL divergence is non-negative. Therefore, the statement is true.
Furthermore, if KL(P || Q) = 0, it implies that there is no difference between the two distributions. In other words, P is equal to Q. This holds true specifically for discrete distributions.
Therefore, both statements are true.