Part 7/8:
A crucial concept in information theory is relative entropy, or Kullback-Leibler (KL) divergence, which quantifies the difference between two probability distributions. The KL divergence offers insightful properties, such as always being non-negative, being zero only if the two distributions are identical, and not functioning as a true distance metric due to its asymmetry.
Lastly, the notion of mutual information arises as a powerful tool to describe the relationship between variables that may not necessarily correlate linearly. Expressing dependencies between random variables, mutual information serves as a gauge for how much knowing one variable reduces uncertainty about another.