Understanding KL Divergence: A Fundamental Measure in Machine Learning
In the vast realm of machine learning and statistical analysis, several mathematical tools and techniques play a crucial role in quantifying the differences and similarities between probability distributions. One such tool is Kullback-Leibler (KL) divergence, named after Solomon Kullback and Richard Leibler, who introduced it in 1951. KL divergence is widely employed in various domains, including information theory, natural language processing, and reinforcement learning. In this blog post, we will delve into the concept of KL divergence, its significance, and how it is used in machine learning.
What is KL Divergence?
KL divergence is a measure of how one probability distribution differs from another. It quantifies the information lost when one distribution is used to approximate another. It is also referred to as relative entropy, as it measures the discrepancy between two distributions in terms of the amount of information required to encode one distribution compared to the other.
Mathematically, the KL divergence between two probability distributions P and Q is defined as:
KL(P || Q) = ∑ P(x) log(P(x) / Q(x))
Where P(x) and Q(x) represent the probabilities of observing the event x according to distributions P and Q…
