KLdivergenciával

KLdivergencia, also known as Kullback-Leibler divergence or relative entropy, is a measure of how one probability distribution differs from a second, reference probability distribution. It is not a true metric because it is not symmetric; the KL divergence from distribution P to distribution Q is not necessarily equal to the KL divergence from Q to P. However, it is widely used in information theory, statistics, and machine learning.

Mathematically, the KL divergence of a distribution Q from a distribution P is defined as DKL(P || Q) = Σx P(x) log(P(x)/Q(x)) for discrete distributions, or DKL(P || Q) = ∫ P(x) log(P(x)/Q(x)) dx for continuous distributions. The logarithm is typically the natural logarithm, but can also be base 2 or base 10, affecting the units of the divergence (nats, bits, or dits, respectively). A KL divergence of zero indicates that the two distributions are identical.

The KL divergence quantifies the information lost when Q is used to approximate P. It can be interpreted as the expected number of extra bits required to encode samples from P using a code optimized for Q, compared to using a code optimized for P. This property makes it useful in tasks such as model selection, where one might choose the model whose predictive distribution has the lowest KL divergence from the true data-generating distribution. It is also a fundamental component in variational inference and various machine learning algorithms, including some forms of clustering and dimensionality reduction.