probabilitydivergence

Probability divergence refers to a class of mathematical measures used to quantify the difference between two probability distributions. These measures are fundamental in various fields, including machine learning, statistics, and information theory, for tasks such as model comparison, clustering, and anomaly detection. Unlike distance metrics, probability divergences are not necessarily symmetric (the divergence from distribution P to distribution Q may not be the same as from Q to P) and do not always satisfy the triangle inequality.

A common example of a probability divergence is the Kullback-Leibler divergence (KL divergence), often denoted as D_KL(P || Q). It measures how much information is lost when distribution Q is used to approximate distribution P. Another important measure is the Jensen-Shannon divergence (JS divergence), which is a symmetric and smoothed version of the KL divergence, making it a true metric. Other divergences include the total variation distance, Hellinger distance, and Rényi divergence, each with different properties and applications. The choice of divergence often depends on the specific problem and desired characteristics of the measure.