Search results
Results From The WOW.Com Content Network
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
In statistics, the Bhattacharyya distance is a quantity which represents a notion of similarity between two probability distributions. [1] It is closely related to the Bhattacharyya coefficient , which is a measure of the amount of overlap between two statistical samples or populations.
Hamming distance; Jaro distance; Similarity between two probability distributions. Typical measures of similarity for probability distributions are the Bhattacharyya distance and the Hellinger distance. Both provide a quantification of similarity for two probability distributions on the same domain, and they are mathematically closely linked.
The two most important classes of divergences are the f-divergences and Bregman divergences; however, other types of divergence functions are also encountered in the literature. The only divergence for probabilities over a finite alphabet that is both an f -divergence and a Bregman divergence is the Kullback–Leibler divergence. [ 8 ]
In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance , statistical difference or variational distance .
In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.
In addition to measuring the distances between curves, the Fréchet distance can also be used to measure the difference between probability distributions. For two multivariate Gaussian distributions with means and and covariance matrices and , the Fréchet distance between these distributions is given by [5]
MAUVE is a measure of the statistical gap between two text distributions, such as the difference between text generated by a model and human-written text. This measure is computed using Kullback-Leibler divergences between the two distributions in a quantized embedding space of a foundation model.