![]() For example, the words "dog" and "dot", which differ by just one letter, are closer than "dog" and "cat", which have no letters in common. In computer science, an edit distance or string metric between two strings measures how different they are. Other important statistical distances include the Mahalanobis distance and the energy distance. Statistical manifolds corresponding to Bregman divergences are flat manifolds in the corresponding geometry, allowing an analog of the Pythagorean theorem (which holds for squared Euclidean distance) to be used for linear inverse problems in inference by optimization theory. The most important in information theory is the relative entropy ( Kullback–Leibler divergence), which allows one to analogously study maximum likelihood estimation geometrically this is an example of both an f-divergence and a Bregman divergence (and in fact the only example which is both). The most elementary is the squared Euclidean distance, which is minimized by the least squares method this is the most basic Bregman divergence. There are many kinds of statistical distances, typically formalized as divergences these allow a set of probability distributions to be understood as a geometrical object called a statistical manifold. In statistics and information geometry, statistical distances measure the degree of difference between two probability distributions. Many abstract notions of distance used in mathematics, science and engineering represent a degree of difference or separation between similar objects.
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