as maximum likelihood and maximum spacing estimators. Symmetrised divergence also considered the symmetrized function: which they referred to as the "divergence", though today the "KL divergence" refers to the asymmetric function (see for the evolution of the term). This function is symmetric and nonnegative, and had already been defined and used by Harold Jeffreys in 1948; it is accordingly called the Jeffreys divergence. This quantity has sometimes been used for feature selection in classification problems, where and are the conditional pdfs of a feature under two different classes. In the Banking and Finance industries, this quantity is referred to as Population Stability Index (PSI), and is used to assess distributional shifts in model features through time. An alternative is given via the divergence, which can be interpreted as the expected information gain about from discovering which probability distribution is drawn from, or , if they currently have probabilities and respectively. The value gives the Jensen–Shannon divergence, defined by where is the average of the two distributions, can also be interpreted as the capacity of a noisy information channel with two inputs giving the output distributions and . The Jensen–Shannon divergence, like all f-divergences, is locally proportional to the Fisher information metric. It is similar to the Hellinger metric (in the sense that it induces the same affine connection on a statistical manifold). Furthermore, the Jensen-Shannon divergence can be generalized using abstract statistical M-mixtures relying on an abstract mean M. Relationship to other probability-distance measures There are many other important measures of probability distance. Some of these are particularly connected with relative entropy. For example: The total variation distance, . This is connected to the divergence through Pinsker's inequality: Pinsker's inequality is vacuous for any distributions where , since the total variation distance is at most . For such distributions, an alternative bound can be used, due to Bretagnolle and Huber (see, also, Tsybakov): The family of Rényi divergences generalize relative entropy. Depending on the value of a certain parameter, , various inequalities may be deduced. Other notable measures of distance include the Hellinger distance, histogram intersection, Chi-squared statistic, quadratic form distance, match distance, Kolmogorov–Smirnov distance, and earth mover's distance. Data differencing Just as absolute entropy serves as theoretical background for data compression, relative entropy serves as theoretical background for data differencing – the absolute entropy of a set of data in this sense being the data required to reconstruct it