a divergence is a scoring of how one distribution differs from another, where calculating the divergence for distributions P and Q would give a different score from Q and P. Divergence scores provide shortcuts for calculating scores such as mutual information (information gain) and cross-entropy used as a loss function for classification models. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. where $KLD$ is the Kullback-Leibler divergence, and $M=\frac{1}{2}(P+Q)$ 10331040. It is also known as Information radius (IRad) or total divergence to the average. 1 If None, the weights are This means that the divergence of P from Q is the same as Q from P: M See the middle of column two on page 1859. Addendum: Note that a mixture of normals is not the same as a linear combination of normals. n = It is worth pointing out that the entropy of a multivariate normal is invariant with respect to the mean, as the expression above shows. In essence, if \(X\) and \(Y\) are each an urn containing colored balls, and I randomly selected one of the urns and draw a ball from it, then the Jensen-Shannon divergence is the mutual information between which urn I drew the ball from, and the color of the ball drawn. JS(P || Q) == JS(Q || P), The JS divergence can be calculated as follows: ) yongchaohuang.github.io, How to Calculate the KL Divergence for Machine Learning, Importantly, the KL divergence score is not symmetrical, i.e. The following shows the symmetry with KL Divergence: For more background, one of the better technical papers on JS Divergence is written by Frank Nielsen of Sony Computer Science Laboratories. Learn more about Stack Overflow the company, and our products. {\displaystyle (\rho _{1},\ldots ,\rho _{n})} np.random.seed(0) . ; Panos, C. Information entropy, information distances, and complexity in atoms. 2004. One alternative is to use population stability index along with an out-of-distribution binning technique to handle zero bins. https://doi.org/10.3390/e22020221, Nielsen F. On a Generalization of the JensenShannon Divergence and the JensenShannon Centroid. , and its distribution is the mixture distribution. S Copyright 2013-2018, dit contributors , That is not necessarily the case with JS divergence. To learn more, see our tips on writing great answers. ) @KaushikRoy Well, I have read this, the inputs are two tensors. It is more useful as a measure as it provides a smoothed and normalized version of KL divergence, with scores between 0 (identical) and 1 (maximally different), when using the base-2 logarithm. that is used to switch between Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. to produce the mixture. How to Calculate the KL Divergence for Machine Learning
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