Let, Since the vector-skew JensenShannon divergence is an f-divergence for the generator, For example, consider the ordinary JensenShannon divergence with, Notice that we can truncate an exponential family [, The entropy of a density belonging to a mixture family. ; Sriperumbudur, B.K. This has several advantages compared to KL divergence for troubleshooting data model comparisons. Revision 611ca699. total KL divergence to the average distribution, entropy of the average distribution minus the average of the entropies, extended scalar KullbackLeibler divergence, The vector-skew JensenShannon divergences, Since the vector-skew Jensen divergence is an f-divergence, we easily obtain Fano and Pinsker inequalities following [, symmetric scalar -skew JensenShannon divergence, We can always symmetrize a vector-skew JensenShannon divergence by doubling the dimension of the skewing vector. = 1 if For the two-distribution case described above, P As $n \to \infty$, $KLD_{approx}(P|M) \to KLD(P|M)$. [. 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. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The Jensen-Shannon divergence can be derived from other, more well known information measures; notably the Kullback-Leibler Divergence and the Mutual Information. ) future research directions and describes possible research applications. The Jensen-Shannon distance between two probability vectors p and q is defined as, D ( p m) + D ( q m) 2 where m is the pointwise mean of p and q and D is the Kullback-Leibler divergence. Jeffreys, H. An invariant form for the prior probability in estimation problems. where $h(P)$ denotes the (differential) entropy corresponding to the measure $P$. {\displaystyle P_{1}=P,P_{2}=Q,\pi _{1}=\pi _{2}={\frac {1}{2}}.\ }, Hence, for those distributions In model monitoring, JS divergence is similar to PSI in that it is used to monitor production environments, specifically around feature and prediction data. if p[x] != 0.0 or p[x] != 0 is used to make sure that we don't consider entries which are zero, whether they are floats or integers, is that what you were referring to? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. / ditException Raised if there dists and weights have unequal lengths. Drift monitoring can be especially useful for teams that receive delayed ground truth to compare against production model decisions.