correlation between Kullback–Leibler (KL) divergence and Jensen–Shannon (JS) divergence? : r/MachineLearning
I am wondering if there is a correlation between JSD and KLD (except the fact that JSD is derived from KLD and JSD is symmetrical), for example if JSD(p,q) is decreased, whether KLD(p||q) will decrease as well? This question comes from the comparison between the variational objective and the adversarial objective in training deep generative models. No, JSD[Q,P] is not monotonically related to KL[Q||P]. To see this consider the following argument: You can certainly find a triplet Q_1,Q_2 and P such that KL[Q_1||P] > KL[Q_2||P] but KL[P||Q_1] KL[Q_2||P] implies JSD[Q_1||P] > JSD[Q_2||P] then using the symmetry of JSD you'd get that: KL[Q_1||P] > KL[Q_2||P] JSD[Q_1||P] > JSD[Q_2||P] JSD[P||Q_1] > JSD[P||Q_2] KL[P||Q_1] > KL[P||Q_2] which is a cont
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