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We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence...
This article reviews the topic of Bayesian networks. A Bayesian network is a factorisation of a probability distribution along a directed acyclic graph. The relation between graphical d-separation and independence is described. A short article by Arthur Cayley (1853) [7] is discussed, which laid ideas later used in Bayesian networks: factorisation, the noisy `or' gate, applications of algebraic geometry to Bayesian networks. The ideas behind Pearl's intervention calculus when the DAG represents...
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