Arg max

Arg max

Approximate Methods for Calculating Marginals and Likelihoods

Published in Marloes Maathuis, Mathias Drton, Steffen Lauritzen, Martin Wainwright, Handbook of Graphical Models, 2018

Nicholas Ruozzi

Whenever ρ $ \rho $ is chosen so that the reweighted entropy approximation is concave, the convex hull of Tθ $ \mathcal T _\theta $ will be equal to Tθ $ \mathcal T _\theta $ as the set of optima of a concave function must form a convex set. If the reweighted entropy approximation is not concave, then there may exist points in the convex hull which are not elements of the argmax $ \arg \max $ . In principle, this means that there could exist some empirical marginals that are difficult, if not impossible, to learn in practice when the entropy approximation is not concave (for an example of such a case, see [8]). As a result, concave entropy approximations are often preferred in practice (even if they may produce poorer estimates of the partition function).

Multi-objective dynamic virtual machine consolidation in the cloud using ant colony system

View Article

Journal Information

Published in International Journal of Parallel, Emergent and Distributed Systems, 2018

Adnan Ashraf, Ivan Porres

where denotes the amount of pheromone and represents the heuristic value associated with a particular tuple. is a parameter to determine the relative importance of the heuristic value with respect to the pheromone value. The expression arg max returns the tuple for which attains its maximum value. is the set of tuples that remain to be traversed by ant k. is a uniformly distributed random variable and is a parameter. S is a random variable selected according to the probability distribution given in (7), where the probability of an ant k to choose tuple s to traverse next is defined as

Explore chapters and articles related to this topic

Approximate Methods for Calculating Marginals and Likelihoods

Multi-objective dynamic virtual machine consolidation in the cloud using ant colony system