B find the rankings obtained using the penalty

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Unformatted text preview: nts α, η , T ideal , λ. Give ψ explicitly. You are free (indeed, encouraged) to check your formula using CVX, with made up values for the constants. Disclaimer. The focus of this course is not on deriving 19th century pencil and paper solutions to problems. But every now and then, a practical problem will actually have an analytical solution. This is one of them. 145 17 Miscellaneous applications 17.1 Earth mover’s distance. In this exercise we explore a general method for constructing a distance between two probability distributions on a finite set, called the earth mover’s distance, Wasserstein metric, or Dubroshkin metric. Let x and y be two probability distributions on {1, . . . , n}, i.e., 1T x = 1T y = 1, x 0, y 0. We imagine that xi is the amount of earth stored at location i; our goal is to move the earth between locations to obtain the distribution given by y . Let Cij be the cost of moving one unit of earth from location j to location i. We assume that Cii = 0, and Cij = Cji > 0 for i = j . (We allow Cij = ∞, which means that earth cannot be...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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