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In a number of situations, collecting a function value for every data pointmay be prohibitively expensive, and random sampling ignores any structure inthe underlying data. We introduce a scalable optimization algorithm with nocorrection steps (in contrast to Frank-Wolfe and its variants), a variant ofgradient ascent for coreset selection in graphs, that greedily selects aweighted subset of vertices that are deemed most important to sample. Ouralgorithm estimates the mean of the function by taking a weighted sum only atthese vertices, and we provably bound the estimation error in terms of thelocation and weights of the selected vertices in the graph. In addition, weconsider the case where nodes have different selection costs and provide boundson the quality of the low-cost selected coresets. We demonstrate the benefitsof our algorithm on the semi-supervised node classification of graphconvolutional neural network, point clouds and structured graphs, as well assensor placement where the cost of placing sensors depends on the location ofthe placement. We also elucidate that the empirical convergence of our proposedmethod is faster than random selection and various clustering methods whilestill respecting sensor placement cost. The paper concludes with validation ofthe developed algorithm on both synthetic and real datasets, demonstrating thatit outperforms the current state of the art.

Coresets for Estimating Means and Mean Square Error with Limited Greedy Samples