Coresets Estimation.pdf

The authors propose a greedy algorithm for coreset selection in graphs to estimate the mean of a function by selecting a weighted subset of vertices. The algorithm is scalable, has no correction steps, and provides bounds on the estimation error. It is applied to various problems, including semi-supervised node classification, point clouds, structured graphs, and sensor placement. The algorithm outperforms random selection, clustering methods, and state-of-the-art techniques, while respecting sensor placement costs. Key contributions include:

A greedy optimization algorithm for coreset selection with theoretical guarantees
Bounds on the estimation error of the mean of a function in terms of the selected vertices and their weights
Extension to non-uniform costs for node selection, with characterization of the error in estimating the mean
Empirical evaluation on various applications, demonstrating faster convergence and better performance than existing methods

The algorithm is based on a variant of gradient ascent and selects a weighted subset of vertices that are deemed most important to sample. The weighted sum of function values at these vertices is used to estimate the mean of the function over the entire graph. The authors also provide an upper-bound on the estimation error, which can be used to bound any mean estimation problem with a sufficiently low-frequency function.