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

TL;DR

This paper introduces a scalable greedy algorithm for coreset selection that efficiently estimates means and mean square errors in graph-structured data, outperforming existing methods in accuracy and speed.

Contribution

The paper presents a novel gradient ascent-based coreset selection algorithm that handles variable node costs and provides theoretical error bounds, with extensive empirical validation.

Findings

Faster empirical convergence than random and clustering methods

Effective in semi-supervised node classification and sensor placement

Outperforms current state-of-the-art algorithms

Abstract

In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction steps (in contrast to Frank-Wolfe and its variants), a variant of gradient ascent for coreset selection in graphs, that greedily selects a weighted subset of vertices that are deemed most important to sample. Our algorithm estimates the mean of the function by taking a weighted sum only at these vertices, and we provably bound the estimation error in terms of the location and weights of the selected vertices in the graph. In addition, we consider the case where nodes have different selection costs and provide bounds on the quality of the low-cost selected coresets. We demonstrate the benefits of our algorithm on the semi-supervised node classification of graph convolutional neural network, point clouds and structured graphs, as well as sensor placement where the cost of placing sensors depends on the location of the placement. We also elucidate that the empirical convergence of our proposed method is faster than random selection and various clustering methods while still respecting sensor placement cost. The paper concludes with validation of the developed algorithm on both synthetic and real datasets, demonstrating that it outperforms the current state of the art.