Streaming Submodular Maximization Under Noises

Motivated by the need for analyzing the rapidly producing data streams, such as images, videos, sensor data, etc, in a timely manner, the study on the streaming algorithms to extract representative information from massive data to maximize some objective function is therefore important and urgent. Most of previous works are assumed under a noise-free environment, while in many realistic applications obtaining the exact function value is hard or computing the function value may cost much, which brings the noisy version. Hence in this paper, we address a more general problem to select a subset of at most k elements from the stream to maximize a noisy set function (not necessarily submodular). To be specific, we cast our problem as the streaming submodular maximization problem under multiplicative and additive noise models. We develop an efficient thresholding streaming algorithm, which calls several copies of a subroutine in parallel. Therefore, this algorithm only requires two passes over data and has a memory independent of data size. For both of noisy models, its approximation guarantee approaches 2/k. In our numerical experiments, we extensively evaluate the effectiveness of our thresholding streaming algorithm on some applications in real data set.