Neural Information Processing Systems http://nips.cc/

Correlation clustering is a fundamental optimization problem at the intersection of machine learning and theoretical computer science. Motivated by applications to big data processing, recent years have witnessed a flurry of results on this problem in the streaming model. In this model, the algorithm needs to process the input n-vertex graph by making one or few passes over the stream of its edges and using a limited memory, much smaller than the input size. All previous work on streaming correlation clustering has focused on semistreaming algorithms with Ω(n) memory, whereas in this work, we study streaming algorithms with much smaller memory requirements of only polylog(n) bits. This stringent memory requirement is in the same spirit of classical streaming algorithms that instead of recovering a full solution to the problem--which can be prohibitively large with such small memory as is the case in our problem--, aimed to learn certain statistical properties of their inputs.

Increasingly, copious amounts of consumer data are used to learn high-revenue mechanisms via machine learning. Existing research on mechanism design via machine learning assumes that there is a distribution over the buyers' values for the items for sale and that the learning algorithm's input is a training set sampled from this distribution. This setup makes the strong assumption that no noise is introduced during data collection. In order to help place mechanism design via machine learning on firm foundations, we investigate the extent to which this learning process is robust to noise. Optimizing revenue using noisy data is challenging because revenue functions are extremely volatile: an infinitesimal change in the buyers' values can cause a steep drop in revenue. Nonetheless, we provide guarantees when arbitrarily correlated noise is added to the training set; we only require that the noise has bounded magnitude or is sub-Gaussian. We conclude with an application of our guarantees to multi-task mechanism design, where there are multiple distributions over buyers' values and the goal is to learn a high-revenue mechanism per distribution. To our knowledge, we are the first to study mechanism design via machine learning with noisy data as well as multi-task mechanism design.