Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning problem, we show how we can strategically summarize the data (control space) in order to trade off risk and time when data is generated by a probabilistic model. Our summarization is based on coreset constructions from computational geometry. We also develop an algorithm, TRAM, to navigate the space/time/data/risk tradeoff in practice. In particular, we show that for a fixed risk (or data size), as the data size increases (resp. risk increases) the running time of TRAM decreases. Our extensive experiments on real data sets demonstrate the existence and practical utility of such tradeoffs, not only for k-means but also for Gaussian Mixture Models.

@inproceedings{lucic15tradeoffs,
	author = {Mario Lucic and Mesrob I. Ohannessian and Amin Karbasi and Andreas Krause},
	booktitle = {In Proc. International Conference on Artificial Intelligence and Statistics (AISTATS)},
	month = {May},
	title = {Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning},
	year = {2015}}