Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning
This addresses the problem of scalability in large-scale machine learning for practitioners, though it is incremental as it applies existing coreset methods to known tradeoffs.
The paper tackles the challenge of trading off statistical risk, computational space, and time in unsupervised learning with massive data, showing that strategic data summarization via coresets can reduce running time as data size or risk increases, with experiments on k-means and Gaussian Mixture Models demonstrating practical utility.
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.