Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning

Mario Lucic; Mesrob Ohannessian; Amin Karbasi; Andreas Krause

Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning

Mario Lucic, Mesrob Ohannessian, Amin Karbasi, Andreas Krause ;

Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:663-671, 2015.

Abstract

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.

Related Material

@InProceedings{pmlr-v38-lucic15, title = {{Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning}}, author = {Mario Lucic and Mesrob Ohannessian and Amin Karbasi and Andreas Krause}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {663--671}, year = {2015}, editor = {Guy Lebanon and S. V. N. Vishwanathan}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/lucic15.pdf}, url = {http://proceedings.mlr.press/v38/lucic15.html}, abstract = {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.} }

%0 Conference Paper %T Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning %A Mario Lucic %A Mesrob Ohannessian %A Amin Karbasi %A Andreas Krause %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-lucic15 %I PMLR %J Proceedings of Machine Learning Research %P 663--671 %U http://proceedings.mlr.press %V 38 %W PMLR %X 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.

TY - CPAPER TI - Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning AU - Mario Lucic AU - Mesrob Ohannessian AU - Amin Karbasi AU - Andreas Krause BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics PY - 2015/02/21 DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-lucic15 PB - PMLR SP - 663 DP - PMLR EP - 671 L1 - http://proceedings.mlr.press/v38/lucic15.pdf UR - http://proceedings.mlr.press/v38/lucic15.html AB - 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. ER -

Lucic, M., Ohannessian, M., Karbasi, A. & Krause, A.. (2015). Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in PMLR 38:663-671