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.
@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
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