Experimental Design on a Budget for Sparse Linear Models and Applications

Sathya Narayanan Ravi, Vamsi Ithapu, Sterling Johnson, Vikas Singh
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:583-592, 2016.

Abstract

Budget constrained optimal design of experiments is a classical problem in statistics. Although the optimal design literature is very mature, few efficient strategies are available when these design problems appear in the context of sparse linear models commonly encountered in high dimensional machine learning and statistics. In this work, we study experimental design for the setting where the underlying regression model is characterized by a \ell_1-regularized linear function. We propose two novel strategies: the first is motivated geometrically whereas the second is algebraic in nature. We obtain tractable algorithms for this problem and also hold for a more general class of sparse linear models. We perform an extensive set of experiments, on benchmarks and a large multi-site neuroscience study, showing that the proposed models are effective in practice. The latter experiment suggests that these ideas may play a small role in informing enrollment strategies for similar scientific studies in the short-to-medium term future.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-ravi16, title = {Experimental Design on a Budget for Sparse Linear Models and Applications}, author = {Ravi, Sathya Narayanan and Ithapu, Vamsi and Johnson, Sterling and Singh, Vikas}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {583--592}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/ravi16.pdf}, url = {https://proceedings.mlr.press/v48/ravi16.html}, abstract = {Budget constrained optimal design of experiments is a classical problem in statistics. Although the optimal design literature is very mature, few efficient strategies are available when these design problems appear in the context of sparse linear models commonly encountered in high dimensional machine learning and statistics. In this work, we study experimental design for the setting where the underlying regression model is characterized by a \ell_1-regularized linear function. We propose two novel strategies: the first is motivated geometrically whereas the second is algebraic in nature. We obtain tractable algorithms for this problem and also hold for a more general class of sparse linear models. We perform an extensive set of experiments, on benchmarks and a large multi-site neuroscience study, showing that the proposed models are effective in practice. The latter experiment suggests that these ideas may play a small role in informing enrollment strategies for similar scientific studies in the short-to-medium term future.} }
Endnote
%0 Conference Paper %T Experimental Design on a Budget for Sparse Linear Models and Applications %A Sathya Narayanan Ravi %A Vamsi Ithapu %A Sterling Johnson %A Vikas Singh %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-ravi16 %I PMLR %P 583--592 %U https://proceedings.mlr.press/v48/ravi16.html %V 48 %X Budget constrained optimal design of experiments is a classical problem in statistics. Although the optimal design literature is very mature, few efficient strategies are available when these design problems appear in the context of sparse linear models commonly encountered in high dimensional machine learning and statistics. In this work, we study experimental design for the setting where the underlying regression model is characterized by a \ell_1-regularized linear function. We propose two novel strategies: the first is motivated geometrically whereas the second is algebraic in nature. We obtain tractable algorithms for this problem and also hold for a more general class of sparse linear models. We perform an extensive set of experiments, on benchmarks and a large multi-site neuroscience study, showing that the proposed models are effective in practice. The latter experiment suggests that these ideas may play a small role in informing enrollment strategies for similar scientific studies in the short-to-medium term future.
RIS
TY - CPAPER TI - Experimental Design on a Budget for Sparse Linear Models and Applications AU - Sathya Narayanan Ravi AU - Vamsi Ithapu AU - Sterling Johnson AU - Vikas Singh BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-ravi16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 583 EP - 592 L1 - http://proceedings.mlr.press/v48/ravi16.pdf UR - https://proceedings.mlr.press/v48/ravi16.html AB - Budget constrained optimal design of experiments is a classical problem in statistics. Although the optimal design literature is very mature, few efficient strategies are available when these design problems appear in the context of sparse linear models commonly encountered in high dimensional machine learning and statistics. In this work, we study experimental design for the setting where the underlying regression model is characterized by a \ell_1-regularized linear function. We propose two novel strategies: the first is motivated geometrically whereas the second is algebraic in nature. We obtain tractable algorithms for this problem and also hold for a more general class of sparse linear models. We perform an extensive set of experiments, on benchmarks and a large multi-site neuroscience study, showing that the proposed models are effective in practice. The latter experiment suggests that these ideas may play a small role in informing enrollment strategies for similar scientific studies in the short-to-medium term future. ER -
APA
Ravi, S.N., Ithapu, V., Johnson, S. & Singh, V.. (2016). Experimental Design on a Budget for Sparse Linear Models and Applications. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:583-592 Available from https://proceedings.mlr.press/v48/ravi16.html.

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