Faster Algorithms for Testing under Conditional Sampling

Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapati, Ananda Theertha Suresh
Proceedings of The 28th Conference on Learning Theory, PMLR 40:607-636, 2015.

Abstract

There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size k. We study two of the most important tests under the conditional-sampling model where each query specifies a subset S of the domain, and the response is a sample drawn from S according to the underlying distribution. For identity testing, which asks whether the underlying distribution equals a specific given distribution or ε-differs from it, we reduce the known time and sample complexities from \widetilde\mathcalO(ε^-4) to \widetilde\mathcalO(ε^-2), thereby matching the information theoretic lower bound. For closeness testing, which asks whether two distributions underlying observed data sets are equal or different, we reduce existing complexity from \widetilde\mathcalO(ε^-4 \log^5 k) to an even sub-logarithmic \widetilde\mathcalO(ε^-5 \log \log k) thus providing a better bound to an open problem in Bertinoro Workshop on Sublinear Algorithms (Fisher, 2014).

Cite this Paper

BibTeX
@InProceedings{pmlr-v40-Falahatgar15, title = {Faster Algorithms for Testing under Conditional Sampling}, author = {Falahatgar, Moein and Jafarpour, Ashkan and Orlitsky, Alon and Pichapati, Venkatadheeraj and Suresh, Ananda Theertha}, booktitle = {Proceedings of The 28th Conference on Learning Theory}, pages = {607--636}, year = {2015}, editor = {Grünwald, Peter and Hazan, Elad and Kale, Satyen}, volume = {40}, series = {Proceedings of Machine Learning Research}, address = {Paris, France}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v40/Falahatgar15.pdf}, url = {https://proceedings.mlr.press/v40/Falahatgar15.html}, abstract = {There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size k. We study two of the most important tests under the conditional-sampling model where each query specifies a subset S of the domain, and the response is a sample drawn from S according to the underlying distribution. For identity testing, which asks whether the underlying distribution equals a specific given distribution or ε-differs from it, we reduce the known time and sample complexities from \widetilde\mathcalO(ε^-4) to \widetilde\mathcalO(ε^-2), thereby matching the information theoretic lower bound. For closeness testing, which asks whether two distributions underlying observed data sets are equal or different, we reduce existing complexity from \widetilde\mathcalO(ε^-4 \log^5 k) to an even sub-logarithmic \widetilde\mathcalO(ε^-5 \log \log k) thus providing a better bound to an open problem in Bertinoro Workshop on Sublinear Algorithms (Fisher, 2014).} }
Endnote
%0 Conference Paper %T Faster Algorithms for Testing under Conditional Sampling %A Moein Falahatgar %A Ashkan Jafarpour %A Alon Orlitsky %A Venkatadheeraj Pichapati %A Ananda Theertha Suresh %B Proceedings of The 28th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2015 %E Peter Grünwald %E Elad Hazan %E Satyen Kale %F pmlr-v40-Falahatgar15 %I PMLR %P 607--636 %U https://proceedings.mlr.press/v40/Falahatgar15.html %V 40 %X There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size k. We study two of the most important tests under the conditional-sampling model where each query specifies a subset S of the domain, and the response is a sample drawn from S according to the underlying distribution. For identity testing, which asks whether the underlying distribution equals a specific given distribution or ε-differs from it, we reduce the known time and sample complexities from \widetilde\mathcalO(ε^-4) to \widetilde\mathcalO(ε^-2), thereby matching the information theoretic lower bound. For closeness testing, which asks whether two distributions underlying observed data sets are equal or different, we reduce existing complexity from \widetilde\mathcalO(ε^-4 \log^5 k) to an even sub-logarithmic \widetilde\mathcalO(ε^-5 \log \log k) thus providing a better bound to an open problem in Bertinoro Workshop on Sublinear Algorithms (Fisher, 2014).
RIS
TY - CPAPER TI - Faster Algorithms for Testing under Conditional Sampling AU - Moein Falahatgar AU - Ashkan Jafarpour AU - Alon Orlitsky AU - Venkatadheeraj Pichapati AU - Ananda Theertha Suresh BT - Proceedings of The 28th Conference on Learning Theory DA - 2015/06/26 ED - Peter Grünwald ED - Elad Hazan ED - Satyen Kale ID - pmlr-v40-Falahatgar15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 40 SP - 607 EP - 636 L1 - http://proceedings.mlr.press/v40/Falahatgar15.pdf UR - https://proceedings.mlr.press/v40/Falahatgar15.html AB - There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size k. We study two of the most important tests under the conditional-sampling model where each query specifies a subset S of the domain, and the response is a sample drawn from S according to the underlying distribution. For identity testing, which asks whether the underlying distribution equals a specific given distribution or ε-differs from it, we reduce the known time and sample complexities from \widetilde\mathcalO(ε^-4) to \widetilde\mathcalO(ε^-2), thereby matching the information theoretic lower bound. For closeness testing, which asks whether two distributions underlying observed data sets are equal or different, we reduce existing complexity from \widetilde\mathcalO(ε^-4 \log^5 k) to an even sub-logarithmic \widetilde\mathcalO(ε^-5 \log \log k) thus providing a better bound to an open problem in Bertinoro Workshop on Sublinear Algorithms (Fisher, 2014). ER -
APA
Falahatgar, M., Jafarpour, A., Orlitsky, A., Pichapati, V. & Suresh, A.T.. (2015). Faster Algorithms for Testing under Conditional Sampling. Proceedings of The 28th Conference on Learning Theory, in Proceedings of Machine Learning Research 40:607-636 Available from https://proceedings.mlr.press/v40/Falahatgar15.html.

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