NDLI: Random projections for Bayesian regression

Content Provider	Springer Nature Link
Author	Geppert, Leo N. Ickstadt, Katja Munteanu, Alexander Quedenfeld, Jens Sohler, Christian
Copyright Year	2015
Abstract	This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire d-dimensional distribution is approximately preserved under random projections by reducing the number of data points from n to $$k\in O({\text {poly}}(d/\varepsilon ))$$ in the case $$n\gg d$$ . Under mild assumptions, we prove that evaluating a Gaussian likelihood function based on the projected data instead of the original data yields a $$(1+O(\varepsilon ))$$ -approximation in terms of the $$\ell _2$$ Wasserstein distance. Our main result shows that the posterior distribution of Bayesian linear regression is approximated up to a small error depending on only an $$\varepsilon $$ -fraction of its defining parameters. This holds when using arbitrary Gaussian priors or the degenerate case of uniform distributions over $$\mathbb {R}^d$$ for $$\beta $$ . Our empirical evaluations involve different simulated settings of Bayesian linear regression. Our experiments underline that the proposed method is able to recover the regression model up to small error while considerably reducing the total running time.
Starting Page	79
Ending Page	101
Page Count	23
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	27
Issue Number	1
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2015-11-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bayesian regression Random projections Data reduction Posterior approximation Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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