Learning Poisson Binomial Distributions

Constantinos Daskalakis, Ilias Diakonikolas, Rocco A. Servedio

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

We consider a basic problem in unsupervised learning: learning an unknown Poisson Binomial Distribution. A Poisson Binomial Distribution (PBD) over {0,1,...,n} is the distribution of a sum of n independent Bernoulli random variables which may have arbitrary, potentially non-equal, expectations. These distributions were first studied by S. Poisson in 1837 and are a natural n-parameter generalization of the familiar Binomial Distribution. Surprisingly, prior to our work this basic learning problem was poorly understood, and known results for it were far from optimal. We essentially settle the complexity of the learning problem for this basic class of distributions. As our main result we give a highly efficient algorithm which learns to ε-accuracy using O(1/ε3) samples independent of n. The running time of the algorithm is quasilinear in the size of its input data, i.e. ~O(log(n)/ε3) bit-operations (observe that each draw from the distribution is a log(n)-bit string). This is nearly optimal since any algorithm must use Ω(1/ε2) samples. We also give positive and negative results for some extensions of this learning problem.
Original languageEnglish
Title of host publicationProceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing
Place of PublicationNew York, NY, USA
PublisherACM
Pages709-728
Number of pages20
ISBN (Print)978-1-4503-1245-5
DOIs
Publication statusPublished - 2012

Publication series

NameSTOC '12
PublisherACM

Keywords / Materials (for Non-textual outputs)

  • applied probability, computational learning theory, learning distributions

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