A unified approach to universal prediction: Generalized upper and lower bounds

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dc.citation.epage651en_US
dc.citation.issueNumber3en_US
dc.citation.spage646en_US
dc.citation.volumeNumber26en_US
dc.contributor.authorVanli, N. D.en_US
dc.contributor.authorKozat, S. S.en_US
dc.date.accessioned2016-02-08T09:58:40Z
dc.date.available2016-02-08T09:58:40Z
dc.date.issued2015en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe study sequential prediction of real-valued, arbitrary, and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios, we achieve matching lower and upper bounds, demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result, we also prove that for the worst case scenario, the performance of randomized output algorithms can be achieved by sequential algorithms so that randomized output algorithms do not improve the performance. © 2012 IEEE.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:58:40Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2015en
dc.identifier.doi10.1109/TNNLS.2014.2317552en_US
dc.identifier.issn0216-2237X
dc.identifier.urihttp://hdl.handle.net/11693/22325
dc.language.isoEnglishen_US
dc.publisherInstitute of Electrical and Electronics Engineers Inc.en_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/TNNLS.2014.2317552en_US
dc.source.titleIEEE Transactions on Neural Networks and Learning Systemsen_US
dc.subjectOnline learningen_US
dc.subjectComputation theoryen_US
dc.subjectForecastingen_US
dc.subjectSequential switchingen_US
dc.subjectComputational learning theoryen_US
dc.subjectLower and upper boundsen_US
dc.subjectOnline learningen_US
dc.subjectSequential learning algorithmen_US
dc.subjectSequential predictionen_US
dc.subjectSquared prediction errorsen_US
dc.subjectUpper and lower boundsen_US
dc.subjectWorst-case performanceen_US
dc.subjectAlgorithmsen_US
dc.titleA unified approach to universal prediction: Generalized upper and lower boundsen_US
dc.typeArticleen_US

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