This paper considers the problem of online piecewise linear regression for big data applications. We introduce an algorithm, which sequentially achieves the performance of the best piecewise linear (affine) model with optimal partition of the space of the regressor vectors in an individual sequence manner. To this end, our algorithm constructs a class of 2 D sequential piecewise linear models over a set of partitions of the regressor space and efficiently combines them in the mixture-of-experts setting. We show that the algorithm is highly efficient with computational complexity of only O(m D 2 ), where m is the dimension of the regressor vectors. This efficient computational complexity is achieved by efficiently representing all of the 2 D models using a "lexicographical splitting graph." We analyze the performance of our algorithm without any statistical assumptions, i.e., our results are guaranteed to hold. Furthermore, we demonstrate the effectiveness of our algorithm over the well-known data sets in the machine learning literature with computational complexity fraction of the state of the art.
3Turk Telekom Labs, istanbul, TUrkiye ibrahim.delibalta@turktelekom.com.trOzetr;e -Bu bildiride, denetimli ogrenim i.;in gorgiiJ stfirbir kaYlp altmda ytiksek performans gosteren .;evrimi.;i bir algoritma sunuyoruz. Sunulan bu yontem uyarlamr olarak oznitelik uzayml hiyerar §ik bir §ekilde par.;alara aymp etkili bir smtflandlrma algoritmasl olu §turmak i.;in bu basit modeller i.;in gti.;Iti bir birle §im olu §turmaktadlr. Burada ortaya koydugumuz yontem hesaplama karma §lkhgl a';lsmdan olduk.;a ol.;eklendirilebilir dtizeydedir. om. oznitelik uzaymm boyutlan ile dogrusal olarak i:il.;eklenebilir. Yaygm olarak kullamlan veri ktimeleri tizerinde yaptJgumz deneylerde sunulan algoritmanm diger geli §mi § tekniklere gore daha tisttin performans gosterdigini de bildiriyoruz. AnahtarKelimeler ----r;evrimir;i ogrenme, smiflandlrma, uyarlamr agar;lar, etkili hesaplama. Abstract-We introduce an on-line classification algorithm based on the hierarchical partitioning of the feature space which provides a powerful performance under the defined empirical loss. The algorithm adaptively partitions the feature space and at each region trains a different classifier. As a final classification result algorithm adaptively combines the outputs of these basic models which enables it to create a linear piecewise classifier model that can work well under highly non-linear complex data. The introduced algorithm also have scalable computational complexity that scales linearly with dimension of the feature space, depth of the partitioning and number of processed data. Through experiments we show that the introduced algorithm outperforms the state-of-the-art ensemble techniques over various well-known machine learning data sets. Keywords--on-line learning, classification, adaptive trees, computational efficiency. I. GiRi~GUnUmUzde bilgi teknolojilerindeki geli~meler nedeniyle genellikle yaptlanmaml~ karrna~lk formda hlZh bir ~ekilde akan verileri i~lememiz gerekmektedir [1] , [2]. Bu nedenle, biz bu bildiride ozellikle bUyUk ihtimalle ilintili olan rastgele veri akllulan i<;in ozgUn ve etkili bir <;evrimi<;i slmflandlrrna algoritmasl sunuyoruz.Algoritmamlz karma~lk (fazlaslyla dogrusal olmayan) slmflandlrma slmrlanm yakmsamak i<;in par<;ah dogrusal fonksiyonlarl ve yakmsama problemlerini azaltmak i<;in de 978-1-5090-1679-2/16/$31.00 © 2016 IEEE bOlgesel dUzenleri kullanmaktadlr. Ozellikle de her bolUmUnde slralt olarak egittigimiz basit dogrusal smlflandlflctlar kullanan hiyerar~ik bir yapl kullanmaktadlr. Bu ozellik sayesinde her bir par<;a bizim temel slmflandlflcl olarak adlandlrdlglmlz farklt bir dogrusal olmayan slmflandlrrna modeline kar~lltk gelmektedir ve bizim sisternimizde bu modellerin tarn amI temel slmflandlflctlarm rekabet slmfim olu~turmaktadlr. Tammladlglmlz bu rekabet smdim biz daha sonra bolUm parametreleri (bolge aymcllar) Uzerine parametrize edip olaslhksal baYlr ini~i yontemi ile optimize etmekteyiz. Bu optimizasyon sayesinde gelen veri akl~l dogrultusunda rekabet slmfi bolUmlendirme yapIslm degi~tirerek stirekli b...
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