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Intro duction - SVMs

ATutorialonSupportVectorRegressionAlexJ Smola GMD BernhardSch olkopf GMD NeuroCOLT TechnicalReportSeriesNC TR October ProducedaspartoftheESPRITW orkingGroupinNeuralandComputationalLearn ingII NeuroCOLT FormoreinformationseetheNeuroCOLT websitehttp www neurocolt comoremailneurocolt neurocolt com smola first gmd deGMDFIRST RudowerChaussee Berlin Germany bs first gmd deGMDFIRST RudowerChaussee Berlin Germany Received OCT Introduction AbstractInthistutorialwegiveanoverviewof thebasicideasunderlyingSupportVector SV machinesforregressionandfunctionestimati on Further more weincludeasummaryofcurrentlyusedalgorith msfortrainingSVmachines coveringboththequadratic orconvex programmingpartandadvancedmethodsfordeal ingwithlargedatasets Finally wementionsomemodi cationsandextensionsthathavebeenappliedt othestandardSValgorithm anddiscusstheaspectofregularizationandca pacitycontrolfromaSVpointofview IntroductionThepurposeofthispaperistwofo ld Itshouldserveasaself containedintro ductiontoSupportVectorregressionforreade rsnewtothisrapidlydeveloping eldofresearch Ontheotherhand itattemptstogiveanoverviewofrecentdevelo pmentsinthe eld Tothisend wedecidedtoorganizetheessayasfollows Westartbygiv ingabriefoverviewofthebasictechniquesins ections and plusashortsummarywithanumberof guresanddiagramsinsection Section reviewscurrentalgorithmictechniquesusedf oractuallyimplementingSVma chines Thismaybeofmost

Intro duction problem Hence w e arriv e at the form ulation stated in V apnik minimize i k w C P i i sub ject to i y h w x i b h w x i i b y i i i The constan t C

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