Storage device performance prediction with CART models(18)
时间:2025-07-10
时间:2025-07-10
Storage device performance prediction is a key element of self-managed storage systems and application planning tasks, such as data assignment. This work explores the application of a machine learning tool, CART models, to storage device modeling. Our appr
AppendixA:ConstructingCARTModels
ACARTmodelisapiecewise-constantfunctiononamulti-dimensionalspace.Thisappendixgivesabriefdescriptionofthemodelconstructionalgorithm.Pleasereferto[4]foracompletediscussionofCARTmodels.
TheCARTmodelhasabinarytreestructurebuiltbyrecursivebinarysplits.SupposewehaveNobser-vations,Xii12N,withcorrespondingoutputsYii12N.Eachobservationconsistsofpinputfeatures,Xixi1xip).Theconstructionalgorithmstartswithatreewithonlyarootnodeandgrowsthetreedownwardbysplittingonenodeatime.Thechosensplitoffersthemostbene tinreducingthemeansquarederror.TheaverageYiforalltheXisinaleafnodeisusedasthepredictivevaluefortheleafnode.Thealgorithmcontinuesuntilcertaincriteriaaremet.
Wedescribehowthesplitischosenindetailnext.Thealgorithmevaluatesallthepossibledistinctsplitsonalltheleafnodesofthetree(ortherootnodeinthe rststep).Anodecorrespondstoahyer-rectangleregionoftheinputvectorspace,andasplitdecidesalongwhichfeatureandatwhatvaluetheregionshouldbedividedintotwo.Forexample,atnodet,asplitonfeaturejatvaluevde nestwonodes,nodet1andnodet2.
Xi
nodet1
Xixij
v
Xi
nodet
Xi
nodet2
Xixij
v
Xinodet
IfwedenotethenumberofobservationsinnodetasNtandthepredictivevalueasYt,themeansquarederroratnodetbeforethesplitis
MSEt
i:Xinodet
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Nt1
Yi
¯t1Y
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i:Xinodet2
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1
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