2codec codecEstimatetheconditionaldependencecoef2cientCODEC DescriptionTheconditionaldependencecoef2cientCODECisameasureoftheamountofconditionaldependencebetweenarandomvariableYandarandomve ID: 855136
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1 Package`FOCI'March19,2021TypePackageTitl
Package`FOCI'March19,2021TypePackageTitleFeatureOrderingbyConditionalIndependenceVersion0.1.3MaintainerMonaAzadkia&#xmona; zad;&#xkia@;&#xgmai;&#xl.co;&#xm000;DescriptionFeatureOrderingbyConditionalIndependence(FOCI)isavariableselectionalgo-rithmbasedonthemeasureofconditionaldependence.Formoreinformation,seethepaper:AzadkiaandChatterjee(2019), Asimplemeasureofcon-ditionaldependence rXi;─v:1910.12327.LicenseGPL-3EncodingUTF-8LazyDatatrueVignetteBuilderknitrRoxygenNote7.1.0Suggestsknitr,rmarkdown,testthatDependsR rXi;─(=3.6.0),data.tableImportsRANN,proxy,parallel,gmpNeedsCompilationnoAuthorMonaAzadkia[aut,cre],SouravChatterjee[aut,ctb],NormanMatloff[aut,ctb]RepositoryCRANDate/Publication2021-03-1823:00:07UTCRtopicsdocumented:codec............................................2foci.............................................3Index61 2codec codecEstimatetheconditionaldependencecoefcient(CODEC) DescriptionTheconditionaldependencecoefcient(CODEC)isameasureoftheamountofconditionaldepen-dencebe
2 tweenarandomvariableYandarandomvectorZgi
tweenarandomvariableYandarandomvectorZgivenarandomvectorX,basedonani.i.d.sampleof(Y,Z,X).Thecoefcientisasymptoticallyguaranteedtobebetween0and1.Usagecodec(Y,Z,X=NULL,na.rm=TRUE)ArgumentsYVector(lengthn)ZMatrix(nbyq)XMatrix(nbyp),defaultisNULLna.rmRemoveNAsifTRUEDetailsThevaluereturnedbycodeccanbepositiveornegative.Asymptotically,itisguaranteedtobebetween0and1.AsmallvalueindicateslowconditionaldependencebetweenYandZgivenX,andahighvalueindicatesstrongconditionaldependence.Thecodecfunctionisusedbythefocifunctionforvariableselection.ValueTheconditionaldependencecoefcient(CODEC)ofYandZgivenX.IfX==NULL,thisisjustameasureofthedependencebetweenYandZ.Author(s)MonaAzadkia,SouravChatterjee,NormanMatloffReferencesAzadkia,M.andChatterjee,S.(2019).Asimplemeasureofconditionaldependence.https://arxiv.org/pdf/1910.12327.pdf.SeeAlsofoci,xicor foci3Examplesn=1000xmatrix(runif(n*2),nrow=n)y(x[,1]+x[,2])%%1#givenx[,1],yisafunctionofx[,2]codec(y,x[,2],x[,1])#yisafunctionofxcodec(y,x)zrnorm(n)#yisafunctionofxgivenzcodec(y,x,z)#yisindepende
3 ntofzgivenxcodec(y,z,x) fociVariablesele
ntofzgivenxcodec(y,z,x) fociVariableselectionbytheFOCIalgorithm DescriptionFOCIisavariableselectionalgorithmbasedonthemeasureofconditionaldependencecodec.Usagefoci(Y,X,num_features=NULL,stop=TRUE,na.rm=TRUE,standardize="scale",numCores=parallel::detectCores(),parPlat="none",printIntermed=TRUE)ArgumentsYVectorofresponses(lengthn)XMatrixofpredictors(nbyp)num_featuresNumberofvariablestobeselected,cannotbelargerthanp.ThedefaultvalueisNULLandinthatcaseitwillbesetequaltop.Ifstop==TRUE(seebelow),thennum_featuresisirrelevant.stopStopsattherstinstanceofnegativecodec,ifTRUE.na.rmRemovesNAsifTRUE. 4focistandardizeStandardizecovariatesifsetequalto"scale"or"bounded".Otherwisewillusetherawinputs.Thedefaultvalueis"scale"andnormalizeseachcolumnofXtohavemeanzeroandvariance1.Ifsetequalto"bounded"mapthevaluesofeachcolumnofXto[0,1].numCoresNumberofcoresthataregoingtobeusedforparallelizingthevariableselecc-tionprocess.parPlatSpeciestheparallelplatformtochunkdatabyrows.Itcantakethreevalues:1-Thedefaultvalueissetto'none',inwhichcasenorowch
4 unkingisdone;2-theparallelclustertobeuse
unkingisdone;2-theparallelclustertobeusedforrowchunking;3-"locThreads",specifyingthatrowchunkingwillbedoneviathreadsonthehostmachine.printIntermedThedefaultvalueisTRUE,inwhichcaseprintintermediateresultsfromtheclusternodesbeforenalprocessing.DetailsFOCIisaforwardstepwisealgorithmthatusestheconditionaldependencecoefcient(codec)ateachstep,insteadofthemultiplecorrelationcoefcientasinordinaryforwardstepwise.Ifstop==TRUE,theprocessisstoppedattherstinstanceofnonpositivecodec,therebyselectingasubsetofvariables.Otherwise,asetofcovariatesofsizenum_features,orderedaccordingtopredictivepower(asmeasuredbycodec)isproduced.Parallelcomputation:Thecomputationcanbelengthy,sothepackageofferstwokindsofparallelcomputation.Therst,controlledbytheargumentnumCores,speciesthenumberofcorestobeusedonthehostmachine.Ifatagivensteptherearekcandidatevariablesunderconsiderationforinclusion,thesektasksareassignedtothevariouscores.Thesecondapproach,controlledbytheargumentparPlat("parallelplatform"),involvestheuserrstsettingupaclus
5 terviatheparallelpackage.Thedataaredivid
terviatheparallelpackage.Thedataaredividedintochunksbyrows,witheachclusternodeapplyingFOCItoitsdatachunk.Theunionoftheresultsisthenformed,andfedthroughFOCIonemoretimetoadjustthediscrepancies.Theideaisthatthatlaststepwillnotbetoolengthy,asthenumberofcandidatevariableshasalreadybeenreduced.Aclustersizeofrmayactuallyproduceaspeedupfactorofmorethanr(Matloff2016).Potentiallythebestspeedupisachievedbyusingthetwoapproachestogether.TherstapproachcannotbeusedonWindowsplatforms,asparallel::mcapplyhasnoeffect.Windowsusersshouldthususethesecondapproachonly.Inadditiontospeed,thesecondapproachisusefulfordiagnostics,astheresultsfromthedifferentchunksgivestheuseranideaofthedegreeofsamplingvariabilityintheFOCIresults.Inthesecondapproach,arandompermutationisappliedtotherowsofthedataset,asmanydatasetsaresortedbyoneormorecolumns.Notethatifacertainvalueofafeatureisrareinthefulldataset,itmaybeabsententirelyinsomechunk.ValueAnobjectofclass"foci",withattributesselectedVar,showingtheselectedvariablesindecreasingorderof(conditional)predictivepowe
6 r,andstepT,listingthe'codec'values.Typic
r,andstepT,listingthe'codec'values.Typicallythelatterwillbegintoleveloffatsomepoint,withadditionalmarginalimprovementsbeingsmall. foci5Author(s)MonaAzadkia,SouravChatterjee,andNormanMatloffReferencesAzadkia,M.andChatterjee,S.(2019).Asimplemeasureofconditionaldependence.https://arxiv.org/pdf/1910.12327.pdf.Matloff,N.(2016).SoftwareAlchemy:TurningComplexStatisticalComputationsintoEmbarrassingly-ParallelOnes.J.ofStat.Software.SeeAlsocodec,xicorExamples#Example1n=1000p=100xmatrix(rnorm(n*p),nrow=n)colnames(x)=paste0(rep("x",p),seq(1,p))yx[,1]*x[,10]+x[,20]^2#withnum_featuresequalto3andstopequaltoFALSE,fociwillgivealistof#threeselectedfeaturesresult1=foci(y,x,num_features=3,stop=FALSE,numCores=1)result1#Example2#sameexample,butstopaccordingtothestoppingruleresult2=foci(y,x,numCores=1)result2##Notrun:#Windowsuseofmulticorelibrary(parallel)clsmakeCluster(parallel::detectCores())foci(y,x,parPlat=cls)#runonphysicalclusterclsmakePSOCKcluster('machineA','machineB')foci(y,x,parPlat=cls)##End(Notrun) Indexcodec,2,3–5foci,2,3xicor,2,