(Ebook) Inference and Learning from Data: Volume 2: Inference by Sayed, Ali H. ISBN 9781009218269, 1009218263 download
https://ebooknice.com/product/inference-and-learning-from-datavolume-2-inference-55196410
Start reading on any device today!
(Ebook) Inference and Learning from Data: Volume 3: Learning by Ali H. Sayed ISBN 9781009218283, 100921828X
https://ebooknice.com/product/inference-and-learning-from-datavolume-3-learning-54244136
ebooknice.com
(Ebook) Inference and Learning from Data: Volume 1: Foundations by Ali H. Sayed ISBN 9781009218122, 1009218123
https://ebooknice.com/product/inference-and-learning-from-datavolume-1-foundations-54244458
ebooknice.com
(Ebook) Biota Grow 2C gather 2C cook by Loucas, Jason; Viles, James ISBN 9781459699816, 9781743365571, 9781925268492, 1459699815, 1743365578, 1925268497
https://ebooknice.com/product/biota-grow-2c-gather-2c-cook-6661374
ebooknice.com
(Ebook) Scientific Inference: Learning From Data by Simon Vaughan ISBN 9781107024823, 9781107607590, 9781139176071, 110702482X, 1107607590, 1139176072
https://ebooknice.com/product/scientific-inference-learning-from-data-35169050
ebooknice.com
(Ebook) Handbook of Statistics_29B, Volume 29: Sample Surveys: Inference and Analysis by Danny Pfeffermann, C.R. Rao ISBN 9780444531247, 0444531246
https://ebooknice.com/product/handbook-of-statistics-29b-volume-29-samplesurveys-inference-and-analysis-1958348
ebooknice.com
(Ebook) Airplane Flying Handbook: FAA-H-8083-3A by Federal Aviation Administration ISBN 9781560275572, 156027557X
https://ebooknice.com/product/airplane-flying-handbook-faa-h-8083-3a-1399456
ebooknice.com
(Ebook) Primary Mathematics 3A by HOERST ISBN 9789810185046, 9810185049
https://ebooknice.com/product/primary-mathematics-3a-33552624
ebooknice.com
(Ebook) The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie, Robert Tibshirani, Jerome Friedman ISBN 9780387848846, 0387848843
https://ebooknice.com/product/the-elements-of-statistical-learning-data-mininginference-and-prediction-50970994
ebooknice.com
(Ebook) Master SAT II Math 1c and 2c 4th ed (Arco Master the SAT Subject Test: Math Levels 1 & 2) by Arco ISBN 9780768923049, 0768923042
https://ebooknice.com/product/master-sat-ii-math-1c-and-2c-4th-ed-arco-masterthe-sat-subject-test-math-levels-1-2-2326094
ebooknice.com
InferenceandLearningfromData
VolumeII
Thisextraordinarythree-volumework,writteninanengagingandrigorousstylebya worldauthorityinthefield,providesanaccessible,comprehensiveintroductiontothe fullspectrumofmathematicalandstatisticaltechniquesunderpinningcontemporary methodsindata-drivenlearningandinference.
Thissecondvolume, Inference,buildsonthefoundationaltopicsestablishedin VolumeItointroducestudentstotechniquesforinferringunknownvariablesand quantities,includingBayesianinference,MarkovchainMonteCarlomethods,maximumlikelihood,variationalinference,hiddenMarkovmodels,Bayesiannetworks, andreinforcementlearning.
Aconsistentstructureandpedagogyisemployedthroughoutthisvolumeto reinforcestudentunderstanding,withover350end-of-chapterproblems(including solutionsforinstructors),180solvedexamples,almost200figures,datasets,and downloadableMatlabcode.Supportedbysistervolumes Foundations and Learning, anduniqueinitsscaleanddepth,thistextbooksequenceisidealforearly-career researchersandgraduatestudentsacrossmanycoursesinsignalprocessing,machine learning,statisticalanalysis,datascience,andinference.
AliH.Sayed isProfessorandDeanofEngineeringatÉcolePolytechniqueFédérale deLausanne(EPFL),Switzerland.HehasalsoservedasDistinguishedProfessor andChairmanofElectricalEngineeringattheUniversityofCalifornia,LosAngeles (UCLA),USA,andasPresidentoftheIEEESignalProcessingSociety.Heisa memberoftheUSNationalAcademyofEngineering(NAE)andTheWorldAcademy ofSciences(TWAS),andarecipientofseveralawards,includingthe2022IEEE FourierAwardandthe2020IEEENorbertWienerSocietyAward.HeisaFellow oftheIEEE,EURASIP,andAAAS.
InferenceandLearningfromData
VolumeII:Inference
ALIH.SAYED
ÉcolePolytechniqueFédéraledeLausanne
UniversityofCaliforniaatLosAngeles
ShaftesburyRoad,CambridgeCB28EA,UnitedKingdom
OneLibertyPlaza,20thFloor,NewYork,NY10006,USA
477WilliamstownRoad,PortMelbourne,VIC3207,Australia
314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467
CambridgeUniversityPressispartofCambridgeUniversityPress&Assessment, adepartmentoftheUniversityofCambridge.
WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle: www.cambridge.org/highereducation/isbn/9781009218269
DOI: 10.1017/9781009218245
©AliH.Sayed2023
Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisions ofrelevantcollectivelicensingagreements,noreproductionofanypartmaytake placewithoutthewrittenpermissionofCambridgeUniversityPress&Assessment.
Firstpublished2023
PrintedintheUnitedKingdombyBellandBainLtd
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
ISBN-3VolumeSet978-1-009-21810-8Hardback
ISBN-VolumeI978-1-009-21812-2Hardback
ISBN-VolumeII978-1-009-21826-9Hardback
ISBN-VolumeIII978-1-009-21828-3Hardback
Additionalresourcesforthispublicationat www.cambridge.org/sayed-vol2 CambridgeUniversityPress&Assessmenthasnoresponsibilityforthepersistence oraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhis publicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill remain,accurateorappropriate.
Inlovingmemoryofmyparents
VOLUMEIFOUNDATIONS
26.6ATCTrackingMethod
26.7UnifiedDecentralizedAlgorithm
26.8ConvergencePerformance
VOLUMEIIINFERENCE
P.2GlimpseofHistory
P.3OrganizationoftheText
P.4HowtoUsetheText
P.5SimulationDatasets
P.6Acknowledgments
29.6Minimum-VarianceUnbiasedEstimation
29.7CommentariesandDiscussion
45.BConvergenceofValueIteration
45.CProofof -Optimality
45.DConvergenceofPolicyIteration
45.EPiecewiseLinearProperty
45.FBellmanPrincipleofOptimality
46.1Model-BasedLearning
46.2MonteCarloPolicyEvaluation
46.3TD(0)Algorithm
46.4Look-AheadTDAlgorithm
46.5TD(λ)Algorithm
46.6TrueOnlineTD(λ)Algorithm
46.7Off-PolicyLearning
46.8CommentariesandDiscussion
46.AUsefulConvergenceResult
46.BConvergenceofTD(0)Algorithm
46.CConvergenceofTD(λ)Algorithm
46.DEquivalenceofOfflineImplementations
47.1SARSA(0)Algorithm
47.2Look-AheadSARSAAlgorithm
47.3SARSA(λ)Algorithm
47.4Off-PolicyLearning
47.5OptimalPolicyExtraction
47.6 Q-LearningAlgorithm
47.7ExplorationversusExploitation
47.8 Q-LearningwithReplayBuffer
47.9Double Q-Learning
47.10CommentariesandDiscussion
47.AConvergenceofSARSA(0)Algorithm
47.BConvergenceof Q-LearningAlgorithm
48.1StochasticGradientTD-Learning
48.2Least-SquaresTD-Learning
VOLUMEIIILEARNING
P.3OrganizationoftheText
P.4HowtoUsetheText
P.5SimulationDatasets
60.ACountingTheorem
64.7CommentariesandDiscussion
65.6DropoutStrategy
66.4Pre-TrainingusingStackedRBMs
Preface
Learningdirectlyfromdataiscriticaltoahostofdisciplinesinengineering andthephysical,social,andlifesciences.Modernsocietyisliterallydrivenbyan interconnectedwebofdataexchangesatratesunseenbefore,anditreliesheavilyondecisionsinferredfrompatternsindata.Thereisnothingfundamentally wrongwiththisapproach,exceptthattheinferenceandlearningmethodologies needtobeanchoredonsolidfoundations,befairandreliableintheirconclusions, andberobusttounwarrantedimperfectionsandmaliciousinterference.
P.1EMPHASISONFOUNDATIONS
Giventheexplosiveinterestindata-drivenlearningmethods,itisnotuncommon toencounterclaimsofsuperiordesignsintheliteraturethataresubstantiated mainlybysporadicsimulationsandthepotentialfor“life-changing”applications ratherthanbyanapproachthatisfoundedonthewell-testedscientificprincipletoinquiry.Forthisreason,oneofthemainobjectivesofthistextisto highlight,inaunifiedandformalmanner,thefirmmathematicalandstatistical pillarsthatunderliemanypopulardata-drivenlearningandinferencemethods. Thisisanontrivialtaskgiventhewidescopeoftechniquesthatexist,andwhich haveoftenbeenmotivatedindependentlyofeachother.Itisneverthelessimportantforpractitionersandresearchersaliketoremaincognizantofthecommon foundationalthreadsthatrunacrossthesemethods.Itisalsoimperativethat progressinthedomainremainsgroundedonfirmtheory.Astheaphorismoften attributedtoLewin(1945)states,“ thereisnothingmorepracticalthanagood theory.”AccordingtoBedeian(2016),thissayinghasanevenolderhistory.
Rigorousdataanalysis,andconclusionsderivedfromexperimentationand theory,havebeendrivingsciencesincetimeimmemorial.AsreportedbyHeath (1912),theGreekscientistArchimedesofSyracusedevisedthenowfamous Archimedes’Principleaboutthevolumedisplacedbyanimmersedobjectfrom observinghowthelevelofwaterinatubrosewhenhesatinit.Intheaccount byHall(1970),Gauss’formulationoftheleast-squaresproblemwasdrivenby hisdesiretopredictthefuturelocationoftheplanetoidCeresfromobservationsofitslocationover41priordays.Therearenumeroussimilarexamples bynotablescientistswhereexperimentationledtohypothesesandfromthere
tosubstantiatedtheoriesandwell-foundeddesignmethodologies.Scienceisalso fullofprogressinthereversedirection,wheretheorieshavebeendevelopedfirst tobevalidatedonlydecadeslaterthroughexperimentationanddataanalysis. Einstein(1916)postulatedtheexistenceofgravitationalwavesover100years ago.Ittookuntil2016todetectthem!Regardlessofwhichdirectiononefollows, experimentationtotheoryorthereverse,thematchbetweensolidtheoryand rigorousdataanalysishasenabledscienceandhumanitytomarchconfidently towardtheimmenseprogressthatpermeatesourmodernworldtoday.
Forsimilarreasons,data-drivenlearningandinferenceshouldbedeveloped withstrongtheoreticalguarantees.Otherwise,theconfidenceintheirreliability canbeshakenifthereisover-relianceon“proofbysimulationorexperience.” Wheneverpossible,weexplaintheunderlyingmodelsandstatisticaltheoriesfor alargenumberofmethodscoveredinthistext.Agoodgraspofthesetheorieswill enablepractitionersandresearcherstodevisevariationswithgreatermastery. Weweavethroughthefoundationsinacoherentandcohesivemanner,andshow howthevariousmethodsblendtogethertechniquesthatmayappeardecoupled butareactuallyfacetsofthesamecommonmethodology.Inthisprocess,we discoverthatagoodnumberoftechniquesarewell-groundedandmeetproven performanceguarantees,whileothermethodsaredrivenbyingeniousinsights butlacksolidjustificationsandcannotbeguaranteedtobe“fail-proof.”
Researchersonlearningandinferencemethodsareofcourseawareofthe limitationsofsomeoftheirapproaches,somuchsothatweencountertoday manystudies,forexample,onthetopicof“explainablemachinelearning.”The objectivehereistounderstandwhylearningalgorithmsproducecertainrecommendations.Whilethisisanimportantareaofinquiry,itneverthelesshighlights oneinterestingshiftinparadigm.Inthepast,theemphasiswouldhavebeenon designinginferencemethodsthatrespondtotheinputdataincertaindesirable andcontrollableways.Today,inmanyinstances,theemphasisistosticktothe availablealgorithms(often,outofconvenience)andtrytounderstandorexplain whytheyarerespondingincertainwaystotheinput!
Writingthistexthasbeenarewardingjourneythattookmefromtheearly daysofstatisticalmathematicaltheorytothemodernstateofaffairsinlearningtheory.Onecanonlystandinaweatthewondrousideasthathavebeen introducedbynotableresearchersalongthistrajectory.Atthesametime,one observeswithsomeconcernanemergingtrendinrecentyearswheresolidfoundationsreceivelessattentioninlieuof“speedpublishing”andover-relianceon “illustrationbysimulation.”Thisisofcoursenotthenormandmostresearchers inthefieldstayhonesttothescientificapproachtoinquiryanddesign.After concludingthiscomprehensivetext,Istandhumbledattherealizationof“ how littleweknow !”Therearecountlessquestionsthatremainopen,andevenfor manyofthequestionsthathavebeenanswered,theiranswersrelyonassumptionsor(over)simplifications.Itisunderstandablethatthecomplexityofthe problemswefacetodayhasincreasedmanifold,andingeniousapproximations becomenecessarytoenabletractablesolutions.
P.2GLIMPSEOFHISTORY
Readingthroughthetext,thealertreaderwillquicklyrealizethatthecorefoundationsofmodern-daymachinelearning,dataanalytics,andinferencemethods datebackforatleasttwocenturies,withcontributionsarisingfromarange offieldsincludingmathematics,statistics,optimizationtheory,informationtheory,signalprocessing,communications,control,andcomputerscience.Forthe benefitofthereader,IreproduceherewithpermissionfromIEEEsomehistoricalremarksfromtheeditorialIpublishedinSayed(2018).Iexplainedthere thatthesedisciplineshavegeneratedastringof“bigideas”thataredrivingtoday multi-facetedeffortsintheageof“bigdata”andmachinelearning.Generationsof studentsinthestatisticalsciencesandengineeringhavebeentrainedintheartof modeling,problemsolving,andoptimization.Theiralgorithmspowereverything fromcellphones,tospacecraft,roboticexplorers,imagingdevices,automated systems,computingmachines,andalsorecommendersystems.Thesestudents masteredthefoundationsoftheirfieldsandhavebeenwellpreparedtocontribute totheexplosivegrowthofdataanalysisandmachinelearningsolutions.
Asthelistbelowshows,manywell-knownengineeringandstatisticalmethods haveactuallybeenmotivatedbydata-driveninquiries,evenfromtimesremote. Thelistisatourofsomeolderhistoricalcontributions,whichisofcoursebiasedbymypersonalpreferencesandisnotintendedtobeexhaustive.Itis onlymeanttoillustratehowconceptsfromstatisticsandtheinformationscienceshavealwaysbeenatthecenterofpromotingbigideasfordataandmachinelearning.Readerswillencountertheseconceptsinvariouschaptersinthe text.Readerswillalsoencounteradditionalhistoricalaccountsintheconcluding remarksofeachchapter,andinparticularcommentsonnewercontributionsand contributors.
LetmestartwithGausshimself,whoin1795attheyoungageof18,was fittinglinesandhyperplanestoastronomicaldataandinventedtheleast-squares criterionforregressionanalysis–seethecollectionofhisworksinGauss(1903). Heevendevisedtherecursiveleast-squaressolutiontoaddresswhatwasa“big” dataproblemforhimatthetime:Hehadtoavoidtediousrepeatedcalculations byhandasmoreobservationaldatabecameavailable.Whatawonderfulbigidea foradata-drivenproblem!Ofcourse,Gausshadmanyotherbigideas.
deMoivre(1730),Laplace(1812),andLyapunov(1901)workedonthecentral limittheorem.Thetheoremdealswiththelimitingdistributionofaveragesof “large”amountsofdata.Theresultisalsorelatedtothelawof“large”numbers, whichevenhasthequalification“large”initsname.Again,bigideasmotivated by“large”dataproblems.
Bayes(camid-1750s)andLaplace(1774)appeartohaveindependentlydiscoveredtheBayesrule,whichupdatesprobabilitiesconditionedonobservations–seethearticlebyBayesandPrice(1763).Theruleformsthebackboneofmuch ofstatisticalsignalanalysis,Bayesclassifiers,Naïveclassifiers,andBayesian networks.Again,abigideafordata-driveninference.
