learning theory an approximation theory viewpoint

《learning theory an approximation theory viewpoint》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LearningTheoryAnApproximationTheoryViewpointForewordThisbookbyFelipeCuckerandDing-XuanZhougivessolidmathematicalfoundationsandnewinsightstothesubjectcalled“learningtheory”.SomeyearsagoFelipeandIweretryingtofindsomethingaboutbrainscienceandartificialintelligencestartingfromli

2、teratureonneuralnets.Itwasinthissettingthatweencounteredthebeautifulideasandfastalgorithmsoflearningtheory.Eventuallyweweremotivatedtowriteonthemathematicalfoundationsofthisnewareaofscience.Ihavefoundthisarenatobeexcitingwithitsnewchallengesandgrowingnumberofapplica-tions.

3、Forexampleamajorproblemistheunificationofdynamicalsystemsandlearningtheory.Anotheristodevelopacomparativestudyofthepresentusefulalgorithmsandtogiveunitytothesealgorithms.Howcanonetalkaboutthe“bestalgorithm”orfindthemostappropriatealgorithmforaparticulartaskwhentherearesomany

4、desirablefeatureswiththeirassociatedtrade-off?Howcanoneseetheworkingofaspectsofthehumanbrainandmachinevisioninthesameframework?Iknowbothauthorswell.IvisitedFelipeinBarcelonaovertwelveyearsagoforseveralmonths,andwhenItookapositioninHongKongin1995,Iaskedhimtojoinme.ThereLenor

5、eBlum,MikeShub,Felipe,andIfinishedabookonrealcomputationandcomplexity.AlthoughIreturnedtotheUSAin2001,FelipecontinueshisjobattheCityUniversityofHongKong.Inspiteofthedistancewehavecontinuedtowritepaperstogether.IcametoknowDing-XuanasacolleagueinthemathdepartmentatCityUnivers

6、ity.Wehavewrittenanumberofpaperstogetheronvariousaspectsoflearningtheory.Itgivesmegreatpleasuretocontinuetoworkwithbothmathematicians.Iamproudofourjointaccomplishments.Ileavetotheauthorsthetaskofdescribingthecontentsoftheirbook.Iwillgivesomepersonalperspectiveandmotivation

7、forwhattheyaredoing.Computationalsciencedemandsanunderstandingoffast,robustalgorithms.Thesameappliestomoderntheoriesofartificialandhumanintelligence.Partofthisunderstandingisacomplexitytheoreticanalysis.HereIdon’tspeakofaliteralcountofarithmeticoperations(althoughthatisaby-

8、product),butrathertothequestion:“whatsamplesizeyieldsagivenaccuracy?”Betteryet,describeth