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1、InductiveandAnalyticalLearningInductivelearningAnalyticallearningHypothesis?tsdataHypothesis?tsdomaintheoStatisticalinferenceDeductiveinferenceRequireslittlepriorknowledgeLearnsfromscarcedataSyntacticinductivebiasBiasisdomaintheory?WhatWeWouldLikeAnalytical learningInductive learningPlentiful data N
2、o prior knowledgePerfect prior knowledgeScarce dataGeneralpurposelearningmethod?Nodomaintheory?learnaswellasinductivemethods?Perfectdomaintheory?learnaswellasProlog?EBG?Accomodatearbitraryandunknownerrorsindomaintheory?Accomodatearbitraryandunknownerrorsintrainingdata?Domaintheory?Cup?Stable?Liftabl
3、e?OpenVesselStable?BottomIsFlatLiftable?Graspable?LightGraspable?HasHandleOpenVessel?HasConcavity?ConcavityPointsUpTrainingexamples?CupsNon?CupsBottomIsFlatppppppppConcavityPointsUppppppppExpensiveppppFragileppppppHandleOnTopppHandleOnSidepppHasConcavitypppppppppHasHandlepppppLightppppppppMadeOfCera
4、micppppMadeOfPaperppMadeOfStyrofoampppp?KBANNKBANN?dataD?domaintheoryB?CreateafeedforwardnetworkhequivalenttoB?UseBackproptotunehto?tD?NeuralNetEquivalenttoDomainTheoryHasHandle HandleOnTop HandleOnSideBottomIsFlatHasConcavity ConcavityPointsUpLightMadeOfCeramicMadeOfPaperMadeOfStyrofoamExpensiveFra
5、gileCupStableLiftableOpenVesselGraspable?CreatingNetworkEquivalenttoDo?mainTheoryCreateoneunitperhornclauserule?i?e?anANDunit?Connectunitinputstocorrespondingclauseantecedents?Foreachnon?negatedantecedent?correspondinginputweightw?W?whereWissomeconstant?Foreachnegatedantecedent?inputweightw?W?Thresh
6、oldweightw?n?W?wherenisnumberofnon?negatedantecedentsFinally?addmanyadditionalconnectionswithnear?zeroweightsLiftable?Graspable?Heavy?Resultofre?ningthenetworkHasHandle HandleOnTop HandleOnSideBottomIsFlatHasConcavity ConcavityPointsUpLightMadeOfCeramicMadeOfPaperMadeOfStyrofoamExpensiveFragileStabl
7、eLiftableOpen-VesselLarge positive weight Large negative weight Negligible weightCupGraspable?KBANNResultsClassifyingpromoterregionsinDNAleaveoneouttesting?Backpropagation?errorrate?KBANN?Similarimprovementsonotherclassi?cation?controltasks?HypothesisspacesearchinKBANNHypothesis SpaceHypotheses that
8、 fit training data equally well Initial hypothesis for KBANNInitial hypothesis for BACKPROPAGATION?EBNNKeyidea?Previouslylearnedapproximatedomaintheory?Domaintheoryrepresentedbycollectionofneuralnetworks?Learntargetfunctionasanotherneuralnetwork?BottomIsFlat ConcavityPointsUp Expensive Fragile Handl
9、eOnTop HandleOnSide HasConcavity HasHandle Light MadeOfCeramic MadeOfPaper MadeOfStyrofoamCupBottomIsFlat ConcavityPointsUp Expensive Fragile HandleOnTop HandleOnSide HasConcavity HasHandle Light MadeOfCeramic MadeOfPaper MadeOfStyrofoam= T = T = T = T = F = T = T = T = T = T = F = FGraspableStableO
10、penVesselLiftableCupTarget network:0.20.8Training derivativesCuptargetExplanation of training example in terms of domain theory:Cup = T?Modi?edObjectiveforGradientDescentE?Xi?f?xi?f?xi?iXj?BBB?A?x?xj?f?x?xj?CCCA?x?xi?where?i?jA?xi?f?xi?jc?f?x?istargetfunction?f?x?isneuralnetapproximationtof?x?A?x?is
11、domaintheoryapproximationtof?x?xxfxxx123f(x)gh f(x )1 f(x )2 f(x )3x?HypothesisSpaceSearchinEBNNHypotheses that maximize fit to dataHypothesis SpaceBACKPROPAGATION SearchTANGENTPROP SearchHypotheses that maximize fit to data and prior knowledge?SearchinFOCL.2+,32+,32+,44+,2Generated by thedomain the
12、oryCupHasHandleCupHasHandleCupFragileCupBottomIsFlat, Light, HasConcavity, ConcavityPointsUpCup2+,00+,24+,0.CupBottomIsFlat, Light, HasConcavity, ConcavityPointsUp HandleOnTopBottomIsFlat, Light, HasConcavity, ConcavityPointsUp,HandleOnTopBottomIsFlat, Light, HasConcavity, ConcavityPointsUp, HandleOnSideCupCup?FOCLResultsRecognizinglegalchessendgamepositions?positive?negativeexamples?FOIL?FOCL?usingdomaintheorywith?accuracy?NYNEXtelephonenetworkdiagnosis?trainingexamples?FOIL?FOCL?usingdomaintheorywith?accuracy?
