pattern recognition and machine learning solutions

《pattern recognition and machine learning solutions》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、PatternRecognitionandMachineLearningSolutionstotheExercises:Web-EditionMarkusSvensenandChristopherM.Bishop´Copyrightc2002–2009Thisisthesolutionsmanual(web-edition)forthebookPatternRecognitionandMachineLearning(PRML;publishedbySpringerin2006).Itcontainssolutionstot

2、hewwwexercises.ThisreleasewascreatedSeptember8,2009.FuturereleaseswithcorrectionstoerrorswillbepublishedonthePRMLweb-site(seebelow).Theauthorswouldliketoexpresstheirgratitudetothevariouspeoplewhohaveprovidedfeedbackonearlierreleasesofthisdocument.Inparticular,the“

3、BishopReadingGroup”,heldintheVisualGeometryGroupattheUniversityofOxfordprovidedvaluablecommentsandsuggestions.Theauthorswelcomeallcomments,questionsandsuggestionsaboutthesolutionsaswellasreportson(potential)errorsintextorformulaeinthisdocument;pleasesendanysuchfee

4、dbacktoprml-fb@microsoft.comFurtherinformationaboutPRMLisavailablefromhttp://research.microsoft.com/∼cmbishop/PRMLContentsContents5Chapter1:Introduction...........................7Chapter2:ProbabilityDistributions....................20Chapter3:LinearModelsforRegre

5、ssion..................35Chapter4:LinearModelsforClassification................41Chapter5:NeuralNetworks........................46Chapter6:KernelMethods.........................54Chapter7:SparseKernelMachines.....................59Chapter8:GraphicalModels..........

6、..............63Chapter9:MixtureModelsandEM....................68Chapter10:ApproximateInference.....................72Chapter11:SamplingMethods.......................83Chapter12:ContinuousLatentVariables..................85Chapter13:SequentialData.................

7、.......92Chapter14:CombiningModels.......................9756CONTENTSSolutions1.1–1.47Chapter1Introduction1.1Substituting(1.1)into(1.2)andthendifferentiatingwithrespecttowiweobtain!XNXMwxj−txi=0.(1)jnnnn=1j=0Re-arrangingtermsthengivestherequiredresult.1.4Weareofte

8、ninterestedinfindingthemostprobablevalueforsomequantity.Inthecaseofprobabilitydistributionsoverdiscretevariablesthisposeslittleproblem.However,forcontinu