Statistical foundations of machine learning

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1、SYLLABUSStatisticalfoundationsofmachinelearningGianlucaBontempiMachineLearningGroupComputerScienceDepartmentUniversiteLibredeBruxelles,ULBBelgique2ContentsIndex21Introduction11.1Notations.................................72Foundationsofprobability112.1Therandommodelofuncerta

2、inty....................112.1.1Axiomaticdefinitionofprobability...............132.1.2Symmetricaldefinitionofprobability..............132.1.3Frequentistdefinitionofprobability..............142.1.4TheLawofLargeNumbers...................142.1.5Independenceandconditionalprobabilit

3、y...........152.1.6Combinedexperiments......................162.1.7ThelawoftotalprobabilityandtheBayes’theorem.....182.1.8Arrayofjoint/marginalprobabilities..............182.2Randomvariables.............................202.3Discreterandomvariables........................212

4、.3.1Parametricprobabilityfunction.................222.3.2Expectedvalue,varianceandstandarddeviationofadiscreter.v..................................222.3.3Momentsofadiscreter.v.....................242.3.4Entropyandrelativeentropy..................242.4Continuousrandomvariabl

5、e.......................252.4.1Mean,variance,momentsofacontinuousr.v..........262.5Jointprobability.............................262.5.1Marginalandconditionalprobability..............272.6Commondiscreteprobabilityfunctions.................282.6.1TheBernoullitrial............

6、............282.6.2TheBinomialprobabilityfunction...............282.6.3TheGeometricprobabilityfunction..............292.6.4ThePoissonprobabilityfunction................292.7Commoncontinuousdistributions....................302.7.1Uniformdistribution.......................302

7、.7.2Exponentialdistribution.....................312.7.3TheGammadistribution....................312.7.4Normaldistribution:thescalarcase..............312.7.5Thechi-squareddistribution..................332.7.6Student’st-distribution.....................332.7.7F-distribution...

8、........................332.7.8Bivariatecontinuousdistribution................352.