CS 59000 Machine learningLecture 3Yuan (Alan) Qi ([email protected])Bayes’ Theoremposterior likelihood × priorThe Multivariate GaussianMaximum (Log) LikelihoodMaximum Likelihood for RegressionDetermine by minimizing sum-of-squares error, .Predictive Distribution by MLMAP: A Step towards BayesDetermine by minimizing regularized sum-of-squares error, .Bayesian Curve FittingBayesian Predictive (Posterior) DistributionModel Selection via Cross-ValidationDecision TheoryInference stepDetermine either or .Decision stepFor given x, determine optimal t.Minimum Misclassification RateMinimum Expected LossExample: classify medical images as ‘cancer’ or ‘normal’DecisionTruthMinimum Expected LossRegions are chosen to minimizeReject OptionDecision Theory for RegressionInference stepDetermine .Decision stepFor given x, make optimal prediction, y(x), for t.Loss function:The Squared Loss FunctionMinimizeThe Squared Loss FunctionMinimizeEntropyImportant quantity in• coding theory• statistical physics• machine learningEntropyCoding theory: x discrete with 8 possible states; how many bits to transmit the state of x?All states equally
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