Transcription of Chapter 2: Entropy and Mutual Information
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Chapter 2: Entropy and Mutual Information
University of Illinois at Chicago ECE 534, Fall 2009, Natasha DevroyeUniversity of Illinois at Chicago ECE 534, Fall 2009, Natasha DevroyeChapter 2: Entropy and Mutual InformationUniversity of Illinois at Chicago ECE 534, Fall 2009, Natasha DevroyeChapter 2 outline Definitions Entropy Joint Entropy , conditional Entropy Relative Entropy , Mutual Information Chain rules Jensen s inequality Log-sum inequality Data processing inequality Fano s inequalityUniversity of Illinois at Chicago ECE 534, Fall 2009, Natasha DevroyeDefinitionsA discrete random variableXtakes on valuesxfrom the discrete probability mass function (pmf) is described bypX(x)=p(x) = Pr{X=x},forx of Illinois at Chicago ECE 534, Fall 2009, Natasha DevroyeDefinitionsCopyright Cambridge University Press 2003. On-screen viewing permitted. Printing not permitted. can buy this book for 30 pounds or $50. See for , Entropy ,andInferenceThischapter,anditss ibling,Chapter8, ,thenameofthesong,andwhatthenameoftheson gwascalled(Carroll,1998),wewillsometimes needtobecarefultodistinguishbetweenarand omvariable,thevalueoftherandomvariable, ,however,Iwillusethemostsimpleandfriendl ynotationpossible, ,ifsomethingis truewithprobability1 ,Iwillusuallysimplysaythatitis true.
University of Illinois at Chicago ECE 534, Fall 2009, Natasha Devroye Chapter 2: Entropy and Mutual Information University of Illinois at …
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