理解深度学习习题答案.docx

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理解深度学习习题答案.docx

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Answerbookletforstudents

July25,2023

PAGE2

Answerbooklet

ThisdocumentaccompaniesthebookUnderstandingDeepLearning.Itcontainsanswerstoaselectedsubsetoftheproblemsattheendofeachchapterofthemainbook.TheremaininganswersareavailableonlytoinstructorsviatheMITPress.

Thisbooklethasnotyetbeencheckedverycarefully.IreallyneedyourhelpinthisregardandI’dbeverygratefulifyouwouldmailmeatudlbookmail@ifyoucannotunderstandthetextorifyouthinkthatyoufindamistake.Suggestionsforextraproblemswillalsobegratefullyreceived!

SimonPrinceJuly25,2023

PAGE4

Chapter2

Supervisedlearning

Problem2.1Towalk“downhill”onthelossfunction(equation2.5),wemeasureitsgradientwithrespecttotheparameters?0and?1.Calculateexpressionsfortheslopes?L/??0and?L/??1.

Problem2.2Showthatwecanfindtheminimumofthelossfunctioninclosed-formbysettingtheexpressionforthederivativesfromproblem2.1tozeroandsolvingfor?0and?1.

Problem2.3Considerreformulatinglinearregressionasagenerativemodelsowehavex=g[y,?]=?0+?1y.Whatisthenewlossfunction?Findanexpressionfortheinversefunctiony=g?1[x,?]thatwewouldusetoperforminference.Willthismodelmakethesamepredictionsasthediscriminativeversionforagiventrainingdataset{xi,yi}?Onewaytoestablishthisistowritecodethatfitsalinetothreedatapointsusingbothmethodsandseeiftheresultisthesame.

Answer

Wecantriviallysolveforxbyrearrangingtheequation:

y=x??0.

Theanswersarenotthesame;youcanshowthisbyfindingequationsfortheslopeandinterceptofthefunctionoflinerelatingxtoyandshowingtheyarenotthesame.Oryoucanjusttryfittingbothmodelstos

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