03Lecture noteLinear and Logistic Regression.docx
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03Lecture noteLinear and Logistic Regression.docx
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03LecturenoteLinearandLogisticRegression
Lecturenote3:
LinearandLogisticRegressioninTensorFlow
CS20:
TensorFlowforDeepLearningResearch(cs20.stanford.edu)
PreparedbyChipHuyen(chiphuyen@cs.stanford.edu)
ThanksLaurenceMoroney,AkshayAgrawalforreviewingthenote
Phew,thelastlecturewaslong.Goodnewsisthatwe’redonewithallthealphabeticallearningandcannowbeofftobuildingthings.Beforestartingtheadventures,let’smakesurethatwe’refamiliarwithallthekeyconcepts.Ifyou’reunsureaboutanyofthese,youshouldgobacktotheprevioustwolectures.
Graphsandsessions
TFOps:
constants,variables,functions
TensorBoard
Lazyloading
LinearRegression:
Predictlifeexpectancyfrombirthrate
Let’sstartwithasimplelinearregressionexample.Ihopeyouallarealreadyfamiliarwithlinearregression.Ifnot,youcanreadaboutitonWikipedia.Basically,we’llbebuildingaverysimpleneuralnetworkconsistingofonelayertoinferthelinearrelationshipbetweenoneexplanatoryvariableXandonedependentvariableY.
Problem
Irecentlycameacrossthevisualizationoftherelationshipbetweenbirthratesandlifeexpectanciesofdifferentcountriesaroundtheworldandfoundthatfascinating.Basically,itlookslikethemorechildrenyouhave,theyoungeryouaregoingtodie!
YoucanplaythevisualizationcreatedbyGooglebasedonthedatacollectedbytheWorldBankhere.
Myquestionis,canwequantifythatrelationship?
Inotherwords,ifthebirthrateofacountryisanditslifeexpectancyis,canwefindalinearfunctionfsuchthat?
Ifweknowthatrelationship,giventhebirthrateofacountry,wecanpredictthelifeexpectancyofthatcountry.
Forthisproblem,wewillbeusingasubsetoftheWorldDevelopmentIndicatorsdatasetcollectedbytheWorldBank.Forsimplicity,wewillbeusingdatafromtheyear2010only.Youcandownloadthedatafromclass’sGitHubfolderhere.
DatasetDescription
Name:
Birthrate-lifeexpectancyin2010
X=birthrate.Type:
float.
Y=lifeexpectancy.Type:
foat.
Numberofdatapoints:
190
Approach
First,assumethattherelationshipbetweenthebirthrateandthelifeexpectancyislinear,whichmeansthatwecanfindwandbsuchthat.
Tofindwandb(inthiscase,theyarebothscalars),wewillusebackpropagationthroughaonelayerneuralnetwork.Forthelossfunction,wewillbeusingmeansquarederror.Aftereachepoch,wemeasurethemeansquareddifferencebetweentheactualvalueYsandthepredictedvaluesofYs.
Youcandownloadthefileexamples/03_linreg_starter.pyfromtheclass’sGitHubrepotogiveitashotyourself.Afteryou’redone,youcancomparewiththesolutionbelow.Youcanalsovisitexamples/03_linreg_placeholder.pyonGitHubfortheexecutablescript.
importtensorflowastf
importutils
DATA_FILE="data/birth_life_2010.txt"
#Step1:
readindatafromthe.txtfile
#dataisanumpyarrayofshape(190,2),eachrowisadatapoint
data,n_samples=utils.read_birth_life_data(DATA_FILE)
#Step2:
createplaceholdersforX(birthrate)andY(lifeexpectancy)
X=tf.placeholder(tf.float32,name='X')
Y=tf.placeholder(tf.float32,name='Y')
#Step3:
createweightandbias,initializedto0
w=tf.get_variable('weights',initializer=tf.constant(0.0))
b=tf.get_variable('bias',initializer=tf.constant(0.0))
#Step4:
constructmodeltopredictY(lifeexpectancyfrombirthrate)
Y_predicted=w*X+b
#Step5:
usethesquareerrorasthelossfunction
loss=tf.square(Y-Y_predicted,name='loss')
#Step6:
usinggradientdescentwithlearningrateof0.01tominimizeloss
optimizer=tf.train.GradientDescentOptimizer(learning_rate=0.001).minimize(loss)
withtf.Session()assess:
#Step7:
initializethenecessaryvariables,inthiscase,wandb
sess.run(tf.global_variables_initializer())
#Step8:
trainthemodel
foriinrange(100):
#run100epochs
forx,yindata:
#Sessionrunstrain_optominimizeloss
sess.run(optimizer,feed_dict={X:
x,Y:
y})
#Step9:
outputthevaluesofwandb
w_out,b_out=sess.run([w,b])
Aftertrainingfor100epochs,wegottheaveragesquarelosstobe30.04withw=-6.07,b=84.93.Itconfirmsourbeliefthatthere’sanegativecorrelationbetweenthebirthrateandthelifeexpectancyofacountry.Andno,itdoesn’tmeanthathavingachildtakesoff6yearsofyourlife.
YoucanmakeotherassumptionsabouttherelationshipbetweenXandY.Forexample,ifwehaveaquadraticfunction:
Tofindw,u,andbforthismodel,weonlyhavetoaddanothervariableuandchangetheformulaforY_predicted.
#Step3:
createvariables:
weights_1,weights_2,bias.Allareinitializedto0
w=tf.get_variable('weights_1',initializer=tf.constant(0.0))
u=tf.get_variable('weights_2',initializer=tf.constant(0.0))
b=tf.get_variable('bias',
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