9）20161014 Classification Logistic Regression

《9）20161014 Classification Logistic Regression》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LogisticRegressionStep1:FunctionSet1Wewanttofind??,??1

2、???=1+???−?If??,??1

3、?≥0.5,outputC1zOtherwise,outputC2??,??1

4、?=???=?∙?+?=෍????+?z?Functionset:Includingall??,??=??,??1

5、?differentwandbStep1:FunctionSetx1w1zwx??,??…ii…ixwizi…z??,??1

6、?…wISigmoidFunctionzxIb1zz

7、1ezLogisticRegressionLinearRegressionStep1:??,??=?෍????+???,??=෍????+???Output:between0and1Output:anyvalueStep2:Step3:Step2:GoodnessofaFunction?1?2?3??Training……Data?1?1?2?1Assumethedataisgeneratedbasedon??,??=??,??1

8、?Givenasetofwandb,whatisitsprobabilityofgeneratingthedata???,

9、?=??1??21−??3⋯????,??,??,??,?Themostlikelyw*andb*istheonewiththelargest??,?.?∗,?∗=???max??,??,??1?2?3123???…………?ො1=1?ො2=0?ො3=1?1?1?2?ො?:1forclass1,0forclass2??,?=??1??21−??3⋯?,??,??,??∗,?∗=???max??,??∗,?∗=???min−????,?=?,??,?−????,?=−????1−?ො11????1+1−?ො1??1−??1?,?0−????2−?ො12??

10、??2+1−?ො2??1−??2?,?0−??1−??3−?ො3????3+1−?ො3??1−??3?,?01……Step2:GoodnessofaFunction??,?=??1??21−??3⋯????,??,??,??,?−????,?=????1+????2+??1−??3⋯?,??,??,??ො?:1forclass1,0forclass2=෍−?ො??????+1−?ො???1−????,??,??CrossentropybetweentwoBernoullidistributionDistributionp:Distributionq:?

11、q?=1=???p?=1=?ොcrossp?=0=1−?ො?entropyq?=0=1−?????,?=−෍???????LogisticRegressionLinearRegressionStep1:??,??=?෍????+???,??=෍????+???Output:between0and1Output:anyvalueTrainingdata:??,?ො?Trainingdata:??,?ො?Step2:?ො?:1forclass1,0forclass2?ො?:arealnumber1??=෍????,?ො???=෍???−?ො?22??Cro

12、ssentropy:????,?ො?=−?ො??????+1−?ො???1−???Question:Whydon’twesimplyusesquareerroraslinearregression?Step3:Findthebestfunction1−??????,??−????,?=෍−?ො??????+1−?ො???1−????,??,????????????????,???????,??????==???????????????????????1???1??==??1−????????????,??=???=?∙?+?=෍????+?=1Τ1+?

13、??−??Step3:Findthebestfunction1−???????????,???,??−????,?=෍−?ො??????+1−?ො???1−????,??,??????????????1−??,?????1−??,??????==????????????????1−??1???1=−=−??1−????1−????1−????,??=???=?∙?+?=෍????+?=1Τ1+???−??Step3:Findthebestfunction1−???????????,???,??−????,?=෍−?ො??????+1−?ො???1−??

14、??,??,???????????=෍−?ො?1−?????−1−?ො???????,???,