RuleFit315b - ! % "& ( '! ! $&...

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Unformatted text preview: ! % "& ( '! ! $& " $% % % % ) ' " #$ * +, & , ! % & +- .% % % $ * +, 0 2 1 ( ( /! $ ( ( + * !0 3445$ &6 ' ) ' '& % & ' / (7 * +, + 8( * % % % 9 ! & #- $% % ' 6 !0 3445$% % - " #- ' ' % ! : 9 & . $ % , % ; - % '0 ! ) $ - 8 <7 % % % & * ) & ' & ; % =+ : - & > - 7 ( ? 0 - & - & ! $ 0 I ( x 14 ≤ u ) x 14 I ( x 14 > u ) u 1 I(x32 ∈{a,b, c}) 2 I(x32 ∉{a,b,c}) I (x7 = z) x32 7 4 I(x14 ≤t) I (x7 ≠ z) {z } {a, b, c} 3 x7 x14 t 5 8 I(x14 >t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x 14 ≤ u ) x 14 I ( x 14 > u ) u 1 I(x32 ∈{a,b, c}) 2 I(x32 ∉{a,b,c}) I (x7 = z) x32 7 4 I(x14 ≤t) 5 I (x7 ≠ z) {z } {a, b, c} 3 x7 x14 t 8 I(x14 >t) 6 !" !" ,7 * * +% + + + + % ", ! + + '$ * % & ' + .+ .+ .+ & . - ,, .# -# . ' + + ( % ' & !$ !$ (' . N - -' ' % . - - - & ; . 7 &* * * ,7 ( * + #- ( % * ! *! * / ! & / & % ! & /& #- * * ; ! ! ) 0 ' % ! 0 ! ! ; % ! 0 0 ! 7* ) % / 6 % G (* 0 1 2 1 3 E O5: % /P O3: 4 / / /P O P 0 % 5HI ! ! G $ '$% 5& ! $% 5& 0 * / ) ./ % ) / ! ! % % ! 80 60 40 0 20 Relative importance 80 60 40 20 0 Relative importance 100 Variable importance − x = 0.5 100 Variable importance − all 6 8 3 7 1 4 5 2 66 1 2 3 4 5 6 7 8 21 Variable importance − low Variable importance − high 80 60 40 0 20 Relative importance 80 60 40 20 0 Relative importance 100 Variable 100 Variable 1 2 3 4 5 6 Variable 7 8 66 1 2 3 4 5 6 Variable 7 8 66 Simulated data − Interactions 0.30 0.25 Interaction strength 0.20 0.15 0.10 0.05 0.00 1 2 3 4 5 6 7 Variable * * * * ) !' #$ 3 3 ! $ / / 8 9 10 Interaction strength Simulated data − interactions with x1 0.4 0.3 0.2 0.1 0.0 2 3 4 5 6 7 8 9 10 Variable Three variable interactions with x1 & x2 Interaction strength 0.20 0.15 0.10 0.05 0.00 3 4 5 6 7 8 9 10 Variable %* , %* * * * !' * #$ 3 !' #$ 3 ! $ ! $ Simulated data − Interactions with x4 Interaction strength 0.4 0.3 0.2 0.1 0.0 1 2 3 5 6 7 8 9 10 9 10 #$ 3 ! Variable Simulated data − Interactions with x5 Interaction strength 0.4 0.3 0.2 0.1 0.0 1 2 3 4 6 7 8 Variable %* , %* * * * * !' !' #$ 3 $ ! $ Partial dependence Partial dependence 2.0 1.5 partia 1.5 l depe partial dependence 1.0 1.0 0.5 e ndenc 0.5 0.0 0.8 0.0 0.6 0.0 0.8 0.6 ble ria Va 0.8 0.2 0.2 1 0.6 0.2 ria Va ble 5 ria Va 0.8 0.0 0.0 0.6 Partial dependence 0.2 0.4 0.6 0.4 0.2 0.0 0.0 Partial dependence 0.8 0.8 1.0 0.0 ble 4 0.4 0.4 0.4 0.6 0.4 ria ble 2 Va 0.2 0.0 0.2 0.4 0.6 0.8 0.0 Variable 6 * 0.2 0.4 Variable 7 Q 0.6 0.8 ,(* ( IJ 8(7* - ' -, # - 0 ! $ % 3IH ! G $ !H4:& 0 =: $ , CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT All Manchester 100 100 80 80 60 60 40 40 20 20 0 0 Low High 100 100 80 80 60 60 40 40 20 20 0 0 : * * * !' Variable #$ 3 ! LSTAT B PTRATIO TAX RAD DIS AGE RM NOX CHAS INDUS ZN CRIM Interaction strength Boston housing − interactions 0.15 0.10 0.05 0.00 $ Interaction strength Boston housing − interactions with RM 0.20 0.15 0.10 0.05 B LSTAT Variable PTRATIO TAX RAD DIS AGE NOX CHAS INDUS ZN CRIM 0.00 Interaction strength Boston housing − interactions with LSTAT 0.20 0.15 0.10 0.05 *+ 5: / B TAX RAD PTRATIO Variable DIS AGE RM NOX CHAS INDUS ZN CRIM 0.00 Partial dependence Partial dependence 20 15 pendence partial de pendence partial de 15 10 5 10 5 8 8 0.4 7 RM RM 6 0.6 16 6 X 18 NO 0.7 5 14 7 0.5 5 IO T RA PT 20 0.8 Partial dependence Partial dependence 15 20 e partial dependenc 5 15 10 e 0.4 10 0.5 0.7 AT 30 0.8 30 20 5 X NO T 0.6 20 LS T LS 10 TA partial dependenc 10 12 10 8 6 DIS , - : 4 2 7 *7* ! $ #" ; # ! %@ : ) - #" ' # TH4444 % % % % % R IJ S H 3 % JI %3 $ 0 % 3IJ ! G 0 " " $ AGE WKCLS FNLWGT EDU EDUNUM MARSTAT OCCUP RELSHP RACE SEX CAPGAIN CAPLOSS HOURS CNTRY AGE WKCLS FNLWGT EDU EDUNUM MARSTAT OCCUP RELSHP RACE SEX CAPGAIN CAPLOSS HOURS CNTRY AGE WKCLS FNLWGT EDU EDUNUM MARSTAT OCCUP RELSHP RACE SEX CAPGAIN CAPLOSS HOURS CNTRY AGE WKCLS FNLWGT EDU EDUNUM MARSTAT OCCUP RELSHP RACE SEX CAPGAIN CAPLOSS HOURS CNTRY All Observation 65 100 100 80 80 60 60 40 40 20 20 0 0 Low High 100 100 80 80 60 60 40 40 20 20 0 0 : * * * Variable !' #$ 3 ! CNTRY HOURS CAPLOSS CAPGAIN SEX RACE RELSHP OCCUP MARSTAT EDUNUM EDU FNLWGT WKCLS AGE Interaction strength Adult census − interactions 0.10 0.08 0.06 0.04 0.02 0.00 $ *+ 5: / Adult census 0.25 0.20 0.15 0.10 0.05 0.00 U − interactions Variable CNTRY HOURS with CAPLOSS CNTRY HOURS CAPLOSS CAPGAIN with CAPGAIN SEX RACE interactions SEX RACE RELSHP Variable RELSHP − OCCUP EDUNUM EDU FNLWGT WKCLS AGE Interaction strength census OCCUP MARSTAT EDUNUM EDU FNLWGT WKCLS Interaction strength Adult MARSTAT 0.15 0.10 0.05 0.00 AGE mach−opr handler farm−fish exec−man craft adm−cler OCCUP 0.5 0.4 0.3 0.2 0.1 0.0 priv−serv tech−sup sales prot−serv prof−spec 0.3 0.2 0.1 0.0 OCCUP 0.3 0.2 0.1 0.0 priv−serv sales prot−serv prof−spec M 0.4 M 0.5 trans−mov 0.6 trans−mov 0.7 tech−sup MARSTAT = separated tech−sup sales 0.4 M trans−mov sales prot−serv prof−spec service farm−fish exec−man OCCUP prot−serv 0.5 priv−serv 0.7 OCCUP prof−spec MARSTAT = never−married service 0.0 service 0.1 mach−opr 0.2 mach−opr 0.3 handler 0.4 farm−fish 0.5 handler MARSTAT = civilian−spouse farm−fish 0.7 craft 0.0 exec−man 0.1 exec−man 0.2 adm−cler 0.3 craft 0.4 Partial dependence 0.5 adm−cler 0.6 Partial dependence M trans−mov tech−sup sales prot−serv prof−spec priv−serv service mach−opr handler farm−fish exec−man craft adm−cler Partial dependence 0.6 craft 0.6 Partial dependence M trans−mov tech−sup sales prot−serv prof−spec priv−serv service mach−opr Partial dependence 0.7 adm−cler M 0.6 M 0.7 trans−mov MARSTAT = widowed trans−mov tech−sup sales OCCUP service handler farm−fish exec−man craft military adm−cler OCCUP prot−serv mach−opr handler farm−fish exec−man craft military adm−cler Partial dependence OCCUP prof−spec priv−serv service Partial dependence MARSTAT = divorced MARSTAT = military−spouse 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 MARSTAT = absent−spouse 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.0 0.1 0.1 0.2 0.2 20 40 60 80 0.3 Partial dependence 0.3 Partial dependence 0.4 0.4 0.5 0.5 SEX = female SEX = male 20 40 AGE > 60 AGE 80 0 L "% 6 , "% * %EE###Q / & / EVN-&E "E 0/ % 0 !3445$% - 0 %EE###Q / & / EVN-&E& E / & / EVN-&E& E -/ & % 0 !344J$% - %EE###Q *% & 0 -' ( / 9 % > C- > (# 9 8 " & & ...
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