An Investigation into How ADABOOST Affects Classifier D iversity

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4,156-2107 (* 8/)623 9/,:(-3
9/,:(-3 ;<7,6==3
>>?@ A4B3 4,106= C1,:=(.
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(.I1,1,: &)/2216-23 =/9((203 =1
56-21073 =6D6,=6,&6J
YZ\Y
(.I1,1,: &)/2216-2 12 /, 620/I)12'6= -6
26/-&' /-6/ 1, 0'6 6)= (* 20/01201&/) D/006-,
-6&(:,101(,J +* <6 '/56 ./,7 =16-6,0 &)/221
6-2 /0 (K- =12D(2/) 10 12 26,21I)6 0( &(.I1,6
0'6. 1, 0'6 '(D6 (* 1,&-6/21,: 0'6 (56-/)) /&
&K-/&7 AFJ +0 '/2 I66, D-(56= 0'6(-601&/))7
0'/0 / :-(KD (* 1,=6D6,=6,0 &)/2216-2 1.
D-(56 KD(, 0'6 21,:)6 I620 &)/2216- <'6, ./
(-107 5(06 &(.I1,/01(, 12 K26=J +0 12 /22K.6=
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%&'(() (* +,*(-./01&23
4,156-2107 (* 8/)623 9/,:(-3
9/,:(-3 ;<7,6==3
>>?@ A4B3 4,106= C1,:=(.
./2FF/HI/,:(-J/&JKL
0'/0 0'6 1.D-(56.6,0 '()=2 *(- (0'6- &(.I1
,/01(, .60'(=2 /2 <6))J +,0K10156)73 0'6 &)/221
6-2 0( I6 &(.I1,6= 2'(K)= I6 =16-6,0 *-(.
6/&' (0'6-3 (- =156-26J 421,: =16-6,0 &)/2
216-2 &/, -62K)0 1, I(0' I6006- D6-*(-./,&6
/,= <(-26 D6-*(-./,&63 =6D6,=1,: (, 0'6 =1*
*6-6,&62J B'K2 =156-2107 &/, I6 I(0' I6,6
&1/) (- '/-.*K) E3 AJ 4,=6-20/,=1,: /,=
.6/2K-1,: 0'626 =16-6,&62 1, =156-2107 12 /,
1.D(-0/,0 122K6 1, &)/2216- &(.I1,/01(, A?
/,= 0'6-6 /-6 2656-/) =16-6,0 .6/2K-62 (* =1
56-2107 I61,: K26=J B'626 .6/2K-62 /1. 0(
K/,01*7 0'6 =6D6,=6,&6 I60<66, &)/2216-2J
%656-/) 06&',1 K62 6120 <'1&' /1. 0( 1.
D-(56 0'6 D6-*(-./,&6 (* &)/2216- 6,26.I)62
I7 ./,1DK)/01,: 0'6 =/0/ 260 <'1&' &)/221
6-2 /-6 0-/1,6= (,J B'626 1,&)K=6 9/::1,:3
9((201,:3 /,= -&1,: G3 J 86 /-6 D/-01&
K)/-)7 1,06-6206= 1, 0'6 =/9((20 /):(-10'.
<'1&' '/2 '/= &(,21=6-/I)6 2K&&622 <10' /-01
&1/) /,= -6/)<(-)= =/0/ D-(I)6.2 AJ =
/9((20 IK1)=2 / &)/2216- 6,26.I)6 I7 20/-0
1,: <10' (,6 &)/2216- /,= /==1,: ,6< &)/2
216-23 (,6 /0 / 01.6J B'6 ,6< &)/221612 &(,20-K&06= I7 .(=1*71,: 0'6 0-/1,1,: 260
/&&(-=1,: 0( 0'6 D-651(K2 &)/2216-2 D6-*(-
./,&6 G33AEJ +0 '/2 I66, *(K,= 0'/0 9((20
1,: &/, I6 D/-/)726= GA3 1J6J3 ,( *K-0'6- 1.
D-(56.6,0 12 /&'1656= <'6, /==1,: ,6< &)/2
216-2 0( 0'6 06/.J
6-6 <6 20K=7 '(< =156-2107 &'/,:62 1, 0'6
6,26.I)6 /2 0'6 ,K.I6- (* &)/2216-2 D-(
=K&6= I7 =/9((20 1,&-6/262 /,= 0-7 0( 62
0/I)12' <'60'6- (- ,(0 =/9((20 <(-L2 I7
*(&K21,: (, /)06-1,: 0'6 =156-2107J B'6 ,60
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26&01(, &(,0/1,2 / =60/1)6= /&&(K,0 (* 0'6 =
/9((20 /):(-10'.J %6&01(, &(,0/1,2 / I-16*
=62&-1D01(, (* 0'6 =156-2107 .6/2K-62J %6&
01(, &(,0/1,2 =60/1)2 (* 0'6 6D6-1.6,0/)
260KD3 %6&01(, ? &(,0/1,2 0'6 -62K)02 /,= %6&
01(, (6-2 / &(,&)K21(,J
+,101/)1 6 3 A +,DK0 F
/
V[ XY
=/9((20 &(,20-K&02 &)/2216-2 I7 .(=1*71,:
0'6 0-/1,1,: 260 I/26= (, 0'6 D-651(K2 &)/2
216-2 D6-*(-./,&6J +0 =(62 0'12 I7 :60
01,: 0'6 ,6< &)/2216- 0( DK0 .(-6 6.D'/
212 (, 0'(26 (I6&02 <'1&' 0'6 D-651(K2 &)/2
216- *(K,= =1 &K)0 0( &)/221*7 /&&K-/06)7J
B'12 12 /&'1656= I7 ./1,0/1,1,: / =120-1IK
01(, (* <61:'02 (56- 0'6 0-/1,1,: 2603 <'1&'
&/, I6 .(=16= /2 -6 K1-6= (, 6/&' 106-
/01(,J %(.6 1.D)6.6,0/01(,2 (* =/9((20
K26 / -62/.D)1,: .60'(= G /,= (0'6-2 K26
-6<61:'01,: AJ B'626 =16- /&&(-=1,: 0(
<'60'6- 7(K -62/.D)6 *-(. 0'6 (-1:1,/) 0-/1,
1,: 260 (- /00/&' <61:'02 0( 6/&' =/0/ D(1,0
/,= -6K26 0'6 <'()6 0-/1,1,: 260 0( IK1)= 0'6
,60 &)/2216-J B'6 &'(1&6 (* 1.D)6.6,0/01(,
=(62 ,(0 /6&0 =/9((20 0(( .K&' /)0'(K:'
I((201,: <10' -6<61:'01,: 12 / .(-6 =1-6&0
1.D)6.6,0/01(, (* 0'6 0'6(-7 AJ 626/-&'
I7 9-61./, 2K::6202 0'/0 0'6-6 12 56-7 )10
0)6 =16-6,&6 1, 0'6 -62K)02 (I0/1,6= K21,: 0'6
0<( .60'(=2 GJ 86 '/56 K26= / -62/.D)1,:
.60'(= I6&/K26 0'12 /))(<2 *(- /,7 07D6 (*
I/21& &)/2216-2 0( I6 K26=J
(- 0'6 -62/.D)1,: 1.D)6.6,0/01(,3 6/&'
<61:'0 =606-.1,62 0'6 D-(I/I1)107 (* 102 /2
2(&1/06= (I6&0 I61,: 26)6&06= *(- 0'6 0-/1,1,:
260 *(- /, 1,=151=K/) &(.D(,6,0 &)/2216- J
+,101/))7 /)) <61:'02 /-6 260 6 K/)J , 6/&'
-(K,= 1* / 0-/1,1,: (I6&0 12 ,(0 /&&K-/06)7
&)/2216= 0'6, 102 &'/,&62 (* I61,: 26)6&06=
/:/1, *(- / 2KI26 K6,0 0-/1,1,: 260 /-6 1,
&-6/26= I7 1,&-6/21,: 0'6 5/)K6 (* 102 /22(&1
/06= <61:'0 AEJ +, 0'12 </7 0'6 ,60 &)/221612 *(-&6= 0( &(,&6,0-/06 (, 0'6 .(-6 =1 &K)0
6/.D)62 1, 0'6 0-/1,1,: 260J +, 1:K-6 A <6
2'(< 0'6 I/21& /):(-10'. *(- =/9((20 K21,:
0'6 -62/.D)1,: 1.D)6.6,0/01(,J
B'6 &(.I1,/01(, <61:'02 /-6 (I0/1,6= /2
A
B-/1, (, 2/.D)6= *-(. K21,: 3 A iiai
/)&K)/06 0'6 |i_djdjo
(* I7 06201,: (, /,= 0'6 &(.I1,/01(,
<61:'0 4D=/06 0'6 <61:'02
K21,: /,= 3 A !
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_ __ _ _ _ _ _ _ _
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K0DK0 &)/2216-2 % & '(
/,= 0'6 &(.I1,/01(, <61:'02
3 A ) *+ ,
0'6 0-/1,1,: 260 0'6 0-/1,1,: 260 *(- 106-/01(, 0'6 &)/2216- 0-/1,6= /0 106-/01(, 0'6 0-/1,1,: 6--(- /0 106-/01(, 0'6 <61:'0 *(- (I6&0 /0 106-/01(, .
A / 0'6 260 (* <61:'02
K26= /0 106-/01(,
J
1:K-6 A
0 1 2 3 4 56 7 8 8 9: 6 ; < 8 = >: 2 ? @ : 2 3
= 3 96 ? A;>B < >? A;3? 3 B:6: >8 B
*())(<2
A C A
8'6, F3 0'6 <61:'02 /-6 -61,101/)
1 6= 0( A J B'6 <61:'02 /0 106-/01(, /-6
&/)&K)/06= /2
G <'6-6 A 1* 0'6 &K--6,0 &)/2216- :1562 0'6 1,&(--6&0 )/I6) (* (I6&0 3 /,= F3 (0'6-<126J B'6 ,/) =6&121(, *(- / ,6< (I
6&0 12 ./=6 I7 <61:'06= 5(01,: I60<66,
0'6 &)/2216-2J 1-203 /)) &)/2216-2 )/I6)
/,= 0'6, *(- /)) 0'/0 :/56 )/I6) 3 <6
&/)&K)/06 0'6 2KDD(-0 *(- 0'/0 &)/22 I7
),
B'6 &)/22 <10' 0'6 ./1./) 2KDD(-0 12 &'(26,
*(- J
B7D1&/))73 0'6 :6,6-/)1 /01(, 6--(- (* =
/9((20 =6&/72 6D(,6,01/))7J +, 0'12 20K=7 <6
<6-6 1,06-6206= 1, =12&(56-1,: D/006-,2 (* =1
56-2107 /2 0'6 IK1)=1,: (* 0'6 &)/2216- 6,26.
I)6 D-(:-622623 2( 0'6 D-(I)6. (* /&&K-/&7 </2
)6*0 (K0J 97 0'6 1=6/ (* 102 =621:,3 =/9((20
<(K)= 6,*(-&6 =156-2107 1, 0'6 06/.3 ./L1,:
,6< &)/2216-2 *(&K2 (, =16-6,0 D/-02 (* 0'6
=/0/ 260J (<656-3 10 </2 *(K,= (K0 0'/0 0'6
.60'(= .1:'0 :60 0( /, 1,6 &16,0 20/:6 <'6-6
/==1,: ,6< &)/2216-2 <1)) ,(0 1.D-(56 0'6
D6-*(-./,&6 IK0 (, 0'6 &(,0-/-73 =606-1(-/06
10 GAJ B'12 12 &/K26= I7 2/.D)1,: -6D601
0156)7 *-(. 21.1)/- =120-1IK01(,2 <'(26 -62K)
0/,0 0-/1,1,: 260 D(262 0'6 2/.6 =1 &K)07 0(
0'6 &'(26, &)/2216- .(=6)J B'6, 0'6 6,26.
I)6 <1)) I6 (56-D(DK)/06= <10' 26.1:((= /,= /).(20 1=6,01&/) 6D6-023 /,= 0'6 66&0 (*
2(.6 :((= K/)107 .6.I6-2 (* 0'6 06/. <1))
I6 =1)K06=J K- 20K=7 (* =156-2107 /1.2 /0
2'(<1,: / D/006-, (* =156-2107 =K-1,: 0-/1,1,:
(* 0'6 6,26.I)6 0( 2KDD(-0 0'12 '7D(0'6212J
[XZ X ZXY B'6-6 /-6 =16-6,0 =156-2107 .6/2K-62 /5/1)
/I)6 *-(. =16-6,0 6)=2 (* -626/-&'J %(.6
(* 0'626 .6/2K-623 2K&' /2 0'6 20/01201& /,=
0'6 &(--6)/01(, &(6 &16,0 '/56 &(.6 =1-6&0)7
*-(. ./1,20-6/. 20/01201&2 <'1)20 (0'6-2 '/56
=656)(D6= 0'-(K:' 0'6 6)= (* 20/01201&/) D/0
06-, -6&(:,101(,3 2D6&1&/))7 *(- 0'6 D-(I)6.2
(* .K)01D)6 &)/2216- 27206.2J B'6 -20 *(K- (*
0'626 .6/2K-62 /-6 &/))6= D/1-<126 I6&/K26
0'67 &(,21=6- 0'6 &)/2216-2 0<( /0 /
01.6 /,= 0'6, /56-/:6 0'6 &/)&K)/06= D/1-
<126 =156-2107J B'6 (0'6- .6/2K-62 <(-L (,
0'6 <'()6 :-(KD (* &)/2216-2J B'6 06,
.6/2K-62 (* =156-2107 K26= 1, 0'12 20K=7 /-6
0/L6, *-(. AG3 A /,= =62&-1I6= 1, B/I)6
AJ B'(26 .6/2K-62 <'1&' '/56 / 07D6 /-6
2K&' 0'/0 0'6 maufi 0'6 5/)K63 0'6 .(-6 =1
56-26 0'6 &)/2216-23 <'1)20 0'(26 <'1&' '/56
/ 07D6 /-6 2K&' 0'/0 0'6 gdogfi 0'6 5/)K63
0'6 .(-6 =156-26 0'6 &)/2216-2J
B/I)6 A 0 36 9! = 3 9 8 " 5 ># 3= 9>:$
% /.6
% (0/ B7D6 %(K-&6
01(,
20/01201&
GG
(--6)/01(,
&
GF
&(6 &16,0
( 3 A(
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' (KI)6*/K)0
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5/-1/,&6
+ 6/2K-6.6,0
(* 1,06--/06,
?
/:-66.6,0
A
- ,0-(D7
./
0
@
+ 6/2K-6 (*
=1 &K)07
;6,6-/)126=
1
A@
=156-2107
(1,&1=6,0
*/1)K-6
2) A
=156-2107
Z 7 Y[ 8 9 Y : 6
(- (K- 6D6-1.6,02 <6 K26= 0'6 ; 1./
+,=1/, ' 1/I6062 =/0/I/26 /,= 0'6 /I6-./,
%K-515/) =/0/I/263 I(0' 0/L6, *-(. 0'6 4+
6D(210(-7 (* + /&'1,6 >6/-,1,: ' /0/I/26 < J
3
456
+, 2K../-7 0 ; 1./ ' 1/I6062 ' /0/I/26 0 G
&)/22623 @ E D/016,023 E *6/0K-62 - /I6-./,
= ©©¨ >??@ @ @ ±ª ¢±A ª± B A ?C D ¤ ?E FG ¨¡¢ª©¡¤ H ±© D
'/,:6 1, =156-2107
Pima
Haberman
1
1
0.5
0.5
0
0
−0.5
0
5
,(0 /, 122K6 '6-63 <6 K26= 0'6 <'()6 =/0/ 2602
*(- 0-/1,1,: /,= .6/2K-1,: =156-2107J
86 K26= =/9((20 %6&01(, G 0( :6,6-/06 6,
26.I)62 (* AF )1,6/- &)/2216-2 *(- 0'6 /I6-
./, =/0/ 0'6 2./))6- =/0/ 260 3 /,= G? )1,
6/- &)/2216-2
*(- 0'6 ; 1./ =/0/J 2 6/&' ,6<
&)/2216- </2 /==6= 0( 0'6 6,26.I)6 <6 .6/
2K-6= 0'6 =156-2107 (* 0'6 6,26.I)6 K21,: 0'6
06, .6/2K-62 %6&01(, J 1,/))7 <6 D)(006=
0'6 &'/,:6 1, =156-2107 /:/1,20 0'6 ,K.I6- (*
&)/2216-2 *(- 6/&' =/0/260 /,= 6/&' =156-2107
.6/2K-6J +0 </2 &)6/- *-(. (K- D-6)1.1,/-7
1,56201:/01(, 0'/0 0'6 &'/,:6 1, =156-2107 *()
)(<6= / 21.1)/- D/006-, *(- 6/&' -K,J B'6-6
*(-63 <6 (,)7 -6D6/06= 6/&' 6D6-1.6,0 06,
01.62 0( :60 /, (56-/)) -62K)0J
−0.5
10
0
10
20
'/,:6 1, & =156-2107
Pima
Haberman
1
1
0.5
0.5
0
0
−0.5
0
5
−0.5
10
0
10
20
'/,:6 1, ) =156-2107
Pima
Haberman
0.4
1
0.8
0.3
0.2
0.4
0.2
0
5
0.1
10
0
10
20
'/,:6 1, , =156-2107
Pima
Haberman
0.5
0.6
0
0.5
0.4
−0.5
0.3
−1
0
5
0.2
10
0
10
20
'/,:6 1, 0 =156-2107
Pima
Haberman
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
1:K-6 G
5
0
10
0
10
20
0
2 6 B < 3 >B : 2 3
? 36 9! = 3 9 8 "
5 ># 3= 9>:$ 6 9 3 6 5 5 ;6 99>" >3 = 9 : 8 : 2 3 3 B
93? ; 3
1:K-62 G /,= 2'(< 0'6 &'/,:62 1, =156-2107
/2 <6 /== &)/2216-2 0( 0'6 6,26.I)6J 1:K-6 G
2'(<2 0'(26 =156-2107 .6/2K-62 *(- <'1&' 0'6
)(<6- 0'6 5/)K6 0'6 .(-6 =156-26 0'6 &)/2216-2
3 <'1)20 1:K-6 2'(<2 0'(26 =156-2107 .6/
2K-62
*(- <'1&' 0'6 '1:'6- 0'6 5/)K6 0'6 .(-6
=156-26 0'6 &)/2216-2 J
2 1:K-6 G 2'(<23 3 & 3 /,= 0 /)) '/56 56-7
21.1)/- 01&L2'/D6= :-/D'2 <'1&' 1,=1&/06
0'/0 0'6 =156-2107 (* 0'6 6,26.I)6 1,&-6/262
2'/-D)7 /2 0'6 -20 *6< &)/2216-2 /-6 /==6=
0( 0'6 6,26.I)63 IK0 0'6, :-/=K/))7 =6&-6/262
/2 <6 /== .(-6 &)/2216-2 0( 0'6 6,26.I)6J
) /,= , I(0' '/56 .(,(0(,1& &K-562 IK0
<'1)20 , 12 206/=1)7 1,&-6/21,:3 1,=1&/01,: 0'/0
=156-2107 :-/=K/))7 -6=K&623 0'6 ) 2 D/006-,
2K::6202 0'/0 0'6 =156-2107 12 1,&-6/21,: :-/=
K/))7 /2 <6 /== .(-6 &)/2216-2 0( 0'6 6,26.
I)6J 1:K-6 2'(<2 &K-562 <10' / 21.1)/- 01&L
2'/D6 IK0 1,56-06= 0( 0'(26 (* 3 & /,= , 3
,/.6)7 0'(26 (* . / 3 1 3 /,= 2 ) J B'6263
:156, 0'/0 0'67 /-6 (* 0'6 07D63 /)2( 1,
=1&/06 0'/0 0'6 =156-2107 (* 0'6 6,26.I)6 1,
&-6/262 2'/-D)7 /2 0'6 -20 *6< &)/2216-2 /-6
/==6=3 IK0 0'6, :-/=K/))7 =6&-6/262 /2 <6 /==
.(-6 &)/2216-2J (, 0'6 (0'6- '/,= '/2 /
&K-56 21.1)/- 0( /, 1,56-06= 56-21(, (* , 1,
=1&/01,:3 )1L6 , 3 0'/0 =156-2107 :-/=K/))7 -6
=K&62 /2 <6 /== &)/2216-2 0( 0'6 6,26.I)6J
* '/2 / 2)1:'0)7 :6,0)6-3 )6222'/-D &K-56 *(
0.6
%K-515/) ' /0/I/26 0 G &)/22623 F D/016,023
*6/0K-62J %1,&6 :6,6-/)1 /01(, /&&K-/&7 </2
X 8YX
0'6 /I6-./, =/0/ 260 IK0 0'6 */.1)1/- 01&L
2'/D6 *(- 0'6 ; 1./ =/0/ 2603 I(0' (* <'1&'
1,=1&/06 /, 1,&-6/26 /,= 0'6, / =6&-6/26 1, =1
56-2107J 2 6D6&06=3 =K6 0( 0'6 2./))6- 2/.
D)6 21 63 0'6 5/-1/I1)107 /.(,: 0'6 06, -6D601
01(,2 </2 :-6/06- <10' 0'6 /I6-./, 260J
2 =12&K226= 6/-)16-3 <6 <(K)= 6D6&0 =156-
2107 0( =6&)1,6 /2 0'6 6,26.I)6 :-(<2 I67(,= /
&6-0/1, D(1,0J B'6 =/9((20 -62/.D)1,: D-(
&6=K-6 <1)) L66D /==1,: ,6< &)/2216-2 IK1)0
(, 21.1)/- 2/.D)62 (* 0-/1,1,: (I6&02 <'1&'
/DD6/- 0( I6 6 K/))7 =1 &K)0 *(- 0'6 2K&&62
2156 .6.I6-2 (* 0'6 6,26.I)6J B'6 -62K)02
<10' I(0' =/0/ 2602 2KDD(-06= 0'12 '7D(0'6
212 6&6D0 *(- 0'6 ' (KI)6 /K)0 ) .6/2K-6
<'1&' 2'(<6= 1,&-6/21,: =156-2107
0'-(K:'(K0
0'6 0-/1,1,:J B'6 -6/2(, *(- 0'/0 &(K)= I6
0'/0 ) 12 -6)/06= 0( 0'6 /&&K-/&7 (* 0'6 06/.
.(-6 0'/, 0'6 (0'6- .6/2K-62 /,= 12 0'6-6*(-6
,(0 6/&0)7 / 0-K6 .6/2K-6 (* ^dtfibdcn AGJ
+0 12 1,06-6201,: 0( 266 '(< 0'6 =-/./01& 1,
&-6/26 1, =156-2107 /2 0'6 -20 *6< &)/221
6-2 /-6 /==6= 0( 0'6 6,26.I)6 01&L2'/D6=
&K-562 3 &/, I6 6D)(106= 0( 102 D(06,01/)J ; 6-
'/D2 20(DD1,: 0'6 0-/1,1,: 0'6-6 /,= /DD)71,:
=16-6,0 &(.I1,/01(, -K)62 <1)) I6 I6,6&1/)J
\ 8 XX
86 20K=7 0'6 =156-2107 (* &)/2216- 6,26.I)62
IK1)0 0'-(K:' 0'6 =/9((20 /):(-10'. J B'6
/):(-10'. 12 6D)/1,6= 1, %6&01(, G /,= 6D6-
1.6,0/) -62K)02 <10' 0<( =/0/ 2602 *-(. 4+
+ > -6D(210(-7 /-6 :156,J 86 *(K,= / &(,
21206,0 D/006-, (* =156-2107 2'(<1,: 0'/0 /0
0'6 I6:1,,1,:3 0'6 ,6< &)/2216-2 /-6 '1:')7
=156-26 IK0 /2 0'6 0-/1,1,: D-(:-622623 0'6 =1
56-2107 :-/=K/))7 -60K-,2 0( 102 20/-01,: )656)J
B'12 2K::6202 0'/0 10 &(K)= I6 I6,6&1/) 0(
20(D =/9((20 I6*(-6 =156-2107 =-(D23 /,=
0-7 0( 6,'/,&6 0'6 D6-*(-./,&6 (* 0'6 6,26.
I)6 *K-0'6- I7 /DD)71,: =16-6,0 &(.I1,/01(,
.60'(=2 (, / -6/2(,/I)7 /&&K-/06 /,= =156-26
6,26.I)6J
86 (I0/1,6= &(,21206,0 D/006-,2 (* =156-2107
<10' /).(20 /)) =156-2107 .6/2K-62 /,= I(0'
=/0/ 2602 K21,: mdjf_i I/26 &)/2216-2J (<
656-3 0'6 D/006-,2 .1:'0 &'/,:6 1* (0'6- &)/2
216- .(=6)2 /-6 K26=J
'/,:6 1, =156-2107
Pima
Haberman
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0
5
0
10
10
20
'/,:6 1, * =156-2107
Haberman
Pima
0.4
0.2
0.3
0.15
0.2
0.1
0.1
0
0.05
0
5
0
10
0
10
20
'/,:6 1, . / =156-2107
Pima
Haberman
1
1
0.5
0.5
0
0
5
0
10
0
10
20
'/,:6 1, 1 =156-2107
Pima
Haberman
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
5
0
10
0
10
20
'/,:6 1, 2 ) =156-2107
Pima
Haberman
1
1
0.8
0.6
0.5
0.4
0
0
1:K-6
5
0.2
10
0
10
20
0
26 B < 3 >B : 2 3 ? 36 9! = 3 9 8 "
5 ># 3 = 9>:$ 6 9 3 6 5 5 ;6 99>">3 = 9 : 8 : 2 3 3B
93 ? ;3
Z \ X
* 1 3 2 4 O 6 c 7 G Z % = & @ @ $) & % =
! "# $ % &
T &% C 9(
3
Z` ` `
p 9 (q C # 9
X
N (9"&C C $ % ) 9%
r , 0 , , 3 5 L 0 , , ' &! ( % $ % ) * + , - . * / / / / J 0
1
4
? "$!@
2
2 5 6 7
A & B (! @
A &=C 3
8 9: ;$% $%)
0
E
F 6 4
? "$!@
2
< ( =$>
* . - , % !=$9% !@
5 6 7
A & B (! @
A &=C G 6 8 9: ;$% $%)
*
s
8 9 %V & (& % "&
0 - - . H I 1 1 5 D / / / F M 5 6 N ! =>
X
8 @ ! C C $? "! = $ 9 % / J - * . - + 4
O 7
P
Q G
R 6 0
B =&(
+ 4 1 S T = ! = $C = $ "! @ : & =# 9U C V 9 ( W ! = & C ! % U
N (9 9 ( = $ 9 % C 4 O 7 P
X
F
L \$C $ 9 % ! % U 8 9 :
B =$%)
X
w
I E G 6
L
N !==&(%
5 Z` ` `
< % ! @b C $C
!% U
4 8 @ ! C C $? & (
HI. I + T bC>
89: >
2 3 7 O 4 7
e G 6 F ^ / / / _ Q a(! % C ! " = $ 9 % C
! "# $ % &
F L O 4 e G 6 5 G ] 9 B ( % ! @ ^ _ 1 B @= $ @ &
X
3
7 G 6 H
G M M S F Y Z : !) &[
Z % = &( >
5 / I H
+
h t =#
I - H ' &" = B (& A 9 = & C $ %
T " $ & % "& -
N ( 9" g
N ! = = & ( % W &"9) % $ = $ 9 % 0 , , , 5 0,, 5 + / . H 5 S K F L E =&(%
3
9%
2 = &: C J
2 3 0,,, 3
< ( =$>
2 4 O 6 L O F 5 D / / / *
1 3 ! (&
5 9%
u Z %V 9 ( : ! = $ 9 %
v
T 9V = >
a&"# % 9 @ 9) b * / H , H. H H / / H 3
89:
c X
B = ! =$ 9 % ! @
G ' &! ( % $ % )
a# &9 ( b f
x 9 B ( =# ` B (9 &! % 8 9 %V & (& % "& . , X
Z % = & @ @$) & % "& 2 K 1c o/ / / / / 0 ^ , _ / / * . , , / / , / I
5
E 5 6 7
c G 6
8 9: ;$% $%)
7
3
4
< ( = $? " $ ! @
2
F 5 6 6 c
7
3
A &B >
G N ( 9" g < : & ( $ "! %
Z % = & @ @ $) & % "& (! @ A & = C - , . 0 - 5 < C C 9" $ ! = $ 9 % V 9 (
3 d < ( = $? " $ ! @
1
d O 6 3 / / + D / / / 0,
/
c E =$ 9 % C
9%
c N ! == &( %
Z` ` `
< % ! @b C $C
!% U
L E 5
5 6 a!y 9 % 9 : b O E S P
a(! % C ! " >
! "# $ % &
Z%>
0 4 O 6 5 E 4 S 4 L O F a(! % C ! " = $ 9 % C
9%
N !==&(%
u
L 3 = & @ @$) & % "& 0 , ^I _ I * 0 . I J J / / I , A B : & ( $ "! @
2 / H * 4 d G 5 < % ! @b C $C
Z` ` `
!% U
B @= $ @ & 8 @ ! C >
X
C $? & ( T b C = & : C 0 , / + ' &" = B (& A 9 = & C
$%
!>
8 9:
X
B = & ( T " $ & % "& . 0 5 0,, "# $ % & Z % = & @ @$) & % "& 0 0 ^ _ J . * H 0 , , , 0 0
F E O e
3 1 5 N (9" g
h i =#
Z % = &( % !=$ 9% !@
! "# $ % & ' &! ( % $ % ) f
8 9 %V & (& % "& 0 H - . 0 I * d / / + 0 1 3 d n
7
jC B ; : $ = = &Uk 2 4 O 6 0,, l m m G G G 6 m
, , m m 6 e o
M r R K N # $ @ g
a(! % C g < / J 0 - H. * / / , ,

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