!"#$"%$#&' !"#"$%"$&#'(')#*+$+,("-).*/( !"#$%##&'()*+',&-'().+','/#0123$41&'4&'5$,$45$465'1663//#-7'8459#/:5' ;,/,-4<=>'4&$/1-36#-'4&'$9#'()?+:5',&-'()@+:5'%,5'/#;2,6#-'AB','&#%'1&#C' 'D945';,/,-4<='/#E#6$5','&#%',&5%#/'$1'$9#'F3&-,=#&$,2'G3#5$41&7' !"#$%&'($%)*+%,*)-%#%./0)/0%#1)'$%#*%'*,*)-*%2'*3$0)*#4%5+.+*5+*36% 0*%)/5+/%$)%+($0&#$+%0$%)*%$"+%1#(0(%)2%)1(+/7#$0)*(8% H&'8459#/:5';,/,-4<='$9#',&5%#/'%,5' 0#/B'/#5$/46$40#I1&#'=35$'J&1%' ,2=15$'#0#/B$94&<C'KLM' D9#'&#%';,/,-4<='10#/6,=#'$9#' /#5$/46$41&'1F'$9#'12-'1&#CN' O2,-4=4/'O,;&4J' 9"+%:#$'/+%)2%;$#$0($03#4%<+#/*0*=% 9"+)/6 'P?+++Q' 0-)(1.*2#'(%)"34(.1(!50( RSD'-#,25'=,4&2B'%4$9' %34)*6$%)7(')#*+$+,( ;/1A2#=5C'' T40#&7' ! ! ,&'4&;3$'PF#,$3/#Q'5;,6#7' X X '' ! ! ,&'13$;3$'P2,A#2Q'5;,6#7' Y Y %% % P$B;46,22B' Y Y 'U' { -1, +1 } Q' $9#' G3#5$41&' 1F' 2#,/&4&<' ,=13&$5' $1' #5$4=,$4&<' ,' F3&6$41&,2' /#2,$41&594;'A#$%##&'$9#'4&;3$',&-'$9#'13$;3$'5;,6#57' f '7' X X � Y R369','=,;;4&<' 2 '45'6,22#-',' &'#%%$8)* C'' H&'1/-#/'$1'-1'$945>'%#'9,0#',66#55'$1'51=#'P2,A#2#-Q'$/,4&4&<'-,$,7'' ( X 1 , Y 1 ), … , ( X n , Y n ) ' � ' X X ! Y Y '' V' &'#%%$8&#"$.+(#',.*$"-2( 45',';/16#-3/#'$9,$'$,J#5'$9#'$/,4&4&<'-,$,' ,5'4&;3$',&-'13$;3$5','62,554W#/' f C'' #'
!"#$"%$#&' 9%%324"$.+%( H&'RSD'1&#'=,J#5'$9#'F1221%4&<',553=;$41&57' ! ! $9#/#'#X45$5','Y14&$';/1A,A424$B'-45$/4A3$41&' > '1&' X X ! Y Y ' ! ! $9#'$/,4&4&<'#X,=;2#5' ( X i , Y i ) '',/#'5,=;2#-'4&-#;#&-#&$2B'F/1=' >% P44-' 5,=;24&<QC' H&';,/$4632,/7'' (C ! Z1',553=;$41&5'1&' > ' ?C ! D9#'-45$/4A3$41&' > '45'3&J&1%&',$'$9#'$4=#'1F'2#,/&4&<' @C ! Z1&[-#$#/=4&45$46'2,A#25'-3#'$1'2,A#2'&145#'1/'10#/2,;;4&<'62,55#5' \C ! D9#'-45$/4A3$41&' > '45'WX#-' 5.%%)%(#+7(*$%:%( ]#'&##-'$1'9,0#'51=#'=#,53/#'1F'^91%'<11-_','F3&6$41&' f '45'%9#&'35#-',5' ,'62,554W#/C'V' 4)((%2'*3$0)* '=#,53/#5'$9#'^615$_'1F'62,554FB4&<'4&5$,&6#' X � X ' ,5' Y � Y Y . D9#' 54=;2#5$' 2155' F3&6$41&' 4&' 62,554W6,$41&' ;/1A2#=5' 45' $9#' 0-1 ( '.%% ' P1/' =4562,5546,$41&'#//1/Q7 D9#' /0(, ' 1F' ,' F3&6$41&' 45' $9#' ,0#/,<#' 2155' 10#/' -,$,' ;14&$5' <#&#/,$#-' ,661/-4&<'$1'$9#'3&-#/2B4&<'-45$/4A3$41&' > 7' D9#' 1+($%34#((0?+/ '45'$9#'1&#'%4$9'$9#'5=,22#5$'/45J' @ P 2 QC' %'
!"#$"%$#&' ;#/)%(&'#%%$8)*%( V=1&<',22';1554A2#'62,554W#/5>'$9#'^A#5$_'1&#'45'$9#' A#6+(%34#((0?+/ 7'' H&';/,6$46#>'4$'45'4=;1554A2#'$1'-4/#6$2B'61=;3$#'$9#'",B#5'62,554W#/',5'$9#' 3&-#/2B4&<';/1A,A424$B'-45$/4A3$41&' > '45'3&J&1%&'$1'$9#'2#,/&#/C'' D9#'4-#,'1F'#5$4=,$4&<' > 'F/1='-,$,'-1#5&:$'353,22B'%1/J'L' ;#/)%<("-).*)2( !K",B#5:'$9#1/#=M'45'$1'$9#'$9#1/B'1F';/1A,A424$B'%9,$' `B$9,<1/,5:'$9#1/#='45'$1'<#1=#$/BCN' a,/12-'b#c/#B5'' ;30+*$0?3%B*2+/+*3+% P()@(Q' P ( h | e ) = P ( e | h ) P ( h ) P ( e | h ) P ( h ) = P ( e ) P ( e | h ) P ( h ) + P ( e | ¬ h ) P ( ¬ h ) ! ! > P " Q7'';/41/';/1A,A424$B'1F'9B;1$9#545' "% ! ! > P " 'd' + Q7'';15$#/41/';/1A,A424$B'1F'9B;1$9#545' " 'P4&'$9#'24<9$'1F'#04-#&6#' + Q' ! ! > P + 'd' " Q7''^24J#24911-_'1F'#04-#&6#' + '1&'9B;1$9#545' "% ('
!"#$"%$#&' 0-)(&'#%%$8&#"$.+(4*.=')2( T40#&7' ! ! ,'5#$'$/,4&4&<';14&$5' ( X 1 , Y 1 ), … , ( X n , Y n ) ' � ' X X ! Y Y -/,%&'44-'F/1=',&' '*,*)-* '-45$/4A3$41&' > '' ! ! ,'2155'F3&6$41&5' e#$#/=4&#','F3&6$41&' f '7' X X � Y '%9469'9,5'/45J' R ( f ) ',5'6215#',5';1554A2#'$1' $9#'/45J'1F'$9#'",B#5'62,554W#/C' >#6)#"? 'Z1$'1&2B'45'4$'4=;1554A2#'$1'61=;3$#'$9#'",B#5'#//1/>'A3$',251'$9#' /45J'1F','F3&6$41&' 2 '6,&&1$'A#'61=;3$#-'%4$913$'J&1%4&<' > C'' V'-#5;#/,$#'54$3,$41&f' 9+()@#24')A( 0-)(+)#*)%"(+)$,-=.*(*3')( !g,/2B'4&'()**'%9#&'H'W/5$'A#<,&'$#,694&<',$'R$,&F1/->','5$3-#&$>' `#$#/'a,/$>'%,2J#-'4&$1'=B'1h6#'%4$9',&'4&$#/#5$4&<';/1A2#=C'a#' 5,4-'$9,$'i9,/2#5'i12#',&-'9#'%#/#'354&<',';,$$#/&'62,554W6,$41&' 569#=#'%9469>'F1/'2,6J'1F','A#$$#/'%1/->'$9#B'-#56/4A#-',5'$9#' +)#*)%"(+)$,-=.*(4*.&)73*) C'' D945'569#=#',554<&#-'$1',&',5'B#$'3&62,554W#-'1A5#/0,$41&'$9#' 62,554W6,$41&'1F'$9#'&#,/#5$'<9A1/C']#/#'$9#/#',&B'<11-' $9#1/#$46,2';/1;#/$4#5'1F'$945';/16#-3/#fN' D91=,5'i10#/'P().?Q' &'
!"#$"%$#&' B(#+7($"%(2)7$)6#'(.*$,$+%( !a#&6#>'%9#&'54<9$';#/6#40#5'51=#'0454A2#'1AY#6$>'$9#'F,632$B' 1F'-456/4=4&,$41&'4==#-4,$#2B'5##J5'4$5'613&$#/;,/$',=1&<' $9#'F1/=5';#/545$4&<'4&'$9#'4=,<4&,$41&>',&-'%9#&'4$'W&-5' 51=#'F1/='4&'$9#'4=,<4&,$41&'$9,$'45'24J#'$9#'F1/='1F'$9,$' 0454A2#'1AY#6$>'4$'%422'/#61<&4j#'$9,$'0454A2#'1AY#6$',&-'%422' ;#/6#40#'%9,$'J4&-'1F'1AY#6$'4$'45CN' V29,j#&>' 9"+%A)),(%)2%C.$03( 'P6C'(+@+Q' Pg&<C'D/,&52C7'kC'R=4$9>'?++(Q' V/<3,A2B'$9#'W/5$'#X;2464$'F1/=32,$41&'1F'$9#'ZZ'62,554W6,$41&'/32#' 1&' /#61/-l' P5##7' kC' `#24221>' ^V29,j#&' ,&-' $9#' &#,/#5$' <9A1/' /32#>_' >#$$+/*%@+3)=*0$0)*%<+$$+/( >'?+(\QC' C.D(,..7($%("-)(EE(*3')F( i10#/',&-'D91=,5'591%#-'$9,$7' R ( f Bayes ) " R # " 2 R ( f Bayes ) %9#/#' @ m '-#&1$#5'$9#'#X;#6$#-'#//1/'/,$#'1F'ZZ'%9#&'$9#'5,=;2#'54j#'$#&-5'$1' 4&W&4$BC' ]#'6,&&1$'5,B',&B$94&<'5$/1&<#/',5'$9#/#',/#';/1A,A424$B'-45$/4A3$41&5'F1/'%9469' $9#';#/F1/=,&6#'1F'$9#'ZZ'/32#',694#0#5'#4$9#/'$9#'3;;#/'1/'21%#/'A13&-C' G#*$#"$.+%A( ! ! ! HEE(*3')A( 35#'$9#' , '&#,/#5$'<9A1/5',&-'$,J#','=,Y1/4$B'01$#'' ! ! ! " HEE(*3')A( $9#'5,=#',5',A10#>'F1/' , * '</1%4&<'%4$9' * ' 0-).*)2( I!".+)J( KLMMN ' HF' n ! " and k ! " , ' 5369' $9,$' k / n ! 0 >' $9#&' F1/' ,22' ;/1A,A424$B' -45$/4A3$41&5' R ( k n -NN) ' ! R ( f Bayes ) ' P$9,$' 45>' $9#' , * [ZZ' /32#' 45' ^3&40#/5,22B'",B#5'61&545$#&$_QC )'
!"#$"%$#&' O24$*$&#'(P$%:(Q$+$2$R#"$.+( !V$'$9#'#&-'1F'$9#'()*+:5>'$9#'$9#1/B'1F'g=;4/46,2'n45J'k4&4=4j,$41&' PgnkQ'F1/'$9#';,$$#/&'/#61<&4$41&';/1A2#='%,5'61&5$/36$#-C' D945'$9#1/B'4&623-#-'A1$9'P,Q'$9#'<#&#/,2' D'#40$#$07+%$"+)/6 '1F' <#&#/,24j,$41&'$9,$'-#56/4A#-'$9#'#55,/B',&-'53h64#&$'61&-4$41&5' F1/'61&545$#&6B'1F'$9#'gnk'4&-36$41&';/4&64;2#'KLMo'' ,&-'PAQ'$9#'<#&#/,2' D'#*$0$#$07+%$"+)/6 '$9,$'-#56/4A#-'$9#'A13&-5'1&' $9#';/1A,A424$B'1F'$9#'PF3$3/#Q'$#5$'#//1/CN' O2,-4=4/'O,;&4J' ;$#$0($03#4%<+#/*0*=%9"+)/6 'P()).Q' 0-)(OPQ(4*$+&$4')( H&5$#,-'1F'211J4&<'F1/','F3&6$41&'%9469'=4&4=4j#5'$9#'$/3#'/45J' R ( f ) >'%#'$/B'$1' W&-'1&#'%9469'=4&4=4j#5'$9#' +&.0/03#4%/0(, 7' T40#&'$/,4&4&<'-,$,' ( X 1 , Y 1 ), … , ( X n , Y n ) ' � ' X X ! Y Y >','F3&6$41&'5;,6#' F F J( ,&-','2155' F3&6$41&>'%#'-#W&#'$9#'62,554W#/' f n ',57 D945' ,;;/1,69' 45' 6,22#-' $9#' +&.0/03#4% /0(,% &0*0&0E#$0)*% PgnkQ' 4&-36$41&' ;/4&64;2#>'$9#'=1$40,$41&'1F'%9469'61=#5'F/1='$9#'2,%'1F'2,/<#'&3=A#/5C' E.")? 'R,=#',5'2#,5$[5G3,/#5pkS'=#$91-5'PA3$L'A4&,/B' 7(F '/#,2'F3&6$41&5lQC' *'
!"#$"%$#&' 9(:)/(S3)%"$.+( ]9,$'9,5'$1'A#'$/3#'1F'$9#'F3&6$41&'62,55' F '51'$9,$>'&1'=,$$#/'%9,$'$9#' 3&J&1%&' A,6J</13&-' ;/1A,A424$B' -45$/4A3$41&>' gnk' #0#&$3,22B' -1#5' ,5' %#22',5';1554A2#'%4$9'/#5;#6$'$1'$9#'/32#5'4&' F f'' V'F3&-,=#&$,2'/#532$'1F'RSD'45'$9,$'$9#'5#$'1F'/32#5'4&' F '6,&&1$'A#'$11' /469>'%9#/#'$9#'/4697'1F' F '45'=#,53/#-'AB'4$5'^Oi'-4=#&541&_C' O%"$2#"$.+( #$% (#44*.@$2#"$.+( H-#,22B'%#'%,&$'$1'=,J#' R ( f n ) # R ( f Bayes ) ',5'5=,22',5';1554A2#>',5' n ! " C'' e#&1$4&<'AB' 2 F '$9#'A#5$'62,554W#/'4&' F >'$9#'-4c#/#&6#'6,&'A#'-#61=;15#-',57' K01&'S3XA3/<',&-'R69q2J1;F>'?++.M' !'
!"#$"%$#&' T+7)*8""$+,( #$% (.6)*8""$+,( underfitting $! overfitting ! ! 5=,22'61=;2#X4$B'1F' F '' � '5=,22'#5$4=,$41&'#//1/>'2,/<#',;;/1X4=,$41&'#//1/'P '*5+/?$$0*= Q' ! ! 2,/<#'61=;2#X4$B'1F' F ' ' � '2,/<#'#5$4=,$41&'#//1/>'5=,22',;;/1X4=,$41&'#//1/'P )7+/?$$0*= Q'' D9#'A#5$'10#/,22'/45J'45',694#0#-'F1/'^=1-#/,$#_'61=;2#X4$B' K01&'S3XA3/<',&-'R69q2J1;F>'?++.M' Q.7)'(%)')&"$.+( +'
Recommend
More recommend
