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CDE FGHI JCJKBEDL NV


48/106

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49/106

!'%1'* $'0'-"R/1 () '- -'&'

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Does it help to know the estimated click probability of the first mainline

ad in order to estimate the click probability of the second mainline ad?

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CDE FGHI JCJKBEDL NY


50/106

!'%1'* $'0'-"R/1 () '- -'&'

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CDE FGHI JCJKBEDL SG


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!'%1'* $'0'-"R/1 () '- -'&'

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?&'&(1&(M1 ')- !'%1'&(")M1..%#',$1"- 6'/% ).%($*,$/% /'#;%

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K",%./%",$1"- Hypothetical: D-%% -+ 3&-* -9 ;( 2&* 8)23(%%&.E

Counterfactual: D58%" 1&4( -+ 3&-*(" -9 ;( 1&" 2&**(" 8)23(%%&.E

M';-',$1"

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J%*%", '(/'"*%- $" *';-'# $"2%.%"*%

(Rubin, 1986) (Spirtes et al., 1993, 2011, )

(Pearl, 2000, 2009, )

CDE FGHI JCJKBEDL SF


53/106

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\ OI] U^

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55/106

=1"*'&(")

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No feedback loops (yet)(,)CDE FGHI JCJKBEDL SS


56/106


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59/106

:0')1$"0&'&(")

Pearls transportation problem

\"O )" $#$15),6$115 9(*,.(6"#9,),"#$1 A*"Q$Q,1,),(% P"* (?A(*,8(#) I3%,#4 6"#9,),"#$1 A*"Q$Q,1,),(% @#"O#P*"8 (?A(*,8(#)% H $#9 F ]

Analogous to Bayes rule : "5M6$16313%=

Known versus estimated

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CDE FGHI JCJKBEDL SY


60/106

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E8A1(8(#) and verify

CDE FGHI JCJKBEDL UH


62/106

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CDE FGHI JCJKBEDL UF


63/106

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CDE FGHI JCJKBEDL UI


64/106

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65/106

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,#)(*(%)=() ()

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CDE FGHI JCJKBEDL VG


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CDE FGHI JCJKBEDL VF


73/106

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CDE FGHI JCJKBEDL VI


74/106

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J0,% ,% ($%5 )"

(%),8$)(

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76/106

Q*'4()2 H(&J #'()*()/ 0/1/0./1

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78/106

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W"*19 %(1(6) 6"#)(?) L($*#(* 60""%(% 9,%6*()( $6),"# = 1

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80/106

?&0%M&%0/

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CDE FGHI JCJKBEDL XG


81/106

:J/ M'%1'* 20'$J J'1 1&0%M&%0/

CDE FGHI JCJKBEDL XH


82/106

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2?$8A1(h 3%(*% 61,6@ O,)0"3) @#"O,#4 )0( $9 %6"*(% "* )0( 61,6@ A*,6(%=

Technique: shifting the reweighting variables


83/106

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Technique: shifting the reweighting variables


84/106

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Q(P"*( $P)(*

CDE FGHI JCJKBEDL XN

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85/106

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87/106

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88/106

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0$9 3%(9 8"9(1 /1,6@M)0*3M*$)( ,P O(0$9 3%(9 8"9(1 =

CDE FGHI JCJKBEDL XX


89/106

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CDE FGHI JCJKBEDL XY


90/106

`K 5/'0)()2


91/106

A1&(#'&()2 -/0(.'&(./1K"2$"$,%-$+'# $",%./%",$1"-

Related to policy gradient in RL.

KA),8,c$),"# $14"*,)08% 1($*# 8"9(1 A$*$8()(*% =

/1,6@ *$)( ,P O( 0$9

3%(9 ( + ) /1,6@ *$)( ,P O( 0$9

3%(9 8"9(1 = d

CDE FGHI JCJKBEDL YH


92/106

A1&(#'&()2 -/0(.'&(./1

M1;",%.2'*,;'# ($-,.$4;,$1"

= 1

O,)0 = $#9 =() =

This ratio can be large but

CDE FGHI JCJKBEDL YF


93/106

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= +

with

1

log

`W,11,$8%R HYYFa it goes away for small interventions

CDE FGHI JCJKBEDL YI


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