11. Causality(and(conditional
★ Causal(relationship(is(usually(expressed(by(conditional.
★ If(global(warming(continues((W)(then(London(will(be(flooded((L).
★ (If(cause(then(effect)
★ We(can(also(use(conditionals(of(the(form((If(effect.then(cause)
★ The(utility(of(confusing(the(two(forms:$
★ We(should(test(independence(to(find(a(causal(relationship,(before(
considering(the(directionality.
★ If(we(allow(for(directionality,(we(need(two(Bayes(networks,(test(and(
choose(one(from(the(two.(This(is(cognitively(heavy(for(intuition.
directed mode
undirected mode
Model 1 C E
Model C ? E
Model 2 C E
12. Material(implication
★ Modeling(conditional(by(material.implication
★ Rif(p,(then(qR(⇔Rnot(p,(or(qR A(⊃(C C=T C=F
A=T T F
★ Paradoxes(of(material(implication(1
A=F T T
★ If(there(is(no(gravity,(then(I(am(the(king(of(Japan.
★ If(p((antecedent)(is(false,(Rif(p(then(qR(is(true(no(maSer(what(q(is.
★ Paradoxes(of(material(implication(2
★ If(I(am(the(king(of(Japan,(then(Tokyo(is(the(capital(of(Japan.
★ If(q((consequent)(is(true,(Rif(p(then(qR(is(true(no(maSer(what(p(is.
★ Experiments(show(that(humans(do(not(follow(
material(implication.
13. Material(implication A(⊃(C
A=T
C=T C=F
T F
A=F T T
★ Why(humans(dont(follow(material(implication?
★ Old(paradigm(psychology(of(reasoning:(Its(because(human(are(
irrational(or(effortless((e.(g.,(mental(models(theory)
★ New(paradigm(psychology(of(reasoning:(Humans(reason(
factoring(the(uncertainty(and(the(context((environment(structure)(
into(their(reasoning.
★ Considering(uncertainty((the(truth(value(of(a(proposition(as(
probability(in([0,1](with(1((true)(and(0((false)),(
★ With(the(probability(of(an(event((proposition)(usually(being(very(
small,(material(implication(doesnt(work.
★ Humans(reason(allowing(for(uncertainty.
★ The(meaning(of(Rif(p(then(qR(by(humans(is(modeled(not(by(p#⊃#
q(but(by(q|p.
★ With(q|p,#¬p(cases(are(ignored.
14. Defective(conditional
★ For(half(a(century((since(1966),(it(
has(been(known(that(humans(
follow(the(Rdefective(truth(tableR( Table. defective truth table
when(understanding(and(using(
conditionals,(as(in(the(Table. If A then C C=T C=F
★ Conditional(is(not(truthGfunctional?
A=T true false
★ For(a(conditional(p#=(RIf(A,(then(C,R
★ If(the(truth(value(combination(of( A=F irrelevant irrelevant
antecedent(A(and(consequent(C(is(
TT,(p(is(true.(If(TF,(p#is(false.(When( defective (no truth value assigned)
A(is(false,(participants(of(
experiments(answer(that(FT(and(FF( Psychologically: Wason, 1966; Johnson-Laird
and Tagart, 1969; Wason and Johnson-Laird,
do(not(make(p(true(nor(false(but( 1972; Evans et al., 1993.
irrelevant(to(the(truth(value(of(p.
Theoretically: Strawson 1950; Quine 1952
14
15. Defective(biconditional
★ There(is(our(tendency(of( If and only if
C=T C=F
A then C
interpreting(Rif(A(then(CR(
as(Rif(A(then(C,(and(if(C( A=T true false
then(AR(or(RA(if(and(only(if(
CR((biconditional(reading). A=F false irrelevant
★ Here(the(interpreted(
biconditional(is(called(
defective(biconditional. conjunction
★ True(for(TT,(false(for(TF(
If A If C
and(FT,(irrelevant(only(for( then C
C=T C=F
then A
C=T C=F
FF.
A=T T F
★ In(deductive(tasks,(this( A=T T I
paSern(has(been(known(
(Evans(&(Over,(2004). A=F I I A=F F I
15
21. defective conditional and
defective biconditional
★ Defective truth table in the older paradigms
★ (Wason, 1966; Johnson-Laird and Tagart, 1969;
Wason and Johnson-Laird, 1972; Evans et al., 1993)
★ is normative and coherent in the new paradigm
old(paradigm new(paradigm
defective( conditional(
→
conditional event(q|p
defective( biconditional(
→
biconditional 21
event(p⟛q
22. de(FineSis(conditional$event
★ Conditional(event,(formerly(called(defective(conditional,(is(a(
core(notion(in(the(new(paradigm(psychology(of(reasoning.
★ The(Equation:(the(probability(of(a(conditional(is(the(
conditional(probability(of(the(consequent(given(the(
antecedent.
★ P(if$p$then$q)$=$P(q|p)$(the$Equation)
★ ¬p(cases(are(neglected,(and(Rq|pR(is(itself(a((conditional)(event.
de Finetti
material conditional conditional biconditional
conditional event event event
p q p⊃q q|p p|q p⟛q
T T T T T conjunction T
T F F F V F
F T T V F F V: void case
F F T V V V
25. Causal(induction(experiment(
Stimulus$presentation:(a( showing b-cell type joint event
pair(of(two(kinds(of(
pictures(illustrating(the(
presence(and(absence(of(
cause(and(effect,(at(left(
and(right,(respectively
Response:(participants(
evaluate(the(causal(
intensity(they(felt(from(0(
to(100,(using(a(slider(
E ¬E
C a b
¬C c d
28. ∆P = P (E|C) − P (E|¬C) = (a + b)(c + d)
(a + b)(c + d)
Framework(and(models(of(causal(
PowerPC = induction + d)
ad − bc
∆P = P (E|C) − P (E|¬C)∆P
=
(a + b)(c
1 − P (E|¬C)
★ The(data((input)(is(coGoccurrence(of(the(target(
effect((E)(and(a(candidate(cause((C).
∆P = P (E|C) − P (E|¬C)
∆P
∆P
PowerPC =
PowerPC =
★ Normative:(Delta:P(and(Power$PC((Cheng,(1997)
1 − P (E|¬C)
1 − P (E|¬C)
★ Descriptive:(H((Dual$Factor$Heuristics)((HaSori(
∆P = P (E|C) − P (E|¬C)
&(Oaksford(2007) ∆P= ad − bc
PowerPC =
∆P
PowerPC − P (E|¬C) (a + b)d
1=
1 − P = ad − bc
∆P = P (E|C) − P (E|¬C)
(E|¬C)
(a + b)(c + d)
∆P ad − bc E ¬E
PowerPC = ∆P = ad − bc
PowerPC = 1 − P (E|¬C) = (a + b)d
ad − bc
∆P = P (E|C) − P (E|¬C) =
C a b
1 − P (E|¬C) (a + b)d
(a + b)(c + d)
a ¬C c d
H= P (E|C)P (C|E) =
∆P ∆P (a +ad −+ c)
b)(a bc
30. Rarity(assumption
H=P (E|C)P (C|E)
★ We(assume(the(effect(in(focus(and(the(candidate(
= cause(to(be(rare:(P(C)(and(P(E)(to(be(small.
P (E|C)P (C|E) =
a
★ Originally(in(Oaksford(&(Chater,(1994,(
(a + b)(a + c)
★ then(in(HaSori(&(Oaksford,(2007,(McKenzie(2007,(
a
in(the(study(of(causal(induction
= P (E|C)P (C|E) =
(a + b)(a + c)
★ C(and(E(to(take(small(proportion(in(U.
U
lim φ =
d→∞
P (E|C)P (C|E) = H C E
ϕ: correlation ba c
extreme coefficient
lim φ =
rarity P (E|C)P (C|E) = H d
d→∞
43. Experiment(2:
c(and(d(in(3x2(table
★ Each(participant(
estimates(the(intensity(
of(causal(relationship( stimulus A q not-q
from(p1(to(q.
p1 6 a 4 b
★ Then(asked(the(value(of( focus
p2 9 c 1 d
c,(as(RHow(often(q( + +
happened(in(the( p3 2 8
absence(of(p1?.R(The(
given(value(of(c(is(
9+2=11.
44. Exp.,2:,Result
c cell d cell
13 14
10 11
7 7
3 4
0 0
r (=(0.99
2 1 2 3 4 1 2 3 4 r2(=(0.49
real c estimated c real d estimated d
★ ParticipantsN,estimation,of,c,and,d,occurrence,were,very,
different.,The,correlation,between,the,estimated,d,and,the,
real,,given,value,of,d,was,significantly,smaller,than,for,c.
48. Exp(3.(The(combinations(of(
affirmation(and(negation
dropped not dropped graduated not
out out graduated
unstable a b unstable a b
not unstable c d not
unstable c d
orange : confirmatory instances, yellow : disconfirmatory instances, white :
irrelevant
dropped not dropped graduated not
out out graduated
mentally
healthy a b mentally
healthy a b
not mentally
healthy c d not mentally
healthy c d
Participants evaluate the intensity of the causal relationship from
the cause unstableness to the effect dropout is evaluated.
48
49. Exp.(3(Result((coinciding(
condition)
coinciding yes/yes coinciding yes/no
100 100
75 75
50 50
25 25
0 0
Mean pARIs Mean pARIs
(2,2,2,8) (1,1,3,10) (1,1,1,15) (1,1,3,14)
coinciding no/yes coinciding no/no
100 100
75 75
50 50
25 25
0 0
Mean pARIs Mean pARIs
49
50. Exp.(3(Result((contradicting(
condition)
contradicting yes/yes contradicting yes/no
100 100
75 75
50 50
25 25
0 0
Mean pARIs Mean pARIs
stimuli : (6,1,1,1) (8,1,2,3) (7,3,1,3) (6,2,2,3)
contradicting no/yes contradicting no/no
100
100
75
75
50 50
25
25
0 0
Mean pARIs
Mean pARIs 50
60. Conditionals(in(development
★ Development,of,understanding,of,conditionals,(Gauffroy,&,
Barouillet,,2009)
★ Four,developmental,stages:,3rd,grader,,6th,grader,,9th,
grader,,adults,(respectively,,8,,11,,15,,24,years,old,in,average)
★ Defective,biconditional,=,biconditional,event,shows,up.
conjunctive defective defective material
probability conditional biconditional conditional
p q p|q q|p p⟛q p⊃q
T T T T T T
T F F F F F
F T F V F T
F F F V V T
61. C. Gauffroy, P. Barrouillet / Developmental Review 29 (2009) 249–282
Indicative conditional Conjunctive
Def Bicond
MP
Other
in development
280 C. Gauffroy, P. Barrouillet / Developmental Review 29 (2009) Def Cond
249–282 NN
90%
80%
Appendix 70%
60%
BB conditionals used in Experiment 1 50%
40%
‘‘If the pupil is a boy then he wears glasses”. 30%
‘‘If the door is open then the light is switched on”. 20%
‘‘If the student is a woman then she wears a shirt with long sleeves”. 10%
‘‘If the piece is big then it is pierced”. 0%
3 6 9 adults
Grades
NN conditionals used in Experiment 1 Conjunctive MP
Def Bicond Other
Def Cond
‘‘If the card is yellow then a triangle is printed on it”. BB
‘‘If there is a star on the screen then there is a circle”. 90%
‘‘If he wears a red t-shirt then he wears a green trousers”. 80%
‘‘If there is a rabbit in the cage then there is a cat”. 70%
60%
name form 50%
Strong causal relations used in Experiment 2
Conjunctive = TT/All 40%
Def Bicond = TT/(TT+TF+FT) are switched on”. 30%
‘‘If the button 3 is turned then the blackboard’s lights 20%
Def Cond = TT/(TT/TF)
‘‘If the lever 2 is down, then the rabbit’s cage is open”. 10%
‘‘If the second button of the machine is green then the machine makes sweets”.
MP = (TT+FT+FF)/All
‘‘If I pour out pink liquid in the vase then stars appear on it”.
0%
3 6 9 adults
Grades
Other = other forms
All := TT+TF+FT+FF
Weak causal relations used in Experiment 2 61 Gauffroy & Barouillet, 2009
Fig. 1. Percent of response patterns categorized as conjunctive, defective biconditional (Def Bicond), defecti
Cond), matching (MP) and others as a function of grades for NN and BB conditionals in Experiment 1.
62. younger participants (third graders), explaining the age-related increase in ‘‘false” r
Causal conditional
p :q case. First of all, as we predicted, conjunctive response patterns predomin
NN conditionals used in Experiment 1
Conjunctive
in development
MP
‘‘If the card is yellow then a triangle is printed on it”. Def Bicond Other
‘‘If there is a star on the screen then there is a circle”. Def Cond Weak
‘‘If he wears a red t-shirt then he wears a green trousers”. 90%
‘‘If there is a rabbit in the cage then there is a cat”. 80%
70%
60%
Strong causal relations used in Experiment 2
50%
40%
‘‘If the button 3 is turned then the blackboard’s lights are switched on”.
‘‘If the lever 2 is down, then the rabbit’s cage is open”. 30%
‘‘If the second button of the machine is green then the machine makes sweets”. 20%
‘‘If I pour out pink liquid in the vase then stars appear on it”. 10%
0%
3 6 9 adults
Weak causal relations used in Experiment 2 Grades
Conjunctive MP
‘‘If the touch F5 is pressed then the computer screen becomes black”. Def Bicond Other
‘‘If the boy eats alkali pills then his skin tans”. Def Cond Strong
‘‘If the fisherman puts flour in the water then he catches a lot of fishes”. 90%
‘‘If the gardener pours out buntil in his garden then he gathers a lot of tomatoes”.
80%
70%
name
Promises used in Experiment 3 form 60%
50%
Conjunctive = TT/All
‘‘If you gather the leafs in the garden then I give you 5 francs”. 40%
‘‘If you score Def Bicond
a goal then I name= TT/(TT+TF+FT)
you captain”. 30%
‘‘If you exercise the dog then I cook you a cake for dinner”. 20%
‘‘If you clean your room then you watchTT/(TT/TF)
Def Cond = the TV”.
10%
MP = (TT+FT+FF)/All 0%
3 6 9 adults
Threats used in Experiment 3
Other = other forms Grades
All := TT+TF+FT+FF
‘‘If you break the vase then I take your ball”.
Gauffroy & Barouillet, 2009
Fig. 3. Percent of response patterns categorized as conjunctive, defective biconditional (Def Bicond), defec
62 Cond), matching (MP), and others as a function of grades for strong and weak causal conditionals in Exp
‘‘If you do not buy the bread then you do not play video games”.
63. ‘‘If I pour out pink liquid in the vase then stars appear on it”.
C. Gauffroy, P. Barrouillet / Developmental Review 29 (2009) 249–282
Weak causal relations used in Experiment 2
Promise and threat Conjunctive
Def Bicond
Equivalence
Other
conditionals in development
‘‘If the touch F5 is pressed then the computer screen becomes black”. Def Cond
Promises
‘‘If the boy eats alkali pills then his skin tans”. 90%
‘‘If the fisherman puts flour in the water then he catches a lot of fishes”. 80%
‘‘If the gardener pours out buntil in his garden then he gathers a lot of tomatoes”. 70%
60%
Promises used in Experiment 3 50%
40%
30%
‘‘If you gather the leafs in the garden then I give you 5 francs”.
‘‘If you score a goal then I name you captain”. 20%
‘‘If you exercise the dog then I cook you a cake for dinner”. 10%
‘‘If you clean your room then you watch the TV”. 0%
3 6 9 Adults
Grades
Threats used in Experiment 3 Conjunctive Equivalence
Def Bicond Other
‘‘If you break the vase then I take your ball”. Def Cond
Threats
‘‘If you do not buy the bread then you do not play video games”. 90%
‘‘If you do not do your homework then you do not go to the attraction park”. 80%
‘‘If you have a bad mark then you do not go to the movie”. 70%
name form 60%
References 50%
Conjunctive = TT/All 40%
Artman, L., Cahan, S., & Avni-Babad, D. (2006). Age, schooling and conditional reasoning. 30% Cognitive Development, 21(2), 131–145.
Def Bicond = TT/(TT+TF+FT)
Barra, B. G., Bucciarelli, M., & Johnson-Laird, P. N. (1995). Development of syllogistic reasoning. American Journal of Psychology,
20%
108(2), 157–193. Cond
Def = TT/(TT/TF) 10%
Barrouillet, P., Gauffroy, C., & Lecas, J. F. (2008). Mental models and the suppositional account of conditionals. Psychological
0%
MP
Review, 115(3), 760–771. = (TT+FT+FF)/All 3 6 9 Adults
Barrouillet, P., Gavens, N., Vergauwe, E., Gaillard, V., & Camos, V. (2009). Memory span development: A time-based resource- Grades
Equivalence = (TT+FF)/All
sharing model account. Developmental Psychology, 45(2), 477–490.
Fig. 4. Percent of response patterns categorized as conjunctive, defective biconditional (Def Bicond), defective
Barrouillet, P., Grosset, N., & Lecas, J. F. (2000). Conditional reasoning by mentaland others as a Chronometric promises and threats in Experiment 3.
Cond), equivalence, models: function of grades for and developmental
All := TT+TF+FT+FF
evidence. Cognition, 75, 237–266. 63 Gauffroy & Barouillet, 2009
64. Probability judgment
in development
C. Gauffroy, P. Barrouillet / Developmental Review 29 (2009) 249–282 269
272 C. Gauffroy, P. Barrouillet / Developmental Review 29 (2009) 249–282
Conjunctive Def Cond
Def Bicond Other
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
6 9 Adults
Grades
Fig. 5. Example of material given to participants in the probability task. of response patterns categorized as conjunctive, defective biconditional (Def Bicond), and defec
Fig. 6. Percent
(Def Cond) responses to the probability task in Experiment 4.
could be expected from previous studies (Evans et al., 2003; Oberauer & Wilhelm, 2003)
responses were very frequent, even in adults. Our interpretation is that the difficulty of t
many participants to base their evaluation on the sole initial model provided by heuristic
s our theory account for the way people evaluate the probability of conditional statements a consequence, it can be observed that the developmental trend resulting from the interv
re its developmental predictions? Our hypothesis is that people evaluate theGauffroy &
64 probability of Barouillet, 2009
analytic system is delayed in the probability task, with sixth graders producing almost 80%
tive responses, a rate never observed with the truth table task in the present study or t
75. Models(for(bandits
★ PolicyGbased(models policy
value of action
★ ε2greedy,policy,and,Softmax, actions
action,selection,rule value function
action function action value
value
★ Value(function(models action action
policy value
★ UCB1,(this,enabled,the, value of actions action
current,performance,of, state
Game,of,Go,AI,with,MCTS)
Agent
★ LS,(our,cognitively–inspired, reward action
model,implementing,
cognitive,properties,that, Environment
appear,to,be,illogical,and,
useless)
Components of reinforcement
learning model
76. The,currently,best,model,for,bandits
Auer(et(al.,(
UCB1,: Machine#learning,(
2002
Value function
considering
the reliability the(term(to(suspend(judgment(and(induce(RsearchR
(sample size)
UCB1@tuned,:
★ A,is,an,action,(arm)
★ E,is,the,presence,of,reward,(E=1).
★ n,is,the,current,step,(=,the,number,of,times,arms,are,chosen).
★ ni,is,the,number,of,times,the,agent,chose,the,arm,Ai.
77. Illustration(of(UCB1(
as the arms
are chosen
many times
0.6 0.6
0.4 the extra 0.4
term
decays
A1 < A2 A1 > A2
★ The,reason,for,the,performance,of,UCB1@tuned,is,
that,it,delays,the,judgement,of,value,as,long,as,possible.
84. Brain
Property$A:$Satisficing
Psychology
science
value reference all arms are over reference
value
of A1 of A2 No pursuit of arms over the reference level given Kolling
et al., Simon, Psy.
reference Science,
2012
Rev., 1956
all arms are under reference
value value
of A1 of A2 Search hard for an arm over the reference level
Property$B:$Risk$aZitude$(Reliability$consideration)
Risk-avoiding over the reference Risk-seeking under the reference
Expected value 0.75 = 75% reflection effect 25% = 25%
Boorman Kahneman
et al., & Tversky,
win (o) and lose ○×○○○ ×○×××
×○○○○ ○×○○ ○×××× ×○×× Neuron, Am. Psy.,
(x) in the past ○○○×○ ×××○× 2009 1984
○○×○× ××○×○
with the boundary of 0.5
comparison
considering > <
reliability
Rely on 15/20 than 3/4. Gamble on 1/4 rather than 5/20.
Property$C:$Relative$evaluation
Try arms other than
A1 by relative
value value evaluation (see-saw) Daw et Tversky &
if absolute of A1 of A2 if relative al., Kahneman,
Nature, Science,
Choose A1 and lose 2006 1974
value value value value
of A1 of A2 of A1 of A2
85. Relative,evaluation(is(especially(
important
★ Relative(evaluation:(
★ is(what(even(slime(molds((粘菌)(and(real(neural(networks(
(conservation(of(synaptic(weights)(do.(Behavioral(economics(found(
that(humans(comparatively(evaluate(actions(and(states.
★ weakens,the,dilemma,between,exploitation,and,exploration,with,
the,see2saw,game,like,competition,among,arms:(
★ Through,failure,(low,reward),,choice,of,greedy,action,may,quickly,
trigger,to,the,next,choice,of,the,previously,second,best,,non@greedy,arm.
★ Through,success,(high,reward),,choice,of,greedy,action,may,quickly,
trigger,to,focussing,on,the,currently,greedy,action,,lessening,the,
possibility,of,choosing,non@greedy,arms,by,decreasing,the,value,of,other,
arms.
Try arms other than
A1 by relative
value value evaluation (see-saw)
if absolute of A1 of A2 if relative
Choose A1 and lose
value value value value
of A1 of A2 of A1 of A2
86. The(framework(of(models(of(the(
three(properties
★ Let(there(only(be(two(arms(A1(
and(A2.
★ On(the(2x2(contingency(table( Reward
of(two(actions(and(two( 1 0
reward(levels(in(the(right,(
★ The(expected(reward(value(
A1 a b
for(each(is A2 c d
★ V(A1)=E(A1)=P(1|A1)=(a/(a+b)
★ V(A2)=E(A2)=P(1|A2)=(c/(c+d)
87. A(model((RRSR)(of(the(three(
properties
★ A(value(function(VRS(equipped(with(the(
three(properties(can(be(given(as:(
★ VRS(A1)(=((a+d)/(a+d+b+c),(
★ VRS(A2)(=((b+c)/(b+c+a+d). Reward
★ with(the(denominator(identical, 1 0
((((((((((((((((((((((((((((((((is(simply(
argmax V (Ai )
Ai
A1 a b
the(sign(of((a+d)G(b+c) A2 c d
★ This(is(the(RS(heuristics:(
★ [if$(a+d$>$b+c)$then$choose$A1,$else$choose$A2[
88. RS(heuristics
★ Property(C((relative(estimation(of(value):
★ Failing(to(get(reward(with(arm(A2,means(A1(is(
relatively,good,(and(vice(versa.
★ The(value(of(A1(and(A2(are(respectively(a+d(and(c+b.
Reward
1 0
A1 a b
A2 c d
VRS(A1) a+d
VRS(A2) c+b
89. RS(heuristics
Reward
★ Property(B((risk(aSitude) 1 0
★ Let((a,b,c,d)(=((70,(30,(7,(3). A1 a b
★ V(A1):V(A2)(=(73:37( A2 c d
★ More(reliable((A1)(is(preferred. VRS(A1) a+d
★ Let((a,b,c,d)(=((30,(70,(3,(7). VRS(A2) c+b
★ V(A1):V(A2)(=(37:73(
★ Less(reliable((A2)(is(preferred((since(A2(has(more(chance(
of(having(beSer(value(than(30%(of(giving(reward).
90. RS(heuristics
★ Property(A((satisficing)
★ Efficiently(realized(by(property(C(&(
B,(with(reference(r,=0.5. Reward
★ If(P(1|A1)(=(P(1|A2)(>(0.5(and(N(A1)( 1 0
>(N(A2)(then(VRS(A1)(>(VRS(A2)(and(
keep(choosing(A1,(indifferently. A1 a b
★ When((a,b,c,d)(=((70,(30,(7,(3),(((( A2 c d
VRS(A1):VRS(A2)(=(73:37.( VRS(A1) a+d
★ If(P(1|A1)(=(P(1|A2)(<(0.5(and(N(A1)( V (A2)
>(N(A2)(then(VRS(A1)(<(VRS(A2)(and(
RS c+b
try(A2,(wondering(if(P(1|A2)(>(r((0.5).
★ When((a,b,c,d)(=((30,(70,(3,(7),((((
VRS(A1):VRS(A2)(=(37:73.
93. LS(model
★ The(performance(of(LS(in(2G Reward
armed(bandit(problems(is(the( 1 0
same(as(RS,(and(LS(can(be(
applied(to(nGarmed(bandit( A1 a b
problems. A2 c d
★ While(RS(compares(an(arm(
with(the(other(arm, a
P (1|A1 ) =
★ LS(compares(an(arm(with(the( a+b
RgroundR(formed(from(the(
whole(set(of(arms. b
a+ b+d d
★ LS(fits(the(intuition(of(human( LS(1|A1 ) = b a
a + b+d d + b + a+c c
about(causal(relationship(with(
very(high,(actually(the(highest(
correlation((r(>(0.85(for(all( RS(1|A1 ) =
a+d
experiments). a+d+b+c
94. LS(describing(causal(intuition
★ LS,fits,the,experiment,data,of,causal,induction,
(inductive,inference,of,causal,relationship),the,best,
among,other,42,models,including,the,most,popular,
ΔP=P(E|C)–P(E|¬C).,
★ Experiment,of,causal,induction:
★ Given,an,effect,E,in,focus,(e.g.,,stomachache),and,a,candidate,
cause,C,(e.g.,,drinking,milk),,answer,the,causal,relationship,
from,C,to,E.,The,co@occurrence,information,of,C,and,E,is,given.
Meta-analysis effect
Experiment AS95 BCC03.1 BCC03.3 H03 H06 LS00 W03.2 W03.6 E ¬E
r2 for LS 0.9 0.96 0.96 0.97 0.94 0.73 0.91 0.72
cause
C a b
r2 for ΔP 0.78 0.84 0.7 0.0 0.5 0.77 0.08 0.21 ¬C c d
95. The(properties(of(LS#
★ Figure–ground(segregation(and(invariance(
of(ground(against(change(in(focus((figure).
★ As(the(background(stays(invariant(when(you(
see(each(of(the(two(possible(objects,(a(rabbit(
or(a(duck,(but(not(both(at(the(same(time.
P:,A1≠A2,,
b ground
a+ b+d d A1 ,,,,A1C≠A2C
(A1C)
LS(1|A1 ) =
a+ b a LS:,A1≠A2,,
b+d d +b+ a+c c
d
,,,,A1C=A2C
c+ d+b b
LS(1|A2 ) = ground
A2 RS:,A1≠A2,,
d c (A2C)
c+ d+b b +d+ a+c a ,,,,,A1C=A2,
96. The(properties(of(LS#
a c
P (1|A1 ) = P (1|A2 ) =
a+b c+d
b ground
a+ b+d d A1
(A1C)
LS(1|A1 ) = b a
a+ b+d d +b+ a+c c
= P:,A1≠A2,,
= c + d+b b
d
= ground
,,,,A1C≠A2C
LS(1|A2 ) = d c (A2C)
A2
LS:,A1≠A2,,
c+ d+b b +d+ a+c a
,,,,A1C=A2C
a + d≠
RS(1|A1 ) = RS:,A1≠A2,,
a+d+b+c ,,,,,A1C=A2,
≠ c+b ≠
RS(1|A2 ) = ,,,,,A2C=A1
c+b+d+a