virtual journal club may 4th 2020 · confidence refers to the “sense of knowing” that comes...
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Virtual Journal Club May 4th 2020
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Confidence refers to the “sense of knowing” that comes with a decision
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Confidence refers to the “sense of knowing” that comes with a decisionConfidence affects the planning of subsequent actions
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Bayesian Confidence Hypothesis Confidence is based on the posterior probability of the chosen category : p(correct)
e.g., Peirce and Jastrow (1884)Galvin et al. (1959)Kepecs and Mainen (2012)Mamassian (2016)Kiani and Shadlen (2009)Kepecs, Uchida, Zariwala and Mainen (2009)Pouget, Drugowitsch and Kepecs (2016)Sanders, Hangya and Kepecs (2016)
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Bayesian Confidence Hypothesis Confidence is based on the posterior probability of the chosen category : p(correct)
Left or right tilted?
1 2Category
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Low confidence
p(L | x) p(R | x)
Left or right tilted?
1 2Category
0
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Post
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babi
lity High confidence
p(L | x) p(R | x)
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Kiani and Shadlen, 2009 Fetsch et al., 2014 Kepecs et al., 2009
Bayesian Confidence Hypothesis Confidence is based on the posterior probability of the chosen category : p(correct)
Adler and Ma, 2018
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People often face more complex decisions involving multiple choices
Distinguish different models of confidence report
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People often face more complex decisions involving multiple choices
Distinguish different models of confidence report
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timeWhich group does the black dot belong to?
How confident are you in your decision?
somewhatlow
verylow
somewhathigh
veryhigh
AExperiment 1 and 3 Experiment 2B C
Fig. 1 Experimental procedure and stimuli.
DEMO
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
Fig. 2 Models.
p(C | x) = p(x |C)
p(x | ′C )′C =1
3
∑
p(x |C) = N (mC ,(σ s +σ )I)
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
Fig. 2 Models.
Categorical decision: Always pick the group with the highest posterior
Confidence report: Three candidate modelsMax, Difference, Entropy
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
Fig. 2 Models.p(C = 1| x) p C x( )log p C x( )
C∑p(C = 1| x)− p(C = 2 | x)
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Max (Maximum a posteriori)
Diff (Difference)
Ent (Negative entropy)p C x( )log p C x( )
C∑
p(C = 1| x)− p(C = 2 | x)
p(C = 1| x)
Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
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Max
Diff
Entropy
Confidence
1 2Category
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Post
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r pro
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p(C = 1| x)
p(C = 1| x)− p(C = 2 | x)
p C x( )log p C x( )C∑
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1 2Category
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Confidence
p C = 1 x( )+ p C = 2 x( ) = 1
p(C = 1| x)
p(C = 1| x)− p(C = 2 | x)
p C x( )log p C x( )C∑
Max
Diff
Entropy
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Confidence
p(C = 1| x)
p(C = 1| x)− (1− p(C = 1| x))
p C = 1 x( )log p C = 1 x( )+ 1− p C = 1 x( )( )log 1− p C = 1 x( )( )
1 2Category
0
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1
Post
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r pro
babi
lity
p C = 1 x( )+ p C = 2 x( ) = 1
Max
Diff
Entropy
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Confidence
Max modelDiff modelEnt model p(C = 1| x)
1 2Category
0
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r pro
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p C = 1 x( )+ p C = 2 x( ) = 1
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
Fig. 2 Models. Sources of variability:(1) sensory noise (noisy measurement of the target dot location)(2) inference noise (decision noise)
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
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Astimulus s measurement x posterior probability
decision
confidence c
P( |x) P( |x)
P( |x)
σ
C^
B
P( |x) P( |x)
P( |x)C
conf
iden
ce
high
low
Max model Difference model Entropy model
post
erio
rpr
obab
ility
low decision noise high decision noise
q ~ Dirichlet(p;α )
The expected value of q is p. The concentration parameter 𝛼, a scalar that determines the magnitude of the decision noise
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Max modelDiff modelEnt model{ } Very
unconfidentSomewhat
unconfidentSomewhatconfident
Veryconfident
b1 b2 b3
c*1 2 3Category
0
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1
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lity
b1,b2 ,b3Criteria:Noise:
Lapse rate:σ ,αλ
Free parameters
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1 2 3 4Confidence
1
2
3
Decision
p(di ,ci | si ,b1,b2 ,b3,σ ,α ,λ)joint probability for trial i
b1,b2 ,b3Criteria:Noise:
Lapse rate:σ ,αλ
Free parameters
Maximum likelihood estimationLM (θ ) = p(di ,ci | si ,b1,b2 ,b3,σ ,α ,λ)
i=1
n
∏
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timeWhich group does the black dot belong to?
How confident are you in your decision?
somewhatlow
verylow
somewhathigh
veryhigh
AExperiment 1 and 3 Experiment 2B C
Fig. 1 Experimental procedure and stimuli.
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Diffe
renc
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axEn
tropy
A
B
1
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4
1
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Target location (deg)
Mea
n co
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repo
rtDataModel fit
-2 0 2 -2 0 2 -2 0 2 -2 0 2
Fig. 3. Experiment 1.
Diffe
renc
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axEn
tropy
A
B
1
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Target location (deg)
Mea
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DataModel fit
-2 0 2 -2 0 2 -2 0 2 -2 0 2
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Diffe
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B
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Target location (deg)
Mea
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rtDataModel fit
-2 0 2 -2 0 2 -2 0 2 -2 0 2
Fig. 3. Experiment 1.
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0
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-2 0 2 -2 0 2 -2 0 2 -2 0 2Target location (deg)
Data
Model fit
Supplementary Figure 2.
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A B Experiment 2Experiment 1
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Model
Fig. 4. Experiment 1. Model comparisons using ΔAIC:AIC of each model compared with the Difference model
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sensory noise and
decision noise
decision noise sensory noiseA
B
C
Model
Diff-Sen-Dir
Max-Sen-Dir
Ent-Sen-Dir0
500100015002000250030003500400045005000
Expe
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relat
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odel
Diff-DirMax-Dir
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500100015002000250030003500400045005000
Expe
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relat
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Diff-DirMax-Dir
Ent-DirDiff-S
enMax-Sen
Ent-Sen
Diff-Sen-Dir
Max-Sen-Dir
Ent-Sen-Dir0
500100015002000250030003500400045005000
Expe
rimen
t 3
AIC
relat
ive to
th
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odel
Diff-DirMax-Dir
Ent-DirDiff-S
enMax-Sen
Ent-Sen
Supplementary Figure 4.
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sensory noise and
decision noise
decision noise sensory noiseA
B
C
Model
Diff-Sen-Dir
Max-Sen-Dir
Ent-Sen-Dir0
500
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Expe
rimen
t 1
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relat
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Diff-DirMax-Dir
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Diff-DirMax-Dir
Ent-DirDiff-S
enMax-Sen
Ent-Sen
Supplementary Figure 6. Fitting confidence reports only
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timeWhich group does the black dot belong to?
How confident are you in your decision?
somewhatlow
verylow
somewhathigh
veryhigh
AExperiment 1 and 3 Experiment 2B C
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Supplementary Figure 1.
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Supplementary Figure 2.
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Target location (x)
Targ
et lo
catio
n (y
)
Fig. 5 Experiment 2.
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A
Diffe
renc
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axEn
tropy
Target location (deg)
Targ
et lo
catio
n (d
eg)
1 2 3 4confidence
B
Fig. 5 Experiment 2.
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A B Experiment 2Experiment 1
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Fig. 4. Experiment 1. Model comparisons using ΔAIC:AIC of each model compared with the Difference model
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1. Feedback2. Sampling from the true stimulus distribution
timeWhich group does the black dot belong to?
How confident are you in your decision?
somewhatlow
verylow
somewhathigh
veryhigh
AExperiment 1 and 3 Experiment 2B C
Experiment 3
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1
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DataModel fit
ModelDiff-S
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Supplementary Figure 11.
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If you are interested in:-Model recovery analysis (Supplementary Figure 3)-Model comparisons using BIC index (Supplementary Figure 5)-Fitting confidence reports alone (Supplementary Figure 6 and 7)-Fitting category decisions alone (Supplementary Figure 9)-21 additional models (various implementations of variabilities; heuristic models; Supplementary Figure 10)-Ratio model (Supplementary Figure 12)
![Page 41: Virtual Journal Club May 4th 2020 · Confidence refers to the “sense of knowing” that comes with a decision Confidence affects the planning of subsequent actions](https://reader033.vdocument.in/reader033/viewer/2022042415/5f2ffda2a9ab7f2160223b1c/html5/thumbnails/41.jpg)
Difference model outperforms Max and Entropy modelPosteriors of unchosen options matter
If you are interested in:-Model recovery analysis (Supplementary Figure 3)-Model comparisons using BIC index (Supplementary Figure 5)-Fitting confidence reports alone (Supplementary Figure 6 and 7)-Fitting category decisions alone (Supplementary Figure 9)-21 additional models (various implementations of variabilities; heuristic models; Supplementary Figure 10)-Ratio model (Supplementary Figure 12)
![Page 42: Virtual Journal Club May 4th 2020 · Confidence refers to the “sense of knowing” that comes with a decision Confidence affects the planning of subsequent actions](https://reader033.vdocument.in/reader033/viewer/2022042415/5f2ffda2a9ab7f2160223b1c/html5/thumbnails/42.jpg)
Difference model outperforms Max and Entropy modelPosteriors of unchosen options matter
THANK YOU! Time to discuss