virtual journal club may 4th 2020 · conﬁdence refers to the “sense of knowing” that comes...

Virtual Journal Club May 4th 2020

Confidence refers to the “sense of knowing” that comes with a decision

Confidence refers to the “sense of knowing” that comes with a decisionConfidence affects the planning of subsequent actions

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)


Left or right tilted?

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Kiani and Shadlen, 2009 Fetsch et al., 2014 Kepecs et al., 2009


Adler and Ma, 2018

People often face more complex decisions involving multiple choices

Distinguish different models of confidence report

timeWhich group does the black dot belong to?

How confident are you in your decision?

somewhatlow

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AExperiment 1 and 3 Experiment 2B C

Fig. 1 Experimental procedure and stimuli.

DEMO

Astimulus s measurement x posterior probability

decision

confidence c

P( |x) P( |x)

P( |x)

σ

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P( |x) P( |x)

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Max model Difference model Entropy model

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Fig. 2 Models.

p(C | x) = p(x |C)

p(x | ′C )′C =1

3

∑

p(x |C) = N (mC ,(σ s +σ )I)


decision

confidence c

P( |x) P( |x)

P( |x)

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Fig. 2 Models.

Categorical decision: Always pick the group with the highest posterior

Confidence report: Three candidate modelsMax, Difference, Entropy


decision

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P( |x) P( |x)

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Fig. 2 Models.p(C = 1| x) p C x( )log p C x( )

C∑p(C = 1| x)− p(C = 2 | x)

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)


decision

confidence c

P( |x) P( |x)

P( |x)

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Confidence

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p C x( )log p C x( )C∑

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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

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( )( )

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Max modelDiff modelEnt model p(C = 1| x)

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decision

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Fig. 2 Models. Sources of variability:(1) sensory noise (noisy measurement of the target dot location)(2) inference noise (decision noise)


decision

confidence c

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confidence c

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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

Max modelDiff modelEnt model{ } Very

unconfidentSomewhat

unconfidentSomewhatconfident

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b1 b2 b3

c*1 2 3Category

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b1,b2 ,b3Criteria:Noise:

Lapse rate:σ ,αλ

Free parameters

1 2 3 4Confidence

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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

∏



somewhatlow

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Fig. 1 Experimental procedure and stimuli.

Diffe

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Fig. 3. Experiment 1.

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Fig. 3. Experiment 1.

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Supplementary Figure 2.

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

sensory noise and

decision noise

decision noise sensory noiseA

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Diff-Sen-Dir

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sensory noise and

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Supplementary Figure 6. Fitting confidence reports only



somewhatlow

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Target location (x)

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et lo

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Fig. 5 Experiment 2.

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Fig. 5 Experiment 2.

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

1. Feedback2. Sampling from the true stimulus distribution



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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)

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)

Difference model outperforms Max and Entropy modelPosteriors of unchosen options matter

THANK YOU! Time to discuss

virtual journal club may 4th 2020 · conﬁdence refers to the “sense of knowing” that comes...

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