Perceptual Decisions in the Face of Explicit Costs and Perceptual Variability Michael S. Landy Deepali Gupta Also: Larry Maloney, Julia Trommershäuser,

Perceptual Decisions in the Face of Explicit Costs and Perceptual

Variability

Michael S. Landy Deepali Gupta

Also: Larry Maloney, Julia Trommershäuser, Ross Goutcher,Pascal Mamassian

Statistical/Optimal Modelsin Vision & Action

• MEGaMove – Maximum Expected Gain model for Movement planning (Trommershäuser, Maloney & Landy)– A choice of movement plan fixes the probabilities pi of

each possible outcome i with gain Gi

– The resulting expected gain EG=p1G1+p2G2+…

– A movement plan is chosen to maximize EG

– Uncertainty of outcome is due to both perceptual and motor variability

– Subjects are typically optimal for pointing tasks

Statistical/Optimal Modelsin Vision & Action

• MEGaMove – Maximum Expected Gain model for Movement planning

• MEGaVis – Maximum Expected Gain model for Visual estimation– Task: Orientation estimation, method of

adjustment– Do subjects remain optimal when motor

variability is minimized?– Do subjects remain optimal when visual

reliability is manipulated?

Task – Orientation Estimation

Task – Orientation Estimation

Payoff(100 points)

Penalty(0, -100 or-500 points, in separate blocks)

Task – Orientation Estimation

Payoff(100 points)

Penalty(0, -100 or-500 points, in separate blocks)

Task – Orientation Estimation

Task – Orientation Estimation

Task – Orientation Estimation

Task – Orientation Estimation

Task – Orientation Estimation

Task – Orientation Estimation

Done!

Task – Orientation Estimation

Task – Orientation Estimation

Task – Orientation Estimation

100

Task – Orientation Estimation

-500

Task – Orientation Estimation

-400

Experiment 1 – Three Variabilities• Three levels of orientation variability

– Von Mises κ values of 500, 50 and 5– Corresponding standard deviations of 2.6, 8 and

27 deg

• Two spatial configurations of white target arc and black penalty arc (abutting or half overlapped)

• Three penalty levels: 0, 100 and 500 points

• One payoff level: 100 points

Stimulus – Orientation Variability

κ = 500, σ = 2.6 deg

Stimulus – Orientation Variability

κ = 50, σ = 8 deg

Stimulus – Orientation Variability

κ = 5, σ = 27 deg

Payoff/Penalty Configurations

Payoff/Penalty Configurations

Payoff/Penalty Configurations

Payoff/Penalty Configurations

Where should you “aim”?Penalty = 0 case

Payoff(100 points)

Penalty(0 points)

Where should you “aim”?Penalty = -100 case

Payoff(100 points)

Penalty(-100 points)

Where should you “aim”?Penalty = -500 case

Payoff(100 points)

Penalty(-500 points)

Where should you “aim”?Penalty = -500, overlapped penalty case

Payoff(100 points)

Penalty(-500 points)

Where should you “aim”?Penalty = -500, overlapped penalty,

high image noise case

Payoff(100 points)

Penalty(-500 points)

Expt. 1 – Variability

Expt. 1 – Setting Shifts

0 20 40 60 80 100

0

20

40

60

80

100

MEG-predicted shift

Act

ual s

hift

HB

Penalty: 0: 100: 500:Sigma: 2.6: 8: 27:Penalty Offset: 11: 22:

Expt. 1 – Score

-100 -50 0 50 100

-100

-50

0

50

100

MEG-predicted points per trial

Act

ual p

oint

s pe

r tr

ial

HB

Penalty: 0: 100: 500:

Sigma: 2.6: 8: 27:

Penalty Offset: 11: 22:

Expt. 1 – Efficiency

DG HB KD JT ML RG0

0.5

1

Subject

Effi

cien

cyExpt. 2 - Circular Statistics

Expt. 1 – Discussion

• Subjects are by and large near-optimal in this task

• That means they take into account their own variability in each condition as well as the penalty level and payoff/penalty configuration

• They respond to changing variability on a trial-by-trial basis.

Expt. 1 – Discussion

However:

• A hint that naïve subjects aren’t that good at the task

• Concerns about obvious stimulus variability categories

• → Re-run using variability chosen from a continuum and more naïve subjects

Expt. 2 – Results

0 0.1 0.2-90

0

90Penalty 0, Far

Shi

ft (

deg)

Stimulus orientation variability (1/)

MSL

Target

Penalty

Expt. 2 – Results

0 0.1 0.2-90

0

90Penalty 0, Far

Shi

ft (

deg)

Stimulus orientation variability (1/)

MSL

Target

Penalty

Expt. 2 – Results (contd.)

0 0.1 0.2-90

0

90Penalty 500, Far

Shi

ft (

deg)

Stimulus orientation variability (1/)

MSL

Target

Penalty

Expt. 2 – Results (contd.)

0 0.1 0.2-90

0

90Penalty 500, Near

Shi

ft (

deg)

Stimulus orientation variability (1/)

MSL

Target

Penalty

Expt. 2 – Results (contd.)

-90

0

90Penalty 0

Far

:

MSL

Penalty 100 Penalty 500

0 0.1 0.2-90

0

90

Nea

r:

Shi

ft (

deg)

Target

Penalty

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

0

0.1

0.2

0.3

0.4

Penalty 0

Far

:

MSLDataLinear fit to Penalty 0

Penalty 100 Penalty 500

0 0.1 0.20

0.1

0.2

0.3

0.4

Nea

r:

Set

ting

varia

bilit

y (1

/)

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

-20

0

20

Penalty 0

Far

:

MSL

Penalty 100 Penalty 500

0 0.1 0.2

-20

0

20

Nea

r:Mea

n S

hift

(de

g)

Target Penalty

DataMEG prediction

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

-90

0

90Penalty 0

Far

:

MMC

Penalty 100 Penalty 500

0 0.1 0.2-90

0

90

Nea

r:

Shi

ft (

deg)

Target

Penalty

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

0

0.5

1Penalty 0

Far

:

MMCDataLinear fit to Penalty 0

Penalty 100 Penalty 500

0 0.1 0.20

0.5

1

Nea

r:

Set

ting

varia

bilit

y (1

/)

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

-20

0

20

Penalty 0

Far

:

MMC

Penalty 100 Penalty 500

0 0.1 0.2

-20

0

20

Nea

r:Mea

n S

hift

(de

g)

Target Penalty

DataMEG prediction

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results, so far

• Subjects MSL (non-naïve) and MMC (naïve) shift away from the penalty with increasing stimulus variability.

• These subjects appear to estimate variability on a trial-by-trial basis and respond appropriately

• Their shifts are near-optimal

• However, …

Expt. 2 – Results (contd.)

-90

0

90Penalty 0

Far

:

AKK

Penalty 100 Penalty 500

0 0.1 0.2-90

0

90

Nea

r:

Shi

ft (

deg)

Target

Penalty

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

-90

0

90Penalty 0

Far

:

AVP

Penalty 100 Penalty 500

0 0.1 0.2-90

0

90

Nea

r:

Shi

ft (

deg)

Target

Penalty

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

-90

0

90Penalty 0

Far

:

AEW

Penalty 100 Penalty 500

0 0.1 0.2-90

0

90

Nea

r:

Shi

ft (

deg)

Target

Penalty

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

-20

0

20

Penalty 0

Far

:

AEW

Penalty 100 Penalty 500

0 0.1 0.2

-20

0

20

Nea

r:Mea

n S

hift

(de

g)

Target Penalty

DataMEG prediction

0 0.1 0.2

Stimulus orientation variability (1/)0 0.1 0.2

Expt. 2 – Results (contd.)

aew akk at avp mhf mmc msl sf smn-40

-20

0

20

40

60

80MEG performance

Subject

Poi

nts

per

tria

l

Experiment 3

Expt. 2 – Results (contd.)

aew akk at avp mhf mmc msl sf smn-1.5

-1

-0.5

0

0.5

1

Subject

Effi

cien

cy

Experiment 3

Expt. 2 – Summary

• Subjects MSL (non-naïve) and MMC (naïve) are near-optimal.

• Other subjects use a variety of sub-optimal strategies, including– Increased setting variability with higher penalty

due to avoiding the penalty/target when task gets difficult

– Aiming at the target center regardless of the penalty

Conclusion

• Subjects can estimate their setting variability and attain near-optimal performance in this task.

• In Expt. 1, the main sub-optimality is an unwillingness to “aim” outside of the target.

• In Expt. 2, naïve subjects do not generally use anything like an optimal strategy, although in some cases efficiency remains high.