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.