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 Models
in 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 Models
in 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
Penalty: 0:
100:
Sigma: 2.6:
8:
Penalty Offset: 11:
500:
27:
22:
Actual shift
100
80
60
40
20
HB
0
0
20
40
60
80
MEG-predicted shift
100
Expt. 1 – Score
Penalty: 0:
100:
Sigma: 2.6:
8:
Penalty Offset: 11:
500:
27:
22:
Actual points per trial
100
50
0
-50
-100
-100
HB
-50
0
50
100
MEG-predicted points per trial
Expt. 1 – Efficiency
Expt. 2 - Circular Statistics
Efficiency
1
0.5
0
DG HB KD JT
Subject
ML RG
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
Penalty 0, Far
90
Shift (deg)
MSL
0
Target
Penalty
-90
0
0.1
Stimulus orientation variability (1/ )
0.2
Expt. 2 – Results
Penalty 0, Far
90
Shift (deg)
MSL
0
Target
Penalty
-90
0
0.1
Stimulus orientation variability (1/ )
0.2
Expt. 2 – Results (contd.)
Penalty 500, Far
90
Shift (deg)
MSL
0
Target
Penalty
-90
0
0.1
Stimulus orientation variability (1/ )
0.2
Expt. 2 – Results (contd.)
Penalty 500, Near
90
Shift (deg)
MSL
0
Target
Penalty
-90
0
0.1
Stimulus orientation variability (1/ )
0.2
Expt. 2 – Results (contd.)
Penalty 0
Shift (deg)
Far:
90
Penalty 100
Penalty 500
MSL
0
-90
Near:
90
0
-90
Target
Penalty
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Far:
Penalty 500
MSL
0.4
Data
Linear fit to
Penalty 0
0.3
0.2
0.1
0
0.4
Near:
Setting variability (1/)
Penalty 100
0.3
0.2
0.1
0
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Penalty 100
Penalty 500
MSL
Far:
0
-20
Data
MEG prediction
20
Near:
Mean Shift (deg)
20
0
-20
Target
0
Penalty
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Shift (deg)
Far:
90
Penalty 100
Penalty 500
MMC
0
-90
Near:
90
0
-90
Target
Penalty
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Far:
Penalty 500
MMC
Data
Linear fit to
Penalty 0
0.5
0
1
Near:
Setting variability (1/)
1
Penalty 100
0.5
0
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Penalty 100
Penalty 500
MMC
Far:
0
-20
Data
MEG prediction
20
Near:
Mean Shift (deg)
20
0
-20
Target
0
Penalty
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
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.)
Penalty 0
Shift (deg)
Far:
90
Penalty 100
Penalty 500
AKK
0
-90
Near:
90
0
-90
Target
Penalty
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Shift (deg)
Far:
90
Penalty 100
Penalty 500
AVP
0
-90
Near:
90
0
-90
Target
Penalty
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Shift (deg)
Far:
90
Penalty 100
Penalty 500
AEW
0
-90
Near:
90
0
-90
Target
Penalty
0
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Penalty 0
Penalty 100
Penalty 500
AEW
Far:
0
-20
Data
MEG prediction
20
Near:
Mean Shift (deg)
20
0
-20
Target
0
Penalty
0.1
0.2
0
0.1
0.2
0
Stimulus orientation variability (1/)
0.1
0.2
Expt. 2 – Results (contd.)
Experiment 3
80
MEG performance
Points per trial
60
40
20
0
-20
-40
aew akk
at
avp mhf mmc msl
Subject
sf
smn
Expt. 2 – Results (contd.)
Experiment 3
1
Efficiency
0.5
0
-0.5
-1
-1.5
aew akk
at
avp mhf mmc msl
Subject
sf
smn
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.