1. Authors: Peter W. Battaglia, Robert A. Jacobs, and Richard N. Aslin
Bayesian integration of visual and auditory signals for spatial localization
Authors: Peter W. Battaglia, Robert A. Jacobs, and Richard N. Aslin
COGS 272, Spring 2010
Instructor: Prof. Angela Yu Presenter: Vikram Gupta

2. Outline
Introduction
Background
Methods
Procedure
Results
Discussion

3. Introduction Spatial Localization is Complex
Integration of multiple sensory and motor signals
Sensory: binaural time, phase, intensity difference
Motor: orientation of the head

4. Introduction ∫ Inconsistent Spatial Cues
Typically, we receive consistent spatial cues
What if this is not true?
Ex: Movie theater, television
Visual capture
Vision dominates over conflicting auditory cue.
Ex: recalibration in juvenile owl
Optimal?

5. Background Models for inconsistent cue integration
Winner Take All (ex. vision capture)
Dominant signal exclusively decides
Blend information from sensory sources
Is blending statistically optimal?
Example: Maximum Likelihood Estimate
Assumption independent sensory signals, normal dist.

6. Background MLE Example
Impact of reliability on MLE estimate

7. MLE Model
Is Normal distribution a good estimate of neural coding of sensory input?
Does this integration always occur? Or are there qualifying conditions?
Does it make sense to integrate if
Lv* and La* are far apart?
v and a are temporally separated?

8. Schematic of MLE Integration
Ernst, 2006 (MLE integration for haptic and visual input

9. Experiment Vision capture or MLE match empirical data? Method summary:
Noise is produced at 1 of 7 locations 1.50 apart
Visual stimulus has noise at 5 levels
10%, 23%, 36%, 49%, 62%
Single sensory modality trial (Audio / noisy Visual )  MLE parameters  predict performance for Audio + noisy Visual  compare with Empirical data

10. Experiment Single-modality BimodalC
Single-modality
Standard stimuli followed by comparison
Is C Left / Right of S?
Bimodal
Standard stimuli has Audio and Visual apart from center
Audio and visual Comparison stimuli are co-located.
Only 1 subject aware of spatial discrepancy in S

11. Results (1 subject) Cumulative normal distribution fits to data
Mean and variance are used for MLE model
Wv receives high value when visual noise is low
Wa receives high value when visual noise is high

12. Results (MLE Estimate of sensory input)
rt = 1 comparison to the right of standard
pt = , probability of rt, given mean and variance
R = set of responses to the independent trials
Assuming normal distribution, MLE estimate of mean and variance parameters
µml = 1/T * (∑ rt) σ2ml = 1/T * (rt - µml) 2

13. L* based on MLE estimates
Mean is calculated according to above weighted average
Variance is smaller than either P(L|v) or P(L|a)

14. L* based on MLE estimates
MLE estimate for wv and wa are found by maximizing RHS of (3) and using (6)
tau is scale parameter or slope

15. Results (bi-modal, same subject, all subjects)
Standard stimulus
Visual
Audio 1.50
Point of Subjective Equality
for low visual noise
0.10 for high noise
Visual input dominates at low noise
Equal weight at high noise

16. Empirical vs. MLE
MLE estimates for visual weight are significantly lower than the empirical results.
A Bayesian model with a prior that reduces variance in visual-only trials provides a good regression fit for the data.

17. Bayesian (MAP) Cue Integration
For visual only trials, instead of using MLE for mean and variance, we multiply the RHS above with the probability of the occurrence of the normal distribution
mean is assumed to have a uniform distribution.
variance is assumed to have inverse gamma distribution with parameters biased for small variance.

18. Discussion
Bayesian approach is a hybrid of MLE and visual capture models.
How are variances encoded?
How are priors encoded?
How does temporal separation in cues impact sensory integration?
Biological basis for Bayesian cue integration?