Bayesian perception: perception as

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Describe the coding of taste and smell signals.
Compare both with audition, vision,
proprioception, and touch.     Describe how
attention affects perception. How does attention
affect neural responses?     What kinds of
information are conveyed by the somatosensory
system? How is that information encoded in the
nervous system?     Describe the various ways
that optic flow can be used in vision?     What
is known about sensory prediction? Why is it
important?
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• What is Bayesian inference?
• How does it apply to perception?

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x y 9
What are x and y?
This is an example of an ill-posed problem
problem that has no unique solution
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Perception is also an ill-posed problem
(youd have to know X to make it well-posed)
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Comparison patch
Same light hits the eye from both patches
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Perception is an ill-posed problem
Example 2
?
3D world
2D retinal image
Question whats out there in the 3D world?

• Ill-posed because there are infinitely many 3D
  worlds that give rise to the same 2D retinal
  image
• need some additional info to make it a
  well-posed problem

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Figure 1. (a) The Necker Cube induces a bi-stable
percept. (b) Disambiguation of the bi-stable
Necker Cube percept by introducing an occlusion
cue and a shadow. (c) An infinite number of 3D
configurations could produce the same
projection image. Here this fact is illustrated
by the cast shadow on the tabletop, but the same
projected images would be formed on the eyes
retina.
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Luckily, having some probabilistic information
can help
x y 9
Tables showing past values of y
x
y
Given this information about past values, what
would you guess to be the values of x? How
confident are you in your answer?
2 1 2
2 2 2
2 3 1
3 1 2
2 2 2
1 2 2
3 2 2
2 2 2
7 7 7
7 7 7
5 7 7
7 6 7
7 7 7
8 7 8
7 7 7
7 7 7
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Bayes rule
very simple formula for manipulating
probabilities
conditional probability probability of B given
that A occurred
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Examples Using Bayes rule to understand how
the brain resolves ambiguous stimuli
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Many different 3D worlds can give rise to the
same 2D retinal image
The Ames Room
A
B
How does our brain go about deciding which
interpretation?
P(image A) and P(image B) are equal! (both
A and B could have generated this image)
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Which dimples are popping out and which popping
in?
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P( image OUT light is above) A P( image
OUT light is below) 0 P(image IN Light is
above) 0 P(image IN Light is below) A
Image equally likely to be OUT or IN given
sensory data alone
What we want to know P(OUT image) vs. P(IN
image)
Apply Bayes rule
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P( image OUT light is above) A P( image
OUT light is below) 0 P(image IN Light is
above) 0 P(image IN Light is below) A
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P( image OUT light is above) A P( image
OUT light is below) 0 P(image IN Light is
above) 0 P(image IN Light is below) A
Bayesian account Out is 10 times more likely!
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Summary

• Perception is an ill-posed problem
• equivalently the world is still ambiguous even
  given all our sensory information
• Probabilistic information can be used to solve
  ill-posed problems (via Bayes theorem)
• Bayes theorem
• The brain takes into account prior knowledge to
  figure out whats in the world given our sensory
  information

prior
likelihood
P(world sense data) ? P(sense data world )
P(world)
(Note that the posterior can be considered the
prior for the next time step in an ongoing
learning process)
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Two take-home facts about what it means to be
Bayesian in psychology / neuroscience
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• What does it mean to perceive optimally?
• What is a Bayesian model of human perception?
• How can we formulate / fit Bayesian models?

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Visual capture Vision and haptics view object
through a cylindrical lens vision dominates, but
a small effect Of haptic info. Vision and
audition sounds are localized to visual source
eg speakers mouth
In other instances, senses complement each other
eg feeling an object where there is no
conflict, info from back is given by haptics,
front by vision.
Auditory capture Number of beeps determines
whether single or multiple flashes are seen
Dominance determined by reliability of the
estimate.
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Figure 3. Visualhaptic size-discrimination
performance determined with a 2-interval
forced-choice task 29. The relative
reliabilities of the individual signals feeding
into the combined percept were manipulated by
adding noise to the visual display. With these
different relative reliabilities four
discrimination curves were measured. As
the relative visual reliability decreased, the
perceived size as indicated by the point of
subjective equality (PSE) was increasingly
determined by the haptic size estimate
(haptic standard, SH) and less by the visual size
estimate (visual standard, SV). This demonstrates
the weighting behaviour the brain adopts and the
smooth change from visual dominance (red circles)
to haptic dominance (orange triangles). As shown,
the PSEs predicted from the individual visual and
haptic discrimination performance
(larger symbols with black outline) correspond
closely to the empirically determined PSEs in the
combined visualhaptic discrimination task. (JND
. just noticeable difference.)
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What does it mean to perceive optimally?
General Goal Decide what stimulus is
present?
Assumptions

1. Our senses provide noisy measurements of the
   environment (e.g., something moving in the
   grass)
2. We have some well-defined (deterministic) cost
   function describing the cost of making different
   errors (e.g., cost
   saying wildebeast when the true stimulus was
   lion)
3. We have some beliefs about the underlying
   probability of different stimuli (e.g.,
   wildebeast more common than lion)

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What does it mean to perceive optimally?
Solution Given a noisy measurement, pick
stimulus that minimizes the expected cost.
Assumptions

1. Our senses provide noisy measurements of the
   environment (e.g., something moving in the
   grass)
2. We have some well-defined (deterministic) cost
   function describing the cost of making different
   errors (e.g., cost
   saying wildebeast when the true stimulus was
   lion)
3. We have some beliefs about the underlying
   probability of different stimuli (e.g.,
   wildebeast more common than lion)

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What does it mean to perceive optimally?
Bayesian Decision Theory
Solution Given a noisy measurement, pick
stimulus that minimizes the expected cost.
Assumptions
noise distribution / likelihood

1. Our senses provide noisy measurements of the
   environment (e.g., something moving in the
   grass)
2. We have some well-defined (deterministic) cost
   function describing the cost of making different
   errors (e.g., cost
   saying wildebeest when the true stimulus was
   lion)
3. We have some beliefs about the underlying
   probability of different stimuli (e.g.,
   wildebeest more common than lion)

cost function
prior
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Two basic approaches
1. Objective approach measure these three
ingredients in the real world. Determine if
observers are in fact optimal. (Bayesian ideal
observer analysis)
noise distribution / likelihood
cost function
prior

• Definitive answer yes or no. Can quantify
  how close observers are to optimal

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Two basic approaches
2. Subjective approach measure stimuli and
observer responses. Is there some setting of
these three under which observer can be said to
be Bayes optimal?
Under-constrained problem in general - have to
make some assumptions
noise distribution / likelihood
cost function
prior

• Not clear if the answer is ever no. (Would
  anyone publish a null result?)
• However do the noise, cost and prior make
  sense? Is it reasonable to think that this is
  what subjects are really doing? (Offers
  parsimonious explanation of percepts)