Bayesian Perception - PowerPoint PPT Presentation

1 / 74
About This Presentation
Title:

Bayesian Perception

Description:

... of nonlinear units with bell shaped tuning curves and a ... VA. Standard Models of ... to either IOC or VA depending on stimulus duration, eccentricity, ... – PowerPoint PPT presentation

Number of Views:100
Avg rating:3.0/5.0
Slides: 75
Provided by: Ale8411
Category:

less

Transcript and Presenter's Notes

Title: Bayesian Perception


1
Bayesian Perception
2
General Idea
  • Perception is a statistical inference
  • The brain stores knowledge about P(I,V) where I
    is the set of natural images, and V are the
    perceptual variables (color, motion, object
    identity)
  • Given an image, the brain computes P(VI)

3
General Idea
  • Decisions are made by collapsing the distribution
    onto a single value
  • or

4
Key Ideas
  • The nervous systems represents probability
    distributions. i.e., it represents the
    uncertainty inherent to all stimuli.
  • The nervous system stores generative models, or
    forward models, of the world (e.g. P(IV)).
  • Biological neural networks can perform complex
    statistical inferences.

5
A simple problem
  • Estimating direction of motion from a noisy
    population code

6
Population Code
Tuning Curves
Pattern of activity (A)
7
Maximum Likelihood
8
Maximum Likelihood
  • The maximum likelihood estimate is the value of
    q maximizing the likelihood P(Aq). Therefore, we
    seek such that
  • is unbiased and efficient.

9
(No Transcript)
10
MT
V1
11
Preferred Direction
MT
V1
Preferred Direction
12
Linear Networks
  • Networks in which the activity at time t1 is a
    linear function of the activity at the previous
    time step.

13
Linear Networks
Equivalent to population vector
14
Nonlinear Networks
  • Networks in which the activity at time t1 is a
    nonlinear function of the activity at the
    previous time step.

15
Preferred Direction
MT
V1
Preferred Direction
16
Maximum Likelihood
17
Standard Deviation of
18
Standard Deviation of
19
Weight Pattern
Amplitude
Difference in preferred direction
20
Performance Over Time
21
(No Transcript)
22
General Result
  • Networks of nonlinear units with bell shaped
    tuning curves and a line attractor (stable smooth
    hills) are equivalent to a maximum likelihood
    estimator regardless of the exact form of the
    nonlinear activation function.

23
General Result
  • Pro
  • Maximum likelihood estimation
  • Biological implementation (the attractors
    dynamics is akin to a generative model )
  • Con
  • No explicit representations of probability
    distributions
  • No use of priors

24
Motion Perception
25
The Aperture Problem
26
The Aperture Problem
27
The Aperture Problem
28
The Aperture Problem
29
The Aperture Problem
30
The Aperture Problem
31
The Aperture Problem
32
The Aperture Problem
33
The Aperture Problem
34
The Aperture Problem
35
The Aperture Problem
36
The Aperture Problem
37
The Aperture Problem
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
38
The Aperture Problem
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
39
The Aperture Problem
40
The Aperture Problem
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
41
The Aperture Problem
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
42
Standard Models of Motion Perception
  • IOC interception of constraints
  • VA Vector average
  • Feature tracking

43
Standard Models of Motion Perception
IOC
VA
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
44
Standard Models of Motion Perception
IOC
VA
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
45
Standard Models of Motion Perception
IOC
VA
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
46
Standard Models of Motion Perception
IOC
VA
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
47
Standard Models of Motion Perception
  • Problem perceived motion is close to either IOC
    or VA depending on stimulus duration,
    eccentricity, contrast and other factors.

48
Standard Models of Motion Perception
  • Example Rhombus

Percept VA
Percept IOC
IOC
IOC
VA
VA
Vertical velocity (deg/s)
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
Horizontal velocity (deg/s)
49
Bayesian Model of Motion Perception
  • Perceived motion correspond to the MAP estimate

50
Prior
  • Human observers favor slow motions

51
Likelihood
  • Weiss and Adelson

52
Likelihood
53
Likelihood
54
Bayesian Model of Motion Perception
  • Perceived motion correspond to the MAP estimate

55
Motion through an Aperture
  • Humans perceive the slowest motion

56
Motion through an Aperture
Likelihood
50
Vertical Velocity
0
-50
-50
0
50
ML
Horizontal Velocity
50
50
Vertical Velocity
Vertical Velocity
MAP
0
0
-50
-50
Prior
Posterior
-50
0
50
-50
0
50
Horizontal Velocity
Horizontal Velocity
57
Motion and Constrast
  • Humans tend to underestimate velocity in low
    contrast situations

58
Motion and Contrast
Likelihood
50
Vertical Velocity
0
-50
High Contrast
-50
0
50
ML
Horizontal Velocity
50
50
Vertical Velocity
Vertical Velocity
MAP
0
0
-50
-50
Prior
Posterior
-50
0
50
-50
0
50
Horizontal Velocity
Horizontal Velocity
59
Motion and Contrast
Likelihood
50
Vertical Velocity
0
-50
Low Contrast
-50
0
50
ML
Horizontal Velocity
MAP
50
50
Vertical Velocity
Vertical Velocity
0
0
-50
-50
Prior
Posterior
-50
0
50
-50
0
50
Horizontal Velocity
Horizontal Velocity
60
Motion and Contrast
  • Driving in the fog in low contrast situations,
    the prior dominates

61
Moving Rhombus
Likelihood
50
50
Vertical Velocity
Vertical Velocity
0
0
-50
-50
High Contrast
-50
0
50
-50
0
50
IOC
Horizontal Velocity
Horizontal Velocity
MAP
50
50
Vertical Velocity
Vertical Velocity
0
0
-50
-50
-50
0
50
-50
0
50
Prior
Posterior
Horizontal Velocity
Horizontal Velocity
62
Moving Rhombus
Likelihood
50
50
0
Vertical Velocity
0
Vertical Velocity
-50
-50
Low Contrast
-50
0
50
-50
0
50
IOC
Horizontal Velocity
Horizontal Velocity
50
50
MAP
Vertical Velocity
Vertical Velocity
0
0
-50
-50
-50
0
50
-50
0
50
Prior
Posterior
Horizontal Velocity
Horizontal Velocity
63
Moving Rhombus
64
Moving Rhombus
  • Example Rhombus

Percept VA
Percept IOC
IOC
IOC
VA
VA
Vertical velocity (deg/s)
Vertical velocity (deg/s)
Horizontal velocity (deg/s)
Horizontal velocity (deg/s)
65
Barberpole Illusion
66
Plaid Motion Type I and II
67
Plaids and Contrast
68
Plaids and Time
  • Viewing time reduces uncertainty

69
Ellipses
  • Fat vs narrow ellipses

70
Ellipses
  • Adding unambiguous motion

71
Biological Implementation
  • Neurons might be representing probability
    distributions
  • How?

72
Biological Implementation
  • Encoding model

73
Biological Implementation
  • Decoding
  • Linear decoder deconvolution

74
Biological Implementation
  • Decoding nonlinear
  • Represent P(VW) as a discretized histogram and
    use EM to evaluate the parameters
Write a Comment
User Comments (0)
About PowerShow.com