A Neural Mechanism for Decision Making K C Y W D K D O P E D B A I Q - - PowerPoint PPT Presentation

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A Neural Mechanism for Decision Making K C Y W D K D O P E D B A I Q - - PowerPoint PPT Presentation

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A Neural Mechanism for Decision Making K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S E N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z C P Q What is a decision? A commitment to a proposition or selection of an

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A Neural Mechanism for Decision Making

K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S E N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z C P Q

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SLIDE 2

What is a decision?

  • A commitment to a proposition or selection
  • f an action
  • Based on

– evidence – prior knowledge – payoff

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SLIDE 3

Why study decisions?

  • They are a model of higher brain function
  • They are experimentally tractable

– Combined behavior and physiology in rhesus monkeys

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SLIDE 4

Direction-Discrimination Task Reaction-time version

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SLIDE 5

Direction-Discrimination Task Direction-Discrimination Task Reaction-time version

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Direction-Discrimination Task Direction-Discrimination Task Reaction-time version

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SLIDE 7
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SLIDE 8

Direction-Discrimination Task Direction-Discrimination Task Reaction-time version

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SLIDE 9

Direction-Discrimination Task

Reward for correct choice

Direction-Discrimination Task Reaction-time version

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SLIDE 10

Psychometric function: Accuracy

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Chronometric function: Speed

Reaction time [ms]

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SLIDE 12
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SLIDE 13

Information is coded by spikes

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SLIDE 14

Hubel, 1988 “Eye, brain and vision”

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SLIDE 15

Sensory “Evidence”

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SLIDE 16
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SLIDE 17

Albright et al., 1984 J. Neurophysiol.

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SLIDE 19

100 ms

120 60 60

Spikes/sec

120 60

Spatially-selective, eye movement-related, persistent activity in area LIP

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SLIDE 20

LIP activity during direction discrimination task

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SLIDE 21

LIP activity during direction discrimination task

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SLIDE 22

LIP activity during direction discrimination task

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SLIDE 23

Average LIP activity in RT motion task

Roitman & Shadlen, 2002 J. Neurosci.

choose Tin choose Tout

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SLIDE 24

High motion strength High motion strength Low motion strength Time ~1 sec Stimulus

  • n

Stimulus

  • ff

Spikes/s Time ~1 sec Stimulus

  • n

Stimulus

  • ff

Spikes/s L

  • w

m

  • t

i

  • n

s t r e n g t h

A Neural Integrator for Decisions?

MT: Sensory Evidence Motion energy “step” LIP: Decision Formation Accumulation of evidence “ramp”

Threshold

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SLIDE 25

Diffusion to bound model

Positive bound Negative bound

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SLIDE 26

Proposed by Wald, 1947 and Turing (WW II, classified); Stone, 1960; then Laming, Link, Ratcliff, Smith, . . .

Diffusion to bound model

Positive bound or Criterion to answer “1” Negative bound or Criterion to answer “2”

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SLIDE 27

Momentary evidence e.g., ∆Spike rate: MTRight– MTLeft Accumulated evidence for Rightward and against Leftward Criterion to answer “Right” Criterion to answer “Left”

Diffusion to bound model

Shadlen & Gold (2004) Palmer et al (in press)

µ = kC

C is motion strength (coherence)

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SLIDE 28

Best fitting chronometric function “Diffusion to bound”

t(C) = B kC tanh(BkC) + tnd

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SLIDE 29

Predicted psychometric function “Diffusion to bound”

P = 1 1+ e

2k C B

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SLIDE 30

µ = kC

Criterion to answer “Right” Criterion to answer “Left” Momentary evidence e.g., ∆Spike rate: MTRight– MTLeft Accumulated evidence for Rightward and against Leftward

Time (ms)

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SLIDE 31

µ = kC

Criterion to answer “Right” Criterion to answer “Left” Momentary evidence e.g., ∆Spike rate: MTRight– MTLeft Accumulated evidence for Rightward and against Leftward

  • LIP represents ∫ dt of momentary motion evidence
  • Momentary evidence is a spike rate difference from area MT
  • The accumulated evidence used by the monkey is in area LIP
  • How and where is the integral computed?
  • How is the bound set?
  • How is a bound crossing detected?
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SLIDE 32
  • More RIGHT choices
  • Faster RIGHT choices
  • Slower LEFT choices
  • More RIGHT choices
  • Faster RIGHT choices
  • Slower LEFT choices

Bound for RIGHT choice Bound for LEFT choice Bound for RIGHT choice Bound for LEFT choice

Stimulate RIGHTWARD MT neurons

The momentary evidence is a ∆ between

  • pposite direction signals in area MT

The accumulated evidence used by the monkey is in area LIP

Stimulate RIGHT CHOICE LIP neurons

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SLIDE 33

µ = kC

Criterion to answer “Right” Criterion to answer “Left” Momentary evidence e.g., ∆Spike rate: MTRight– MTLeft Accumulated evidence for Rightward and against Leftward

  • LIP represents ∫ dt of momentary motion evidence
  • Momentary evidence is a spike rate difference from area MT
  • The accumulated evidence used by the monkey is in area LIP
  • How and where is the integral computed?
  • How is the bound set?
  • How is a bound crossing detected?
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SLIDE 34

Fixation 1st Stim & Targets 2nd Stim 3rd Stim 4th Stim Delay & Sacade 0 ms 500 ms 1000 ms 1500 ms 2000 ms

Time

Probabilistic categorization task: 4-card stud

Tianming Yang

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SLIDE 35
  • -0.9 -0.7 -0.5 -0.3 0.3 0.5 0.7 0.9 +

Favoring Green Favoring Red

0.9

  • 0.9

0.7

  • 0.9
  • 0.2

0.61 0.39 Weight of evidence in favor of red (log10 likelihood ratio)

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From sensorimotor integration to cognition and its disorders

Sensory evidence Motor

  • utput

Prior knowledge Expected payoff Urgency Potential behavior

  • r plan
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SLIDE 37

From sensorimotor integration to cognition and its disorders

Sensory evidence Motor response Area LIP

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SLIDE 38

From sensorimotor integration to cognition and its disorders

Sensory evidence Motor

  • utput

Area MT Area LIP Oculomotor System

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From sensorimotor integration to cognition and its disorders

Leaky integration  confusion

Evanescent sensory stream Plans for the future

dt

  • Sensory

evidence Motor response

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Turing’s strategy: sequential analysis

WOE = 10 log10

1 13

( )

1 26

( )

  • = +3.0 db

match 10 log10

12 13

( )

25 26

( )

  • = 0.17db

non - match

  • Weight of evidence

in favor of common rotor setting

Hypothesis: Messages encrypted by Enigma devices in same state

K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F N E N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

5

Weight of evidence in favor

  • f common settings (decibans)
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SLIDE 41

Turing’s strategy: sequential analysis

WOE = 10 log10

1 13

( )

1 26

( )

  • = +3.0 db

match 10 log10

12 13

( )

25 26

( )

  • = 0.17db

non - match

  • Weight of evidence

in favor of common rotor setting

Hypothesis: Messages encrypted by Enigma devices in same state

K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F N E N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

5

Weight of evidence in favor

  • f common settings (decibans)
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SLIDE 42

K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F N E N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

5

Weight of evidence in favor

  • f common settings (decibans)

K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F N E N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

WOE = 10 log10

1 13

( )

1 26

( )

  • = +3.0 db

match 10 log10

12 13

( )

25 26

( )

  • = 0.17db

non - match

  • Weight of evidence

in favor of common rotor setting

Turing’s strategy: sequential analysis

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SLIDE 43

10 20 30 40 50 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Response (spikes/sec) Probability

Response (spikes/s) Frequency of

  • ccurrence

LEFT preferring MT neurons RIGHT preferring MT neurons

Variable response to weak RIGHTWARD motion

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SLIDE 44
  • 40
  • 20

20 40 0.01 0.02 0.03 0.04 0.05 0.06

Frequency of

  • ccurrence

Response difference (spikes/s)

Difference in spike rate is proportional to the logarithm of the likelihood ratio

Distribution of response DIFFERENCES, right-left, for rightward motion

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SLIDE 45

0.2 0.4 0.6 0.8

Time (s) Accumulated difference (R-L)

Amount of accumulated evidence required to choose “LEFT”

Weight of evidence Decibans Belief Log of Likelihood Ratio

Amount of accumulated evidence required to choose “RIGHT”

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SLIDE 46

Yn = Xi

i=1 n

  • random walk or diffusion

M X() E eX

  • =

f (x)exdx

  • def. of MGF for X

MYn () = M X

n () MGF for sums

M

Y () = P +eA + (1 P +)eA MFG for

Y

  • Y stopped accumulation

Random walk to bounds at ±A

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SLIDE 47

Stochastic processes: partial sums and Wald’s martingale

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Stochastic processes: partial sums and Wald’s martingale

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SLIDE 49

E Zn

[ ] = E M

X

n()eYn

  • = M

X

n()E eYn

  • = M

X

n()MYn ()

= 1 E Zn+1 Y1,Y2,…,Yn

  • = E M X

(n+1)()eYn+1 Y1,Y2,…,Yn

  • = E M X

(n+1)()e(Yn + Xn+1 )

  • = E[M X

1()M X n()eYne Xn+1 ]

= E[ZnM X

1()e Xn+1 ]

= M X

1()ZnE e Xn+1

  • = Zn

Wald’s martingale & identity

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SLIDE 50

E

  • Z
  • = E Zn

[ ] = 1

E M

X

n()e Y

  • = 1

If there were a value for such that M X() = 1, it no longer matters that n is a random number. At this special value, 1, E e1

Y

  • = 1

E.g., for the Normal distribution, with mean and variance 2 , 1 = 2µ 2 M

Y (1) = P +e1A + (1 P +)e1A = 1

P

+ =

1 1+ e1A

Use Wald’s martingale to simplify M

Y ()