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Decision Making Theories in Neuroscience

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Decision Making Theories in Neuroscience

Alexander Vostroknutov

October 2008

From Sugrue, Corrado and Newsome

Nature Neuroscience, 2005, Vol 6, May 2005

- Weak motion – chance performance; strong motion – optimal performance
- “Decision making” area should aggregate noisy signal and suggest the decision

- LIP area – part of visuo-motor pathway
- Its activation is covaried with choice AND modulated by movement strength during motion
- not purely sensory (mistake trials);
- not purely decision oriented (modulated by strength of movement)
- LIP is where “deliberation” takes place

From Sugrue, Corrado and Newsome

Nature Neuroscience, 2005, Vol 6, May 2005

From Bogacz, 2007,TRENDS in Cog. Sci., Vol 11(3)

- Neurons in Visual cortex provide evidence for alternatives (noisy)
- Intergation takes place (in LIP), removes noise
- The choice is made once certain criterion is reached (confidence level)

- This procedure can be formulated as a statistical problem
- Statistical test to optimize decision making
- It can be tested whether the brain implements optimal test (evolution)
- Links optimal tests with neurobiology (basal ganglia)
- and behavior (speed-accuracy tradeoff)

- Sequential Probability Ratio Test (Wald)
- A procedure to distinguish two distributions H0: p=p0 and H1: p= p1 given a sequence of observations {yn}
- Sum log-likelihood ratios of incoming data and stop once threshold is reached: Sn = Sn-1 + log(p0(yn)/p1(yn))
- Given fixed accuracy, SPRT requires the least expected number of observations
- Animals would be interested in implementing SPRT: minimizes reaction time

Input A

A - B

I > 5: choose A

I < -5: choose B

Input B

Integrator (I)

- Is there simple way to implement SPRT?
- Integrator accumulates evidence about the difference of inputs
In = In-1 + An - Bn

- Once threshold is reached (|In| > 5), choose A or B

- Continuous limit of SPRT can be described by Wiener process with drift (Bogacz et al, 2006)
dy = (mA-mB)dt + cdW

- Choose once threshold is reached(assumed: A and B are normal, same variance)
- mA is mean of alternative A
- This is exactly Diffusion Model!
- Thus DM implements SPRT
- Given fixed accuracy, DM has the best reaction time(important for animals)
- Simple to implement in neural networks(requires only addition and subtraction)

- How can we test whether something like diffusion model is implemented in the brain?
- We have evidence (LIP) of the presence of intergators
- We need evidence for the presence of “criterion satisfying” region
- Good candidate: basal ganglia
- They resolve competition between cortical and sub-cortical systems that want expression
- Inhibit all actions; the “winning system” is allowed to express itself through disinhibition

Input A1

A1 – ln[exp(A2)+exp(A3)]

- DMn implements optimal MULTI SPRT
- Uses exponentiation
- Neurons which exponentiate are rare
- Good evidence for Diffusion Model

I1

choose whenever any of these is higher than threshold

Input A2

A2 – ln[exp(A1)+exp(A3)]

I2

Input A3

A3 – ln[exp(A1)+exp(A2)]

I3

- Bogacz, 2007 reports studies that demonstrate that neurons in subthalamic nucleus (STN) perform exponentiation
- STN targets output nuclei of basal ganglia, that “decide” on which system to allow to act

- Difficult to perceive the difference between n and n+1 grains of sugar
- Non-transitivity of indifference
- Beyond the scope of classical preferences model
- DM suggests a simple and natural way to model this

price

A

B

C

quality

A

B

A, B available:

- Violation of Weak Axiom of Revealed Preference(recent evidence: Kroll, Vogt, 08)
- Again, DM with 3 alternatives gives simple explanation
- Prospect Theory, Regret do not account for this
- Can save the “existence” of underlying preferences
- Additional prediction of DM: smaller reaction time in second case

80%

20%

A

B

A, B, C available:

50%

50%

S1 = $1

R1 = ($5, 0.1; $1, 0.89; $0, 0.01)

- Allais paradox: violation of Expected Utility maximization
- In choice between S1 and R1: information about S1 is accumulated much faster than about R1: high chance of hitting S1 threshold
- In choice between S2 and R2: information accumulates at comparable speeds, R2 is almost like S2, only with $5 instead of $1, high chance to hit R2 threshold first
- Additional prediction of DM: reaction time in S1-R1 choice is shorter than in S2-R2
- No need to get rid of Expected Utility

EU maximizer prefers S’s or R’s

Evidence: S1 > R1 and R2 > S2

S2 = ($1, 0.11; $0, 0.89)

R2 = ($5, 0.1; $0, 0. 9)

- It seems like there is evidence that Diffusion Model is implemented in the brain
- Sensory inputs are integrated in the respective pre-motor regions (LIP)
- Basal ganglia check which option should be chosen by comparing competing “integrators” to the threshold
- Important for economists. DM explains with ease many different phenomena