Decision making theories in neuroscience
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Decision Making Theories in Neuroscience. Alexander Vostroknutov October 2008. Choice in the brain. From Sugrue, Corrado and Newsome Nature Neuroscience, 2005, Vol 6, May 2005. Weak motion – chance performance; strong motion – optimal performance

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Decision Making Theories in Neuroscience

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Decision Making Theories in Neuroscience

Alexander Vostroknutov

October 2008


Choice in the brain

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


Monkey brain

  • 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


Three processes of choice

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)


Optimal decision making

  • 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)


Optimality criterion

  • 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)

Diffusion model (2 alternatives)

  • 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


Diffusion Model is optimal

  • 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)


Connection to the brain

  • 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


Diffusion Model (n alternatives)

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


Evidence

  • 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


More evidence


Diffusion Model and Economics

  • 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

Diffusion Model and Economics

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%


Diffusion Model and Economics

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)


Conclusion

  • 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


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