Decision Making Theories in Neuroscience

Alexander Vostroknutov

October 2008

Choice in the brain

From Sugrue, Corrado and NewsomeNature 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 NewsomeNature 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

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

Input A

Input B

A - B

Integrator (I)I > 5: choose AI < -5: choose 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)

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

Input A1

Input A2

A1 – ln[exp(A2)+exp(A3)]

choose whenever any of these is higher than threshold

Input A3

A2 – ln[exp(A1)+exp(A3)]

A3 – ln[exp(A1)+exp(A2)]

I1

I2

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

Diffusion Model and Economics

• 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

quality

priceA

BC

A, B available: A B80% 20%

A, B, C available: A B50% 50%

Diffusion Model and Economics

• 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

S1 = $1R1 = ($5, 0.1; $1, 0.89; $0, 0.01)

S2 = ($1, 0.11; $0, 0.89)R2 = ($5, 0.1; $0, 0. 9)

EU maximizer prefers S’s or R’sEvidence: S1 > R1 and R2 > S2

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