Title: The Computing Brain: Focus on Decision-Making
1The Computing BrainFocus on Decision-Making
Angela Yu ajyu_at_ucsd.edu
2Understanding the Brain/Mind?
Cognitive Neuroscience
A powerful analogy the computing brain
3An Example Decision-Making
?
4An Example Decision-Making
What are the computations involved?
2. Uncertainty
?
1. Decision
3. Costs
5Monkey Decision-Making
Random dots coherent motion paradigm
6Random Dot Coherent Motion Paradigm
30 coherence
5 coherence
7How Do Monkeys Behave?
Accuracy vs. Coherence
ltRTgt vs. Coherence
(Roitman Shadlen, 2002)
8What Are the Neurons Doing?
Saccade generation system
MT Sustained response
(Britten, Shadlen, Newsome, Movshon, 1993)
(Britten Newsome, 1998)
9What Are the Neurons Doing?
Saccade generation system
LIP Ramping response
(Roitman Shalden, 2002)
(Shadlen Newsome, 1996)
10A Computational Description
1. Decision Left or right? Stop now or continue?
?(t) input(1), , input(t) ? left, right, wait
11Timed Decision-Making
12A Computational Description
2. Uncertainty Sensory noise (coherence)
13Timed Decision-Making
14A Computational Description
3. Costs Accuracy, speed
cost(?) Pr(error) c(mean RT)
Optimal policy ? minimizes the cost
15Timed Decision-Making
more accurate
- more time
16Mathematicians Solved the Problem for Us
Wald Wolfowitz (1948)
- Optimal policy
- accumulate evidence over time Pr(left) versus
Pr(right) - stop if total evidence exceeds left or right
boundary
17Model ? Neurobiology
Saccade generation system
Model
LIP Neural Response
18Model ? Behavior
Saccade generation system
Model
RT vs. Coherence
boundary
Coherence
19Putting it All Together
Saccade generation system
- MT neurons signal motion direction and strength
- LIP neurons accumulate information over time
- LIP response reflect behavioral decision (0
coherence) - Monkeys behave optimally (maximize accuracy
speed)
20Understanding the Brain/Mind?
Cognitive Neuroscience
A powerful analogy the computing brain
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22Sequential Probability Ratio Test
rt is monotonically related to qt, so we have
(a,b), alt0, bgt0.
In continuous-time, a drift-diffusion process w/
absorbing boundaries.
23Generalize Loss Function
(Bogacz et al, 2006)
Wald also proved a dual statement
SPRT (with some thresholds) minimizes the
expected sample size lt?gt.
This implies that the SPRT is optimal for all
loss functions that increase with inaccuracy and
(linearly in) delay (proof by contradiction).
24Neural Implementation
Saccade generation system
25Caveat Model Fit Imperfect
(Data from Roitman Shadlen, 2002 analysis from
Ditterich, 2007)
Accuracy
Mean RT
26Fix 1 Variable Drift Rate
(Data from Roitman Shadlen, 2002 analysis from
Ditterich, 2007)
(idea from Ratcliff Rouder, 1998)
27Fix 2 Increasing Drift Rate
(Data from Roitman Shadlen, 2002 analysis from
Ditterich, 2007)
28A Principled Approach
Trials aborted w/o response or reward if monkey
breaks fixation
(Data from Roitman Shadlen, 2002) (Analysis
from Ditterich, 2007)
- More urgency over time as risk of aborting
trial increases - Increasing gain equivalent to decreasing
threshold
29Imposing a Stochastic Deadline
(Frazier Yu, 2007)
Loss function depends on error, delay, and
whether deadline exceed
Optimal Policy is a sequence of monotonically
decaying thresholds
30Timing Uncertainty
(Frazier Yu, 2007)
Timing uncertainty ? lower thresholds
Theory applies to a large class of deadline
distributions delta, gamma, exponential, normal
31Some Intuitions for the Proof
(Frazier Yu, 2007)
Continuation Region
Shrinking!
32Summary
- Review of Bayesian DT optimality depends on
loss function - Decision time complicates things infinite
repeated decisions - Binary hypothesis testing SPRT with fixed
thresholds is optimal - Behavioral neural data suggestive, but
- imperfect fit. Variable/increasing drift
rate both ad hoc - Deadline ( timing uncertainty) ? decaying
thresholds - Current/future work generalize theory, test
with experiments
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