1 / 33

The Computing Brain: Focus on Decision-Making

The Computing Brain: Focus on Decision-Making. Cogs 1 March 5, 2009. Angela Yu ajyu@ucsd.edu. Behavior. Neurobiology. ?. ≈. Understanding the Brain/Mind?. Cognitive Neuroscience. A powerful analogy: the computing brain. An Example: Decision-Making. ?. THUR. 74  /61 . Coolness?.

malini
Download Presentation

The Computing Brain: Focus on Decision-Making

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Computing Brain:Focus on Decision-Making Cogs 1 March 5, 2009 Angela Yu ajyu@ucsd.edu

  2. Behavior Neurobiology ? ≈ Understanding the Brain/Mind? Cognitive Neuroscience A powerful analogy: the computing brain

  3. An Example: Decision-Making ?

  4. THUR 74/61 Coolness? Health? An Example: Decision-Making What are the computations involved? 2. Uncertainty ? 1. Decision 3. Costs:

  5. Monkey Decision-Making Random dots coherent motion paradigm

  6. Random Dot Coherent Motion Paradigm 30% coherence 5% coherence

  7. How Do Monkeys Behave? Accuracy vs. Coherence <RT> vs. Coherence (Roitman & Shadlen, 2002)

  8. Preferred Anti-preferred 25.6% Response Time Time MT tuning function 99.9% Response Time Time Direction () What Are the Neurons Doing? Saccade generation system MT: Sustained response (Britten & Newsome, 1998) (Britten, Shadlen, Newsome, & Movshon, 1993)

  9. What Are the Neurons Doing? Saccade generation system LIP: Ramping response (Roitman & Shalden, 2002) (Shadlen & Newsome, 1996)

  10. A Computational Description 1. Decision: Left or right? Stop now or continue? (t): input(1), …, input(t)  {left, right, wait}

  11. wait wait L R L R L R Timed Decision-Making

  12. A Computational Description 2. Uncertainty: Sensory noise (coherence)

  13. wait wait L R L R L R Timed Decision-Making

  14. A Computational Description 3. Costs: Accuracy, speed cost() = Pr(error) + c*(mean RT) Optimal policy * minimizes the cost

  15. wait wait L R L R L R Timed Decision-Making +: more accurate -: more time

  16. “left” boundary Pr(left) “right” boundary Mathematicians 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

  17. Model  Neurobiology Saccade generation system Model LIP Neural Response

  18. Model  Behavior Saccade generation system Model RT vs. Coherence boundary Coherence

  19. Putting 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)

  20. Behavior Neurobiology ? ≈ Understanding the Brain/Mind? Cognitive Neuroscience A powerful analogy: the computing brain

  21. Log posterior ratio undergoes a random walk: b’ rt 0 a’ Sequential Probability Ratio Test rt is monotonically related to qt, so we have (a’,b’), a’<0, b’>0. In continuous-time, a drift-diffusion process w/ absorbing boundaries.

  22. We assumed loss is linear in error and delay: What if it’s non-linear, e.g. maximize reward rate: Amongst all decision policies satisfying the criterion Generalize Loss Function (Bogacz et al, 2006) Wald also proved a dual statement: SPRT (with some thresholds) minimizes the expected sample size <>. This implies that the SPRT is optimal for all loss functions that increase with inaccuracy and (linearly in) delay (proof by contradiction).

  23. LIP - neural SPRT integrator? (Roitman & Shalden, 2002; Gold & Shadlen, 2004) LIP Response & Behavioral RT LIP Response & Coherence Time Neural Implementation Saccade generation system

  24. RT Distributions Caveat: Model Fit Imperfect (Data from Roitman & Shadlen, 2002; analysis from Ditterich, 2007) Accuracy Mean RT

  25. Accuracy Mean RT RT Distributions Fix 1: Variable Drift Rate (Data from Roitman & Shadlen, 2002; analysis from Ditterich, 2007) (idea from Ratcliff & Rouder, 1998)

  26. Accuracy Mean RT RT Distributions Fix 2: Increasing Drift Rate (Data from Roitman & Shadlen, 2002; analysis from Ditterich, 2007)

  27. A 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

  28. Probability Time Imposing 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

  29. Probability Time Timing Uncertainty (Frazier & Yu, 2007) Timing uncertainty  lower thresholds Theory applies to a large class of deadline distributions: delta, gamma, exponential, normal

  30. Some Intuitions for the Proof (Frazier & Yu, 2007) Continuation Region Shrinking!

  31. Summary • 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

More Related