Copyright © 2005 The Institute of Electronics, Information and Communication Engineers
Special Section on Nonlinear Theory and its Applications -- Papers |
Optimal Decisions: From Neural Spikes, through Stochastic Differential Equations, to Behavior*
1 The authors are with the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA. E-mail: pholmes{at}math.princeton.edu, 2 The authors are with the Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544-5263, USA., 3 The author is with the Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106, USA., 4 The author is with the Department of Computer Science, University of Bristol, Bristol BS8 1UB, UK., 5 The authors are with the Department of Psychiatry, University of Pennsylvania, Philadelphia, PA 19104, USA., 6 The author is with the Department of Psychology, Princeton University, Princeton, NJ 08544-5263, USA.
There is increasing evidence from in vivo recordings in monkeys trained to respond to stimuli by making left- or rightward eye movements, that firing rates in certain groups of neurons in oculo-motor areas mimic drift-diffusion processes, rising to a (fixed) threshold prior to movement initiation. This supplements earlier observations of psychologists, that human reaction-time and error-rate data can be fitted by random walk and diffusion models, and has renewed interest in optimal decision-making ideas from information theory and statistical decision theory as a clue to neural mechanisms. We review results from decision theory and stochastic ordinary differential equations, and show how they may be extended and applied to derive explicit parameter dependencies in optimal performance that may be tested on human and animal subjects. We then briefly describe a biophysically-based model of a pool of neurons in locus coeruleus, a brainstem nucleus implicated in widespread norepinephrine release. This neurotransmitter can effect transient gain changes in cortical circuits of the type that the abstract drift-diffusion analysis requires. We also describe how optimal gain schedules can be computed in the presence of time-varying noisy signals. We argue that a rational account of how neural spikes give rise to simple behaviors is beginning to emerge.
Key Words: stochastic differential equations, drift-diffusion process, dynamical systems, phase oscillators, decision-making models
Manuscript received March 31, 2005. Final manuscript received May 31, 2005.
* This paper is an expanded version of a plenary lecture delivered at the International Symposium on Nonlinear Theory and its Applications (NOLTA2004), Fukuoka, Japan, Nov. 29–Dec. 3, 2004.