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The Journal of Neuroscience, January 14, 2004, 24(2):447-461; doi:10.1523/JNEUROSCI.2908-03.2004

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Behavioral/Systems/Cognitive
Dynamic Analysis of Learning in Behavioral Experiments

Anne C. Smith,^1,2 Loren M. Frank,^1,2 Sylvia Wirth,³ Marianna Yanike,³ Dan Hu,⁴ Yasuo Kubota,⁴ Ann M. Graybiel,⁴ Wendy A. Suzuki,³ and Emery N. Brown^1,2

¹Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, Massachusetts 02114, ²Division of Health Sciences and Technology, Harvard Medical School-Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, ³Center for Neural Science, New York University, New York, New York 10003, and ⁴Department of Brain and Cognitive Sciences and McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Understanding how an animal's ability to learn relates to neural activity or is altered by lesions, different attentional states, pharmacological interventions, or genetic manipulations are central questions in neuroscience. Although learning is a dynamic process, current analyses do not use dynamic estimation methods, require many trials across many animals to establish the occurrence of learning, and provide no consensus as how best to identify when learning has occurred. We develop a state-space model paradigm to characterize learning as the probability of a correct response as a function of trial number (learning curve). We compute the learning curve and its confidence intervals using a state-space smoothing algorithm and define the learning trial as the first trial on which there is reasonable certainty (>0.95) that a subject performs better than chance for the balance of the experiment. For a range of simulated learning experiments, the smoothing algorithm estimated learning curves with smaller mean integrated squared error and identified the learning trials with greater reliability than commonly used methods. The smoothing algorithm tracked easily the rapid learning of a monkey during a single session of an association learning experiment and identified learning 2 to 4 d earlier than accepted criteria for a rat in a 47 d procedural learning experiment. Our state-space paradigm estimates learning curves for single animals, gives a precise definition of learning, and suggests a coherent statistical framework for the design and analysis of learning experiments that could reduce the number of animals and trials per animal that these studies require.

Key words: learning; behavior; state-space model; hidden Markov model; change-point test; association task; EM algorithm

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Received June 11, 2003; revised October 8, 2003; accepted October 20, 2003.

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