Dynamic Analysis of Learning in Behavioral Experiments

Abstract

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 (Ͼ0.95) 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.

A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

“…On the other hand, if β = 0, so that there is no relation between the continuous performance measure and the cognitive state, then (7)- (11) simplify to the recursive filter algorithm for estimating an unobservable cognitive state process from binary performance measures given in Smith et al 2004Smith et al ,2005.…”

“…For the continuous performance measure or reaction time process (2), we chose the parameters α = 1.0489, β = −0.2165, and = 0.4944, and for the binary observation models or series of correct or incorrect responses, (4) we chose γ = 0.99 and μ = −0.5. Because a state-space model of the form we proposed here has not been previously reported, we determined these parameter values for the simulated model based on preliminary analyses of performance data from the experiments described in (Wirth et al 2003;Smith et al 2004Smith et al ,2007. We learned from these analyses that parameter values such as the ones chosen here would generate performance data that were consistent with those reported when learning occurred.…”

“…2b, black curve). We next analyzed the binary observations using the binary filter algorithm (Wirth et al 2003;Smith and Brown 2003;Smith et al 2004Smith et al ,2005 to estimate the cognitive state, and its 95% confidence intervals (Fig. 2c), as well as the learning curve and its 95% confidence intervals (Fig.…”

“…Applications of this paradigm range from control systems (Kitagawa and Gersch 1996;Mendel 1995), speech recognition (Becchetti and Ricotti 1999), studies of protein structure (White et al 1994), analysis of genetic networks (Harbison et al 2004), studies of neural representations of biological signals (Brown et al 1998;Barbieri et al 2004;Eden et al 2004;Smith and Brown 2003) and analyses of learning (Wirth et al 2003;Smith et al 2004). A state-space model consists of two equations: a state equation and an observation equation.…”

“…The state equation defines an unobservable process whose evolution is tracked across time. Because the state process is unobservable, these models are often referred to as hidden Markov or latent process models (Fahrmeir and Tutz 2002;Roweis and Ghahramani 1999;Smith and Brown 2003;Smith et al 2004). The observation equation defines how the state is measured or recorded.…”