Estimation in the three-state markov learning model

The problem of estimation of the parameters of the Bower three-state learning model is discussed for three forms of the model. In the simplest case, a minimum variance unbiased estimator is found and is presented with its asymptotic distribution theory and with a method of obtaining approximate confidence intervals. In the other cases, methods are discussed for obtaining the maximum likelihood estimators at least approximately. All estimation techniques are illustrated by application to a set of data obtained by Theios.This research was supported by the Office of Naval Research Contract Nonr-225(17), (NR 171-034).     

A component model for stimulus variables in discrimination learning

A general function is derived describing the conditioning of a single stimulus component in a discriminative situation. This function, together with the combinatorial rules of statistical learning theory [5, 12], generates empirically testable formulas for learning of classical two-alternative discriminations, probabilistic discriminations, and discriminations based on the outcomes of preceding trials in partial reinforcement experiments.The researches on which this paper is based were facilitated by a grant from the National Science Foundation.     

Derivation of learning process statistics for a general markov model

A Markov learning model may be stated in the form of a transition matrix, starting vector, and response probability vector. Utilizing these and some general properties of absorbing Markov chains, general expressions are derived for several statistics of the learning process which can be applied to any model of this form. Included are derivations for the mean learning curve, number of total errors, trial numbers of the first success and the last error, and the number of error runs. As an illustration, all derivations are worked out for the simple two-state one-element model.     

A configural analysis for feature-negative discrimination learning.

In 4 experiments, rats were initially trained with an A+ AXo discrimination in which Stimulus A by itself signaled the delivery of food, A+, whereas the simultaneous presentation of A and X was followed by nothing, AXo. In each experiment X was then paired with food prior to a test phase in which A and X were again presented for a discrimination. The discrimination was of the form A+ AXo in Experiments 1 and 2, whereas it was of the form X+ AXo for Experiments 3 and 4. In all 4 experiments the test discrimination was acquired more rapidly than a control discrimination. The results are interpreted in terms of the original A+ AXo discrimination resulting in the growth of an association between a representation of the entire AX compound and the effects of nonreinforcement.     

A multivariate model for discrimination methods

We describe a multivariate model for a certain class of discrimination methods in this paper and discuss a multivariate Euclidean model for a particular method, the triangular method. The methods of interest involve the selection or grouping of stimuli drawn from two stimulus sets on the basis of attributes invoked by the subject. These methods are commonly used for estimation and hypothesis testing concerning possible differences between foods, beverages, odorants, tastants and visual stimuli.Mathematical formulation of the bivariate model for the triangular method is provided as well as extensive Monte Carlo results for up to 10-dimensional cases. The effect of correlation structure and variance inequality are discussed. Results from these methods (as probability of a correct response) are not monotonically related to the distance between the means of the stimulus sets from which the stimuli are drawn but depend in a particular way on dimensionality, correlation structure, and the relative orientation of the momentary sensory values in a multidimensional space. The importance of these results to the validity of these methods as currently employed is discussed and the possibility of developing a new approach to multidimensional scaling on the basis of this new theory is considered.     

A model of three-choice discrimination learning under complete and incomplete feedback conditions

The Bower and Trabasso model of concept identification was extended to cover problems in which three stimuli were presented simultaneously and S pointed to the one he thought was correct. The E gave complete feedback by indicating the correct stimulus, or incomplete feedback by saying “correct” or “wrong.” The model accurately accounted for the significant difference in total errors between the two feedback conditions by incorporating process assumptions reflecting the logical difference in information content of the two types of feedback. Using a single set of parameter estimates, the model made satisfactory quantitative predictions of several statistics for both feedback conditions. Some deviations from the model's predictions were found in the length of terminal error runs, indicating that Ss were possibly using memory more extensively than posited by the model.     

A role for stimulus generalization in conditional discrimination learning

In each of three experiments on discrimination learning by rats, whether or not a 10-sec target stimulus was followed by food was determined by the nature of a 2-min background stimulus that accompanied it. A conditional discrimination was employed in Experiment 1 such that background A indicated food would follow one target but not the other, whereas this relationship between the targets and food was reversed in the presence of background B. Experiment 2 employed two feature-positive discriminations. Subsequent test trials revealed that the background for one discrimination was able to enhance responding during the target for the other discrimination. Experiment 3 employed a feature-positive and a feature-negative discrimination prior to test trials in which each target was presented separately during a compound of both background stimuli. The compound enhanced responding to the target from the feature-positive discrimination and reduced it to the target from the feature-negative discrimination. We suggest that to accommodate all these findings, the best explanation is provided by a configural model of Pavlovian conditioning.     

A diffusion model for discrimination of temporal numerosity

This paper presents a model for sequential discrimination between the temporal frequencies of two discrete events. The model results from adjoining a theory for continuous estimation of temporal numerosity to a mathematical representation of the response criterion. A simple set of assumptions is used to describe the time evolution of numerosity estimates by a stochastic diffusion process. The predictions of the model are extensively compared to a body of results presented in a previous report, with an emphasis on individual performances. It is shown that a number of response strategies, observed in actual experiments, can be predicted by generalizing the classical notion of a single-valued response threshold to a stochastic, time-varying process.     

A new protocol for investigating visual two-choice discrimination learning in lizards

Animal Cognition - One of the most widely studied abilities in lizards is discrimination learning. The protocols used to test lizards are often novel or adapted from other taxa without proper...     

A search for contrast effects in discrete-trial discrimination learning by pigeons

Behavioral contrast has often been observed in free-operant experiments with pigeons, rarely in discrete-trial experiments with rats. Although Jenkins (1961) and Terrace (1963) have reported a discrete-trial contrast effect in pigeons, a series of experiments reported here found no evidence that latency of responding to S+ in a discrete-trial situation was reliably decreased by alternating reinforced trials to S+ with nonreinforced trials to S?. Latency of responding to S+ was affected neither by the length of the preceding intertrial interval (within the range of 10–60 sec), nor by whether the preceding trial had been to S+ or to S?. The results of two of these experiments suggested that the appearance of positive contrast in Jenkins's experiment was a consequence of differences in the variability of the intertrial interval experienced by control and discrimination groups. In two final experiments, employing standard free-operant procedures, contrast was observed as an increase in rate of responding to S+, but not as a decrease in latency of the first response on each S+ trial. The implication is that contrast effects are more readily observed with the rate measures of free-operant experiments than with the latency measures of discrete-trial experiments.     

Sensitivity and responsivity measures for discrimination learning

The present report considers alternative measures of sensitivity and response bias for the discrimination learning paradigm. The classical signal detection measures, d′ and β, were compared with their nonparametric equivalents, A′ and B″, with theoretical measures derived from threshold theory and with empirical measures derived from the ROC graph. Differential rabbit eyelid conditioning data from three experiments were analyzed with these measures, and the results of these analyses were used along with other information to determine which measures of sensitivity and response bias are most useful for the analysis of discrimination learning data.     

A cognitive probability model for learning

A quantitative model for the behavior of albino rats in choice-making situations is presented. The model, which is based upon a cognitive conceptualization of the learning process, is shown to yield predictions which are equivalent to those produced by the linear operator stochastic models at the asymptotic limit but which differ from these during early trials in the learning situation.     

A unified model for perceptual learning

Perceptual learning in adult humans and animals refers to improvements in sensory abilities after training. These improvements had been thought to occur only when attention is focused on the stimuli to be learned (task-relevant learning) but recent studies demonstrate performance improvements outside the focus of attention (task-irrelevant learning). Here, we propose a unified model that explains both task-relevant and task-irrelevant learning. The model suggests that long-term sensitivity enhancements to task-relevant or irrelevant stimuli occur as a result of timely interactions between diffused signals triggered by task performance and signals produced by stimulus presentation. The proposed mechanism uses multiple attentional and reinforcement systems that rely on different underlying neuromodulators. Our model provides insights into how neural modulators, attentional and reinforcement learning systems are related.