Inferences about unobserved causes in human contingency learning

Estimates of the causal efficacy of an event need to take into account the possible presence and influence of other unobserved causes that might have contributed to the occurrence of the effect. Current theoretical approaches deal differently with this problem. Associative theories assume that at least one unobserved cause is always present. In contrast, causal Bayes net theories (including Power PC theory) hypothesize that unobserved causes may be present or absent. These theories generally assume independence of different causes of the same event, which greatly simplifies modelling learning and inference. In two experiments participants were requested to learn about the causal relation between a single cause and an effect by observing their co-occurrence (Experiment 1) or by actively intervening in the cause (Experiment 2). Participants' assumptions about the presence of an unobserved cause were assessed either after each learning trial or at the end of the learning phase. The results show an interesting dissociation. Whereas there was a tendency to assume interdependence of the causes in the online judgements during learning, the final judgements tended to be more in the direction of an independence assumption. Possible explanations and implications of these findings are discussed.     

Estimating an unobserved component of a serial response time model

A method is developed for estimating the response time distribution of an unobserved component in a two-component serial model, assuming the components are stochastically independent. The estimate of the component's density function is constrained only to be unimodal and non-negative. Numerical examples suggest that the method can yield reasonably accurate estimates with sample sizes of 300 and, in some cases, with sample sizes as small as 100.The author wishes to thank David Kohfeld, Jim Ramsay, Jim Townsend and two anonymous referees for a number of useful and stimulating comments on an earlier version of this paper.     

SUSTAIN: a network model of category learning

SUSTAIN (Supervised and Unsupervised STratified Adaptive Incremental Network) is a model of how humans learn categories from examples. SUSTAIN initially assumes a simple category structure. If simple solutions prove inadequate and SUSTAIN is confronted with a surprising event (e.g., it is told that a bat is a mammal instead of a bird), SUSTAIN recruits an additional cluster to represent the surprising event. Newly recruited clusters are available to explain future events and can themselves evolve into prototypes-attractors-rules. SUSTAIN's discovery of category substructure is affected not only by the structure of the world but by the nature of the learning task and the learner's goals. SUSTAIN successfully extends category learning models to studies of inference learning, unsupervised learning, category construction, and contexts in which identification learning is faster than classification learning.     

Determinants of political trust: a lifetime learning model

This article addresses questions regarding the origins of individual variations in political trust. Using 2 prospective longitudinal studies, we examine the associations between family background, general cognitive ability (g) and school motivation at early age, educational and occupational attainment in adulthood, and political trust measured in early and mid-adulthood in 2 large representative samples of the British population born in 1958 (N = 8,804) and in 1970 (N = 7,194). A lifetime learning model of political trust is tested using structural equation modeling to map the pathways linking early experiences to adult outcomes. Results show that political trust is shaped by both early and later experiences with institutions in society. Individuals who have accumulated more socioeconomic, educational, and motivational resources throughout their life course express higher levels of political trust than do those with fewer resources.     

Effect of grouping of evidence types on learning about interactions between observed and unobserved causes

When a cause interacts with unobserved factors to produce an effect, the contingency between the observed cause and effect cannot be taken at face value to infer causality. Yet it would be computationally intractable to consider all possible unobserved, interacting factors. Nonetheless, 6 experiments found that people can learn about an unobserved cause participating in an interaction with an observed cause when the unobserved cause is stable over time. Participants observed periods in which a cause and effect were associated followed by periods of the opposite association ("grouped condition"). Rather than concluding a complete lack of causality, participants inferred that the observed cause does influence the effect (Experiment 1), and they gave higher causal strength estimates when there were longer periods during which the observed cause appeared to influence the effect (Experiment 2). Consistent with these results, when the trials were grouped, participants inferred that the observed cause interacted with an unobserved cause (Experiments 3 and 4). Indeed, participants could even make precise predictions about the pattern of interaction (Experiments 5 and 6). Implications for theories of causal reasoning are discussed.     

Temporal constraints on visual learning: a computational model

Given a constant stream of perceptual stimuli, how can the underlying invariances associated with a given input be learned? One approach consists of using generic truths about the spatiotemporal structure of the physical world as constraints on the types of quantities learned. The learning methodology employed here embodies one such truth: that perceptually salient properties (such as stereo disparity) tend to vary smoothly over time. Unfortunately, the units of an artificial neural network tend to encode superficial image properties, such as individual grey-level pixel values, which vary rapidly over time. However, if the states of units are constrained to vary slowly, then the network is forced to learn a smoothly varying function of the training data. We implemented this temporal-smoothness constraint in a backpropagation network which learned stereo disparity from random-dot stereograms. Temporal smoothness was formalized with the use of regularization theory by modifying the standard cost function minimised during training of a network. Temporal smoothness was found to be similar to other techniques for improving generalisation, such as early stopping and weight decay. However, in contrast to these, the theoretical underpinnings of temporal smoothing are intimately related to fundamental characteristics of the physical world. Results are discussed in terms of regularization theory and the physically realistic assumptions upon which temporal smoothing is based.     

Application of a model to paired-associate learning

The proposal is made to consider a paired-associate item as becoming conditioned to its correct response in all-or-none fashion, and that prior to this conditioning event the subject guesses responses at random to an unlearned item. These simple assumptions enable the derivation of an extensive number of predictions about paired-associate learning. The predictions compare very favorably with the results of an experiment discussed below.This research was supported by a grant, M-3849, from the National Institutes of Mental Health, United States Public Health Service.     

From recurrent choice to skill learning: a reinforcement-learning model

The authors propose a reinforcement-learning mechanism as a model for recurrent choice and extend it to account for skill learning. The model was inspired by recent research in neurophysiological studies of the basal ganglia and provides an integrated explanation of recurrent choice behavior and skill learning. The behavior includes effects of differential probabilities, magnitudes, variabilities, and delay of reinforcement. The model can also produce the violation of independence, preference reversals, and the goal gradient of reinforcement in maze learning. An experiment was conducted to study learning of action sequences in a multistep task. The fit of the model to the data demonstrated its ability to account for complex skill learning. The advantages of incorporating the mechanism into a larger cognitive architecture are discussed.     

An associative model of geometry learning: a modified choice rule

In a recent article, the authors (Miller & Shettleworth, 2007) showed how the apparently exceptional features of behavior in geometry learning ("reorientation") experiments can be modeled by assuming that geometric and other features at given locations in an arena are learned competitively as in the Rescorla-Wagner model and that the probability of visiting a location is proportional to the total associative strength of cues at that location relative to that of all relevant locations. Reinforced or unreinforced visits to locations drive changes in associative strengths. Dawson, Kelly, Spetch, and Dupuis (2008) have correctly pointed out that at parameter values outside the ranges the authors used to simulate a body of real experiments, our equation for choice probabilities can give impossible and/or wildly fluctuating results. Here, the authors show that a simple modification of the choice rule eliminates this problem while retaining the transparent way in which the model relates spatial choice to competitive associative learning of cue values.     

Effects of similarity and experience on discrimination learning: a nonassociative connectionist model of perceptual learning.

This article describes a novel connectionist model of perceptual learning (PL) that provides a mechanism for nonassociative differentiation (J. J. Gibson & E. J. Gibson, 1955). The model begins with the assumption that 2 processes--1 that decreases associability and 1 that increases discriminability--operate during preexposure (S. Channell & G. Hall, 1981). In contrast to other models (e.g., I. P. L. McLaren, H. Kaye, & N. J. Mackintosh, 1989), in the current model the mechanisms for these processes are compatible with a configural model of associative learning. A set of simulations demonstrates that the present model can account for critical PL phenomena such as exposure learning and effects of similarity on discrimination. It is also shown that the model can explain the paradoxical result that preexposure to stimuli can either facilitate or impair subsequent discrimination learning. Predictions made by the model are discussed in relation to extant theories of PL.     

Bootstrapping in a language of thought: a formal model of numerical concept learning

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful representational system. We provide an implemented model that is powerful enough to learn number word meanings and other related conceptual systems from naturalistic data. The model shows that bootstrapping can be made computationally and philosophically well-founded as a theory of number learning. Our approach demonstrates how learners may combine core cognitive operations to build sophisticated representations during the course of development, and how this process explains observed developmental patterns in number word learning.     

From exemplar to grammar: a probabilistic analogy-based model of language learning

While rules and exemplars are usually viewed as opposites, this paper argues that they form end points of the same distribution. By representing both rules and exemplars as (partial) trees, we can take into account the fluid middle ground between the two extremes. This insight is the starting point for a new theory of language learning that is based on the following idea: If a language learner does not know which phrase-structure trees should be assigned to initial sentences, s/he allows (implicitly) for all possible trees and lets linguistic experience decide which is the "best" tree for each sentence. The best tree is obtained by maximizing "structural analogy" between a sentence and previous sentences, which is formalized by the most probable shortest combination of subtrees from all trees of previous sentences. Corpus-based experiments with this model on the Penn Treebank and the Childes database indicate that it can learn both exemplar-based and rule-based aspects of language, ranging from phrasal verbs to auxiliary fronting. By having learned the syntactic structures of sentences, we have also learned the grammar implicit in these structures, which can in turn be used to produce new sentences. We show that our model mimicks children's language development from item-based constructions to abstract constructions, and that the model can simulate some of the errors made by children in producing complex questions.     

Learning on a response continuum: Comparison of a linear change and a functional learning model

Two reinforcement schedules were used to compare the predictive validity of a linear change model with a functional learning model. In one schedule, termed “convergent,” the linear change model predicts convergence to the optimum response, while in the other, termed “divergent,” this model predicts that a subject's response will not converge. The functional learning model predicts convergence in both cases. Another factor that was varied was presence or absence of random error or “noise” in the relationship between response and outcome. In the “noiseless” condition, in which no noise is added, a subject could discover the optimum response by chance, so that some subjects could appear to have converged fortuitously. In the “noisy” conditions such chance apparent convergence could not occur.The results did not unequivocally favor either model. While the linear change model's prediction of nonconvergence in the divergent conditions (particularly the “noisy” divergent condition) was not sustained, there was a clear difference in speed of convergence, counter to the prediction inferred from the functional learning model. Evidence that at least some subjects were utilizing a functional learning strategy was adduced from the fact that subjects were able to “map out” the relation between response and outcome quite accurately in a follow-up task. Almost all subjects in the “noisy” conditions had evidently “learned” a strong linear relation, with slope closely matching the veridical one.The data were consistent with a hybrid model assuming a “hierarchy of cognitive strategies” in which more complex strategies (e.g., functional learning) are utilized only when the simpler ones (e.g., a linear change strategy) fail to solve the problem.     

Memoirs of a locust: Density-dependent behavioral change as a model for learning and memory

A locust outbreak is a stupendous natural phenomenon that remains in the memory of whoever has been lucky (or unlucky) enough to witness it. Recent years have provided novel and important insights into the neurobiology of locust swarming. However, the central nervous system processes that accompany and perhaps even lie at the basis of locust phase transformation are still far from being fully understood. Our current work deals with the memory of a locust outbreak from a new perspective: that of the individual locust. We take locust density-dependent phase transformation – a unique example of extreme behavioral plasticity, and place it within the context of the accepted scheme of learning and memory. We confirm that a short time period of exposure to a small crowd of locusts is sufficient to induce a significant behavioral change in a previously solitary locust. Our results suggest that part of the behavioral change is due to long-term habituation of evasive and escape responses. We further demonstrate that the memory of a crowding event lasts for at least 24 h, and that this memory is sensitive to a protein synthesis blocker. These findings add much to our understanding of locust density-dependent phase polyphenism. Furthermore, they offer a novel and tractable model for the study of learning and memory-related processes in a very distinctive behavioral context.     

Practice does not facilitate acquisition of McCollough effects: Evidence against a learning model

Previous investigators (Schmidt, Pinetts, & Finke, 1978) have asserted that McCollough effects (MEs) are acquired more readily by experienced than by inexperienced subjects. The present experiments examine this claim in a paradigm that utilizes quantitative measurements of MEs to evaluate possible changes in subjects’ susceptibility to them. MEs were induced every few days for approximately 2 months; results revealed no progressive increments in either strength or acquisition rats. The lack of facilitation due to practice is inconsistent with learning models proposed to account for MEs.     

Approximate optimal control as a model for motor learning

Current models of psychological development rely heavily on connectionist models that use supervised learning. These models adapt network weights when the network output does not match the target outputs computed by some agent. The authors present a model of motor learning in which the child uses exploration to discover appropriate ways of responding. The model is consistent with what is known about how neural systems evaluate behavior. The authors model the development of reaching and investigate N. Bernstein's (1967) hypotheses about early motor learning. Simulations show the course of learning as well as model the kinematics of reaching by a dynamical arm.     

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.