The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.

There is evidence, beginning with Cheng (1986), that mobile animals may use the geometry of surrounding areas to reorient following disorientation. Gallistel (1990) proposed that geometry is used to compute the major or minor axes of space and suggested that such information might form an encapsulated cognitive module. Research reviewed here, conducted on a wide variety of species since the initial discovery of the use of geometry and the formulation of the modularity claim, has supported some aspects of the approach, while casting doubt on others. Three possible processing models are presented that vary in the way in which (and the extent to which) they instantiate the modularity claim. The extant data do not permit us to discriminate among them. We propose a modified concept of modularity for which an empirical program of research is more tractable.

The core tenet of Bayesian modeling is that subjects represent beliefs as distributions over possible hypotheses. Such models have fruitfully been applied to the study of learning in the context of animal conditioning experiments (and analogously designed human learning tasks), where they explain phenomena such as retrospective revaluation that seem to demonstrate that subjects entertain multiple hypotheses simultaneously. However, a recent quantitative analysis of individual subject records by Gallistel and colleagues cast doubt on a very broad family of conditioning models by showing that all of the key features the models capture about even simple learning curves are artifacts of averaging over subjects. Rather than smooth learning curves (which Bayesian models interpret as revealing the gradual tradeoff from prior to posterior as data accumulate), subjects acquire suddenly, and their predictions continue to fluctuate abruptly. These data demand revisiting the model of the individual versus the ensemble, and also raise the worry that more sophisticated behaviors thought to support Bayesian models might also emerge artifactually from averaging over the simpler behavior of individuals. We suggest that the suddenness of changes in subjects ’ beliefs (as expressed in conditioned behavior) can be modeled by assuming they are conducting inference using sequential Monte Carlo sampling with a small number of samples — one, in our simulations. Ensemble behavior resembles exact Bayesian models since, as in particle filters, it averages over many samples. Further, the model is capable of exhibiting sophisticated behaviors like retrospective revaluation at the ensemble level, even given minimally sophisticated individuals that do not track uncertainty from trial to trial. These results point to the need for more sophisticated experimental analysis to test Bayesian models, and refocus theorizing on the individual, while at the same time clarifying why the ensemble may be of interest. 1

Explaining away has mostly been considered in terms of inference of states in belief networks. We show how it can also arise in a Bayesian context in inference about the weights governing relationships such as those between stimuli and reinforcers in conditioning experiments such as backward blocking. We show how explaining away in weight space can be accounted for using an extension of a Kalman filter model; provide a new approximate way of looking at the Kalman gain matrix as a whitener for the correlation matrix of the observation process; suggest a network implementation of this whitener using an architecture due to Goodall; and show that the resulting model exhibits backward blocking. 1 Introduction The phenomenon of explaining away is commonplace in inference in belief networks. In this, an explanation (a setting of activities of unobserved units) that is consistent with certain observations is accorded a low posterior probability if another explanation for the same ob...

Associative learning theories assume that cue interaction and, specifically, retrospective revaluation occur only when the target cue is previously trained in compound with the to-be-revalued cue. However, there are recent demonstrations of retrospective revaluation in the absence of compound training (e.g., Matute & Pineño, 1998a, 1998b). Nevertheless, it seems reasonable to assume that cue interaction should be stronger when the cues are trained together than when they are trained apart. In two experiments with humans, we directly compared compound and elemental training of cues. The results showed that retrospective revaluation in the elemental condition can be as strong as and, sometimes, stronger than that in the compound condition. This suggests that within-compound associations are not necessary for retrospective revaluation to occur and that these effects can possibly be best understood in the framework of general interference theory. In the literature of animal conditioning and human associative learning, it is well known that if a cue, X, is consistently followed by an outcome, O (i.e., X–O), X is generally learned as a predictor of the occurrence of the outcome. It is also well known that responding to X in a subsequent test phase becomes altered if another cue, A, is trained in compound with X as a predictor of the same outcome. Some classic instances of these cue interaction effects in the animal learning literature are overshadowing (Pavlov, 1927), blocking (Kamin, 1968), conditioned inhibition (Pavlov, 1927), and the relative stimulus validity

Bayesian treatments of animal conditioning start from a generative model that specifies precisely a set of assumptions about the structure of the learning task. Optimal rules for learning are direct mathematical consequences of these assumptions. In terms of Marr’s (1982) levels of analyses, the main task at the computational level

Most theoretical accounts of backward blocking place heavy stress on the necessity of the target cue having been trained in compound with the competing cue to produce a decrement in responding. Yet, other evidence suggests that a similar reduction in responding to the target cue can be observed when the outcome is later paired with a novel cue never trained in compound with the target cue (interference between cues trained apart). The present experiment shows that pairing another nonassociated cue with the same outcome may be sufficient to produce a decremental effect on the target cue, but the presence of a within-compound association between the target and the competing cue adds to this effect. Thus, both interference between cues trained apart and within-compound associations independently contribute to backward blocking.

Explaining away has mostly been considered in terms of inference of states in belief networks. We show how it can also arise in a Bayesian context in inference about the weights governing relationships such as those between stimuli and reinforcers in conditioning experiments such as backward blocking. We show how explaining away in weight space can be accounted for using an extension of a Kalman filter model; provide a new approximate way of looking at the Kalman gain matrix as a whitener for the correlation matrix of the observation process; suggest a network implementation of this whitener using an architecture due to Goodall; and show that the resulting model exhibits backward blocking. 1

this paper was to test whether renewal can be found in human beings in a situation where the context change does not affect acquisition. We used a predictive judgments preparation where fictitious medicines are presented, and the subject has to predict whether they are related to an imaginary illness. Experiment 1 was conducted with the aim of testing our acquisition and extinction procedure. Experiment 2 looked for within subjects renewal, testing whether the return to the acquisition context after receiving extinction in a different but equally familiar context would renew the predicted probability of the medicine causing the illness

Within-compound associations in retrospective revaluation and in direct learning: A challenge for comparator theory