Inducing causal relationships from observations is a classic problem in scientific inference, statistics, and machine learning. It is also a central part of human learning, and a task that people perform remarkably well given its notorious difficulties. People can learn causal structure in various settings, from diverse forms of data: observations of the co-occurrence frequencies between causes and effects, interactions between physical objects, or patterns of spatial or temporal coincidence. These different modes of learning are typically thought of as distinct psychological processes and are rarely studied together, but at heart they present the same inductive challenge—identifying the unobservable mechanisms that generate observable relations between variables, objects, or events, given only sparse and limited data. We present a computational-level analysis of this inductive problem and a framework for its solution, which allows us to model all these forms of causal learning in a common language. In this framework, causal induction is the product of domain-general statistical inference guided by domain-specific prior knowledge, in the form of an abstract causal theory. We identify 3 key aspects of abstract prior knowledge—the ontology of entities, properties, and relations that organizes a domain; the plausibility of specific causal relationships; and the functional form of those relationships—and show how they provide the constraints that people need to induce useful causal models from sparse data.

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

A scheme is described for locally Bayesian parameter updating in models structured as successions of component functions. The essential idea is to back-propagate the target data to interior modules, such that an interior component’s target is the input to the next component that maximizes the probability of the next component’s target. Each layer then does locally Bayesian learning. The approach assumes online trial-by-trial learning. The resulting parameter updating is not globally Bayesian but can better capture human behavior. The approach is implemented for an associative learning model that first maps inputs to attentionally filtered inputs and then maps attentionally filtered inputs to outputs. The Bayesian updating allows the associative model to exhibit retrospective revaluation effects such as backward blocking and unovershadowing, which have been challenging for associative learning models. The back-propagation of target values to attention allows the model to show trial-order effects, including highlighting and differences in magnitude of forward and backward blocking, which have been challenging for Bayesian learning models.

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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

Recent research suggests that cue competition effects in human contingency learning, such as blocking, are due to higher-order cognitive processes. Moreover, some experimental reports suggest that the effect opposite to blocking, augmentation, could occur in experimental preparations that preclude the intervention of reasoning mechanisms. In the present research, we tested this hypothesis by investigating cue interaction effects in an experimental task in which participants had to enter their responses under time pressure. The results show that under these conditions, augmentation, instead of blocking, is observed. Augmentation under time-pressure 2 For decades, studies on human contingency learning have tried to understand how people learn to predict events in their environment based on the presence or absence of cues that are associated with those events. A common finding is that a participants’ tendency to predict an outcome based on the presence of a cue that was previously paired with that outcome also depends on the experience with alternative predictors of that outcome. This principle is well illustrated by a learning effect known as blocking. In a

How do humans learn contingencies between events? Both pathway-strengthening and inference-based process models have been proposed to explain contingency learning. We propose that each of these processes is used in different conditions. Participants viewed displays that contained single or paired objects and learned which displays were usually followed by the appearance of a dot. Some participants predicted whether the dot would appear before seeing the outcome, whereas other participants were required to respond quickly if the dot appeared shortly after the display. In the prediction task, instructions guiding participants to infer which objects caused the dot to appear were necessary in order for contingencies associated with one object to influence participants ’ predictions about the object with which it had been paired. In the response task, contingencies associated with one object affected responses to its pair mate irrespective of whether or not participants were given causal instructions. Our results challenge single-mechanism accounts of contingency learning and suggest that the mechanisms underlying performance in the two tasks are distinct.