Modeling Causal Learning

Alternative Causal Assumptions

When the causal graph includes multiple potential causes of a single effect, two leading classes of models make different assumptions about the integration rule used to combine causal influences. One class (including the classic delta-P model and the associative Rescorla-Wagner model) assumes a linear integration rule: Each candidate cause changes the probability of the effect by a constant amount regardless of the presence or absence of other causes. A second class is represented by the power PC theory, a theory of causal judgments postulating that learners assume that unobservable causal influences operate independently to produce the effect. Guided by this assumption, causal integration is based on probabilistic versions of various logical operators, such as OR and AND-NOT, chosen to reflect the polarity of causal influence (i.e., whether a cause produces or prevents the occurrence of an effect).

When the causal graph includes multiple effects of a single cause (e.g., flu causes headache and chest pain, as shown in Figure 1), the causal Markov assumption states that the probability of one effect occurring is independent of the probability of other effects occurring, given that its own direct causes are present. Statistical models that examine causal relationships adopt the Markov assumption, which guides exploration of conditional independencies that hold in a body of data, thereby constraining the search space by eliminating highly unlikely cause-effect relations. The extent to which humans employ the causal Markov assumption remains controversial.

When observations are limited, human causal learning relies heavily on some type of prior knowledge. Prior knowledge can be specific to a domain (based on known categories), but it can also include abstract assumptions about properties of a system of cause-effect relations (e.g., preference for causal networks that exhibit various types of simplicity). Use of appropriate prior knowledge can explain the rapid acquisition of causal relations often exhibited by humans.

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