Causal Structure Learning in Continuous Systems

Abstract

Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e., those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions with continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss–Markov (“Ornstein–Uhlenbeck”) processes and show how such OU networks can express complex dynamic phenomena, such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world.