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Casual Structure Learning with Continuous Variables in Continuous Time
Abstract
Interventions, time, and continuous-valued variables are all potentially powerful cues to causation. Furthermore, when observed over time, causal processes can contain feedback and oscillatory dynamics that make inference hard. We present a generative model and framework for causal infer- ence over continuous variables in continuous time based on Ornstein-Uhlenbeck processes. Our generative model pro- duces a stochastic sequence of evolving variable values that manifest many dynamical properties depending on the nature of the causal relationships, and a learner’s interventions (man- ual changes to the values of variables during a trial). Our model is also invertible, allowing us to benchmark participant judgments against an optimal model. We find that when in- teracting with systems acting according to this formalism peo- ple directly compare relationships between individual variable pairs rather than considering the full space of possible models, in accordance with a local computations model of causal learn- ing (e.g., Fernbach & Sloman, 2009). The formalism presented here provides researchers in causal cognition with a powerful framework for studying dynamic systems and presents oppor- tunities for other areas in cognitive psychology such as control problems.
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