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.

The Accuracy of Causal Learning Over Long Timeframes: An Ecological Momentary Experiment Approach

“…In most causal learning paradigms, however, the absence and presence of the cause are explicitly stated and therefore made artificially salient. Another related concern is that many real‐world phenomena are not punctate events that happen at a brief moment in time but instead may persist or fluctuate in intensity over periods and grow or recede in awareness over time (e.g., pain, mood; Davis et al., 2020; Soo & Rottman, 2015. Studying causation with other paradigms over long timeframes will help make the research more realistic.…”

“…One of the most major developments in research on causation in the past two decades has been the shift from only focusing how people learn causal strength toward how people learn the causal structure among multiple variables (Bramley, Gerstenberg, Mayrhofer, & Lagnado, 2018;Coenen, Rehder, & Gureckis, 2015;Davis, Bramley, & Rehder, 2020;Rothe, Deverett, Mayrhofer, & Kemp, 2018;Rottman & Keil, 2012;Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003). One reason that this is vitally important is because it helps to distinguish truly causal versus associative representations (though see Fernando (2013) for an associative learning model of causal structure).…”

Continuous time causal structure induction with prevention and generation

“…Given limited short-term memory storage and attention, it seems plausible that participants would abstract cues more locally than from the full observation. In other studies, people are found to often use temporally local (i.e., recent) information to drive causal model learning (Bramley, Dayan et al, 2017;Davis et al, 2020). Furthermore, people are often unable to recall older evidence exactly (Bramley et al, 2015;Harman, 1986), rather remembering whatever conclusions they have drawn on the basis of it.…”

“…The literature on contingency learning suggests humans have some ability to condition on other variables when inferring the role of a target variable (Beckers et al, 2005;Gopnik et al, 2001;Rescorla & Wagner, 1972;Shanks, 1985) and, indeed, sensitivity to base rate is one simple form of this. However, recent evidence also demonstrates human limitations in dealing globally with joint probability outside very simple learning problems (Bonawitz et al, 2014;Bramley, Dayan et al, 2017;Davis et al, 2020;Fernbach & Sloman, 2009;Griffiths et al, 2015;Markant et al, 2016). In the causal structure induction setting, complexity quickly compounds in the number of components and events.…”

“…Nevertheless, human responses were quantitatively better captured by summary-statistic account. This process-level account integrated three principles of bounded cognitive processing: mental simulation (Battaglia et al, 2013;Ullman et al, 2018), local computation (Bramley, Dayan et al, 2017;Davis et al, 2020;Fernbach & Sloman, 2009), and incrementality in processing the evidence (Bramley, Dayan et al, 2017;Davis et al, 2020). These departures from normativity allowed it to explain several characteristic error patterns.…”