Formalizing Neurath’s ship: Approximate algorithms for online causal learning.

Abstract

Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of three experiments.

Testing one or multiple: How beliefs about sparsity affect causal experimentation

“…This finding mirrors research on many other hypothesis-testing tasks suggesting that people have a bias to verify or confirm their hypotheses, even if doing so does not lead to additional information (e.g., Klayman & Ha, 1987;Nickerson, 1998;Ruggeri et al, 2016). In causal intervention tasks, such a tendency has specifically manifested itself in a preference for producing the positive effects (variables turning on) that a particular hypothesis entails (Coenen et al, 2015;Bramley et al, 2017). Because we did not find that participants in the non-sparse group tried to create the expected non-effect, this experiment provides further evidence for this preference to verify positive outcomes in causal systems.…”

“…Evidence for this kind of strategy has been found in different kinds of hypothesis testing experiments in which participants frequently test instances that can confirm their current hypothesis instead of trying to falsify it (e.g., Klayman & Ha, 1987;Wason, 1960;Mckenzie & Mikkelsen, 2000). Recently, a similar tendency was found in a number of causal learning experiments showing that participants were particularly likely to intervene on variables that would yield many effects predicted by a structure that the learner currently considers to be plausible (Bramley et al, 2017;Coenen et al, 2015). There also exists evidence that people in some cases perceive the presence of causal effects as more informative (Coenen & Gureckis, 2015) and more likely (Davis & Rehder, 2017) than non-effects that objectively have the same informational value or likelihood.…”

“…Furthermore, people are sometimes able to come up with highly efficient experiments that optimize information gained per intervention or minimize the total number of tests needed on average to discover the true causal structure (Bramley, Lagnado, & Speekenbrink, 2015;Bramley, Dayan, Griffiths, & Lagnado, 2017; Coenen, Rehder, & Gureckis, 2015;Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003).…”

A theory of learning to infer

“…The blackbox variational inference algorithm that we use (see Appendix) does in fact involve sampling: the gradient of the evidence lower bound is approximated using a set of samples from the variational approximation. Although we are not aware of direct evidence for such an algorithm in brain or behavior, the idea that hypothesis sampling is involved in the learning process is an intriguing possibility that has begun to be studied more systematically (N. Bramley, Rothe, Tenenbaum, Xu, & Gureckis, 2018;N. R. Bramley, Dayan, Griffiths, & Lagnado, 2017;Rule, Schulz, Piantadosi, & Tenenbaum, 2018).…”

Why Higher Working Memory Capacity May Help You Learn: Sampling, Search, and Degrees of Approximation

“…Indeed, it has recently been suggested that, at least when considering more global hypotheses about the world where the hypothesis space becomes particularly complex, only one hypothesis would plausibly be represented (Bramley, Dayan, Griffiths, & Lagnado, 2017). In other words, one could presumably replace a larger number of relatively "dumb" particles/hypotheses with a smaller number of comparatively "smart" particles/hypotheses.…”