A Bayesian Theory of Sequential Causal Learning and Abstract Transfer

Abstract

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about abstract causal constraints? Recent empirical studies have revealed that experience with one set of causal cues can dramatically alter subsequent learning and performance with entirely different cues, suggesting that learning involves abstract transfer, and such transfer effects involve sequential presentation of distinct sets of causal cues. It has been demonstrated that pre-training (or even post-training) can modulate classic causal learning phenomena such as forward and backward blocking. To account for these effects, we propose a Bayesian theory of sequential causal learning. The theory assumes that humans are able to consider and use several alternative causal generative models, each instantiating a different causal integration rule. Model selection is used to decide which integration rule to use in a given learning environment in order to infer causal knowledge from sequential data. Detailed computer simulations demonstrate that humans rely on the abstract characteristics of outcome variables (e.g., binary vs. continuous) to select a causal integration rule, which in turn alters causal learning in a variety of blocking and overshadowing paradigms. When the nature of the outcome variable is ambiguous, humans select the model that yields the best fit with the recent environment, and then apply it to subsequent learning tasks. Based on sequential patterns of cue-outcome co-occurrence, the theory can account for a range of phenomena in sequential causal learning, including various blocking effects, primacy effects in some experimental conditions, and apparently abstract transfer of causal knowledge.

Active Inference, Curiosity and Insight

“…Table 1 provides a summary of these uncertainty-reducing processes, where uncertainty is associated with free energy formulations of surprise such that uncertainty-resolving behavior reduces expected free energy. To motivate and illustrate this formalism, we set ourselves the task of simulating a curious agent that spontaneously learned rules-governing the sensory consequences of her action-from limited and ambiguous sensory evidence (Lu et al, 2016;Tervo, Tenenbaum, & Gershman, 2016). We chose abstract rule learning to illustrate how conceptual knowledge could be accumulated through experience (Botvinick & Toussaint, 2012;Zhang & Maloney, 2012;Koechlin, 2015) and how implicit Bayesian belief updating can be accelerated by applying Bayesian principles not to sensory samples but to beliefs based on those samples.…”

“…Bayesian model reduction refers to the evaluation of reduced forms of a full model to find simpler (reduced) models using only posterior beliefs (Friston & Penny, 2011). Reduced models furnish parsimonious explanations for sensory contingencies that are inherently more generalizable (Navarro & Perfors, 2011;Lu et al, 2016) and, as we will see, provide for simpler and more efficient inference. In brief, we use simulations of abstract rule learning to show that context-sensitive contingencies, which are manifest in a high-dimensional space of latent or hidden states, can be learned using straightforward variational principles (i.e., minimization of free energy).…”

“…This article presents a formal (computational) description of epistemic behavior that calls on two themes in theoretical neurobiology. The first is the use of Bayesian principles for understanding the nature of intelligent and purposeful behavior (Koechlin, Ody, & Kouneiher, 2003;Oaksford & Chater, 2003;Coltheart, Menzies, & Sutton, 2010;Nelson, McKenzie, Cottrell, & Sejnowski, 2010;Collins & Koechlin, 2012;Solway & Botvinick, 2012;Donoso, Collins, & Koechlin, 2014;Seth, 2014;Koechlin, 2015;Lu, Rojas, Beckers, & Yuille, 2016). The second is the role of self-modeling, reflection, and sleep (Metzinger, 2003;Hobson, 2009).…”

Exploring the role of stimulus similarity on the summation effect in causal learning

“…The observation of summation being affected by pretraining with unrelated cues can be explained by recent models based on Bayesian principles (Holyoak & Cheng, 2011;Lu, Rojas, Beckers, & Yuille, 2016;Lucas & Griffiths, 2010). These models are predicated under the assumption that in a causal learning task subjects weigh different hypothesis about the underlying causal structure of the world.…”

“…Using Bayes' rule during training, subjects are able to update possible hypothesis about the form of the relationship between the compound AB and the outcome. This flexibility allows these models to explain why a disjunctive hypothesis such as that found in the noisy-OR rule may be modified to reflect non-linearity as subjects observe instances of other cues which violate this prior assumption of independence (Lu et al, 2016).…”