## Learning a Theory of Causality

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Citations: | 7 - 5 self |

### BibTeX

@MISC{Goodman_learninga,

author = {Noah D. Goodman and Tomer D. Ullman and Joshua B. Tenenbaum},

title = {Learning a Theory of Causality},

year = {}

}

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### Abstract

The very early appearance of abstract knowledge is often taken as evidence for innateness. We explore the relative learning speeds of abstract and specific knowledge within a Bayesian framework, and the role for innate structure. We focus on knowledge about causality, seen as a domain-general intuitive theory, and ask whether this knowledge can be learned from cooccurrence of events. We begin by phrasing the causal Bayes nets theory of causality, and a range of alternatives, in a logical language for relational theories. This allows us to explore simultaneous inductive learning of an abstract theory of causality and a causal model for each of several causal systems. We find that the correct theory of causality can be learned relatively quickly, often becoming available before specific causal theories have been learned—an effect we term the blessing of abstraction. We then explore the effect of providing a variety of auxiliary evidence, and find that a collection of simple “perceptual input analyzers ” can help to bootstrap abstract knowledge. Together these results suggest that the most efficient route to causal knowledge may be to build in not an abstract notion of causality, but a powerful inductive learning mechanism and a variety of perceptual supports. While these results are purely computational, they have implications for cognitive development, which we explore in the conclusion. Pre-print June 2010—to appear in Psych. Review.

### Citations

1460 | Bayesian data analysis
- Gelman, Carlin, et al.
- 1995
(Show Context)
Citation Context ... question we turn to hierarchical Bayesian modeling. The formalism of hierarchical Bayesian modeling makes it possible to express the assumptions relating knowledge at multiple levels of abstraction (=-=Gelman, Carlin, Stern, & Rubin, 1995-=-), and Bayesian inference over such a model describes an ideal learner of abstract knowledge (Tenenbaum, Griffiths, & Kemp, 2006). Though real learning is undoubtedly resource-constrained, the dynamic... |

1280 |
Information Theory, Inference and Learning Algorithms
- MacKay
- 2003
(Show Context)
Citation Context ...cribed in this paper. Fortunately, a large body of work in machine learning and statistics suggests that it is possible to efficiently approximate ideal learning by stochastic search over hypotheses (=-=MacKay, 2003-=-). In recent work Ullman, Goodman, and Tenenbaum (2010) have shown that stochastic search methods can provide a practical and psychologically plausible means of constructing abstract theories. This de... |

1247 |
Causality: models, reasoning, and inference
- Pearl
(Show Context)
Citation Context ... cognition. A long tradition in psychology and philosophy has investigated the principles of causal understanding, largely converging on the interventionist or causal Bayes nets account of causality (=-=Pearl, 2000-=-; Woodward, 2003) as a description of the principles by which causal reasoning proceeds. The principles embodied by the causal Bayes network framework include a directed, probabilistic notion of causa... |

506 | A fast learning algorithm for deep belief nets. Neural Computation
- Hinton, Osindero, et al.
- 2006
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Citation Context ... neural networks has been designed around this intuition, building up increasingly abstract layers of representation on top of lower-level, more specific layers, which are formed earlier in learning (=-=Hinton, Osindero, & Teh, 2006-=-). The blessing of abstraction suggests that this is not a necessary order for the construction of knowledge, but that abstract knowledge can become available before specific knowledge in any of the s... |

287 |
An Enquiry Concerning Human Understanding
- Hume
- 2006
(Show Context)
Citation Context ... believed that it was the principle of association: constant conjunction of events follow from an underlying association; from this principle, and observed events, one may infer a causal association (=-=Hume, 1748-=-). Recent psychological research (Cheng, 1997; Waldmann & Martignon, 1998; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003; Gopnik et al., 2004; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008; Griffiths... |

257 |
From covariation to causation: a causal power theory
- Cheng
- 1997
(Show Context)
Citation Context ...iation: constant conjunction of events follow from an underlying association; from this principle, and observed events, one may infer a causal association (Hume, 1748). Recent psychological research (=-=Cheng, 1997-=-; Waldmann & Martignon, 1998; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003; Gopnik et al., 2004; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008; Griffiths & Tenenbaum, 2005, 2009) has described mathe... |

178 | A theory of causal learning in children: Causal maps and Bayes nets
- Gopnik, Glymour, et al.
- 2004
(Show Context)
Citation Context ...rinciple, and observed events, one may infer a causal association (Hume, 1748). Recent psychological research (Cheng, 1997; Waldmann & Martignon, 1998; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003; =-=Gopnik et al., 2004-=-; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008; Griffiths & Tenenbaum, 2005, 2009) has described mathematical models of how children and adults learn domain-specific causal relations by applying abst... |

119 |
The origins of concepts
- Carey
- 2000
(Show Context)
Citation Context ...ock in models of cognitive development or because it was not clear how such abstract knowledge could be learned. Those who have proposed that our concept of cause is constructed from experience (e.g. =-=Carey, 2009-=-) have not attempted to give a formal learning model. In this paper we will argue that the principles guiding causal understanding in humans can be seen as an intuitive theory, learnable from evidence... |

98 |
Inferring causal networks from observations and interventions
- Steyvers, Tenenbaum, et al.
- 2003
(Show Context)
Citation Context ...llow from an underlying association; from this principle, and observed events, one may infer a causal association (Hume, 1748). Recent psychological research (Cheng, 1997; Waldmann & Martignon, 1998; =-=Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003-=-; Gopnik et al., 2004; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008; Griffiths & Tenenbaum, 2005, 2009) has described mathematical models of how children and adults learn domain-specific causal relat... |

90 | Theory-based Bayesian models of inductive learning and reasoning
- Tenenbaum, Griffiths, et al.
- 2006
(Show Context)
Citation Context ...the assumptions relating knowledge at multiple levels of abstraction (Gelman, Carlin, Stern, & Rubin, 1995), and Bayesian inference over such a model describes an ideal learner of abstract knowledge (=-=Tenenbaum, Griffiths, & Kemp, 2006-=-). Though real learning is undoubtedly resource-constrained, the dynamics of an ideal learner can uncover unexpected properties of what it is possible to learn from a given set of evidence. For instan... |

70 | Teleological reasoning in infancy: the naive theory of rational action
- Gergely, Csibra
- 2003
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Citation Context ...o evaluate learnability and learning dynamics for other domain theories that have been argued to be innate—for instance the physics of objects (Spelke, 1998), or the psychology of intentional agents (=-=Gergely & Csibra, 2003-=-). Where innate structure is required to explain complex cognition, it is often assumed to be abstract conceptual knowledge (Carey, 2009). This step should also be approached with care—simpler innate ... |

59 | Learning overhypotheses with hierarchical Bayesian models
- Kemp, Perfors, et al.
- 2007
(Show Context)
Citation Context ...ubtedly resource-constrained, the dynamics of an ideal learner can uncover unexpected properties of what it is possible to learn from a given set of evidence. For instance, it has been reported (e.g. =-=Kemp, Perfors, & Tenenbaum, 2007-=-) that learning at the abstract level of a hierarchical Bayesian model is often surprisingly fast in relation to learning at the more specific levels. We term this effect the blessing of abstraction1 ... |

36 |
Knowledge acquisition in foundational domains
- Wellman, Gelman
- 1998
(Show Context)
Citation Context ...NBAUM where abstract knowledge is clearly constructed, such as intuitive biology, it has been observed that the most abstract domain knowledge often comes into place first, before specific knowledge (=-=Wellman & Gelman, 1998-=-). The blessing of abstraction provides a potential explanation of this observation as well. Though we have argued that abstract knowledge about causality may be learnable, our results should also not... |

32 |
A Bayesian network model of causal learning
- Waldmann, Martignon
- 1998
(Show Context)
Citation Context ...ant conjunction of events follow from an underlying association; from this principle, and observed events, one may infer a causal association (Hume, 1748). Recent psychological research (Cheng, 1997; =-=Waldmann & Martignon, 1998-=-; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003; Gopnik et al., 2004; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008; Griffiths & Tenenbaum, 2005, 2009) has described mathematical models of how childr... |

31 | Nativism, empiricism, and the origins of knowledge
- Spelke
- 1998
(Show Context)
Citation Context ... the framework we have described here could be applied to evaluate learnability and learning dynamics for other domain theories that have been argued to be innate—for instance the physics of objects (=-=Spelke, 1998-=-), or the psychology of intentional agents (Gergely & Csibra, 2003). Where innate structure is required to explain complex cognition, it is often assumed to be abstract conceptual knowledge (Carey, 20... |

21 | Bayesian generic priors for causal learning
- Lu, Yuille, et al.
- 2008
(Show Context)
Citation Context ...d events, one may infer a causal association (Hume, 1748). Recent psychological research (Cheng, 1997; Waldmann & Martignon, 1998; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003; Gopnik et al., 2004; =-=Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008-=-; Griffiths & Tenenbaum, 2005, 2009) has described mathematical models of how children and adults learn domain-specific causal relations by applying abstract knowledge—knowledge that describes how cau... |

14 | Learning causal schemata
- Kemp, Goodman, et al.
- 2007
(Show Context)
Citation Context ...dge is almost as efficient as a learner with an innate (i.e. fixed) and correct abstract theory. Hierarchical Bayesian models have been used before to study domain-specific abstract causal knowledge (=-=Kemp, Goodman, & Tenenbaum, 2007-=-), and simple relational theories (Kemp et al., 2008). Here we combine these approaches to study knowledge of causality at the most abstract, domain general level. We will also explore the possibility... |

14 | Intuitive theories as grammars for causal inferences
- Tenenbaum, Griffiths, et al.
- 2007
(Show Context)
Citation Context ...intuitive theories—systems of abstract concepts and laws relating them—can be represented in a “language of thought” which includes aspects of probability and logic (Kemp, Goodman, & Tenenbaum, 2008; =-=Tenenbaum, Griffiths, & Niyogi, 2007-=-; Goodman, Tenenbaum, Griffiths,2 NOAH D. GOODMAN, TOMER D. ULLMAN, JOSHUA B. TENENBAUM & Feldman, 2007). Because the assumptions of causal Bayes networks are formalizable via probability and logic, ... |

11 |
The perception of causality in infancy
- Saxe, Carey
- 2006
(Show Context)
Citation Context ...ad serve to make latent abstract concepts more salient and thus more learnable. For instance, the feeling of self-efficacy, advocated by Maine de Biran as a foundation of causality (see discussion in =-=Saxe & Carey, 2006-=-), could be an analyzer which highlights events resulting from one’s own actions, making the latent concept of intervention more salient. Alternatively, an innate or early-developing agency-detector m... |

7 |
Just do it? Investigating the gap between prediction and action in toddlers’ causal inferences
- Bonawitz, Ferranti, et al.
- 2010
(Show Context)
Citation Context ...(Saxe & Carey, 2006). Indeed, very recent empirical results suggest that some aspects of the adult causal sense are not available for children as old as 18 months (Meltzoff, 2007), or even 24 months (=-=Bonawitz et al., 2010-=-). Despite this philosophical and empirical interest, there have been no computational investigations into the learnability of abstract knowledge of causality, nor what learning dynamics may emerge fr... |

7 | Theory acquisition and the language of thought
- Kemp, Goodman, et al.
- 2008
(Show Context)
Citation Context ... We have previously proposed that intuitive theories—systems of abstract concepts and laws relating them—can be represented in a “language of thought” which includes aspects of probability and logic (=-=Kemp, Goodman, & Tenenbaum, 2008-=-; Tenenbaum, Griffiths, & Niyogi, 2007; Goodman, Tenenbaum, Griffiths,2 NOAH D. GOODMAN, TOMER D. ULLMAN, JOSHUA B. TENENBAUM & Feldman, 2007). Because the assumptions of causal Bayes networks are fo... |

4 |
Infants’ causal learning: Intervention, observation, imitation
- Meltzoff
- 2007
(Show Context)
Citation Context ...at a full notion of cause is innate (Saxe & Carey, 2006). Indeed, very recent empirical results suggest that some aspects of the adult causal sense are not available for children as old as 18 months (=-=Meltzoff, 2007-=-), or even 24 months (Bonawitz et al., 2010). Despite this philosophical and empirical interest, there have been no computational investigations into the learnability of abstract knowledge of causalit... |

4 | Theory Acquisition as Stochastic Search - Ullman, Goodman, et al. - 2010 |

4 | Perception of forces exerted by objects in collision events - White - 2009 |

2 | Compositionality in rational analysis: Grammar-based induction for concept learning
- Goodman, Tenenbaum, et al.
- 2007
(Show Context)
Citation Context ... concepts and laws relating them—can be represented in a “language of thought” which includes aspects of probability and logic (Kemp, Goodman, & Tenenbaum, 2008; Tenenbaum, Griffiths, & Niyogi, 2007; =-=Goodman, Tenenbaum, Griffiths, & Feldman, 2007-=-). Because the assumptions of CBN are formalizable via probability and logic, they are potentially expressible in such a language for intuitive theories. This suggests the hypothesis that CBN is not a... |

1 | Theory based causal induction - Griffiths, Tenenbaum - 2009 |