Learning the Form of Causal Relationships Using Hierarchical Bayesian Models

People learn quickly when reasoning about causal relationships, making inferences from limited data and avoiding spurious inferences. Efficient learning depends on abstract knowledge, which is often domain or context specific, and much of it must be learned. While such knowledge effects are well documented, little is known about exactly how we acquire knowledge that constrains learning. This work focuses on knowledge of the functional form of causal relationships; there are many kinds of relationships that can apply between causes and their effects, and knowledge of the form such a relationship takes is important in order to quickly identify the real causes of an observed effect. We developed a hierarchical Bayesian model of the acquisition of knowledge of the functional form of causal relationships and tested it in five experimental studies, considering disjunctive and conjunctive relationships, failure rates, and cross-domain effects. The Bayesian model accurately predicted human judgments and outperformed several alternative models.

[1]  L. Alloy,et al.  Assessment of covariation by humans and animals: The joint influence of prior expectations and current situational information. , 1984 .

[2]  D. Shanks,et al.  FEATURE- AND RULE-BASED GENERALIZATION IN HUMAN ASSOCIATIVE LEARNING , 1998 .

[3]  B. Koslowski Theory and Evidence: The Development of Scientific Reasoning , 1996 .

[4]  Thomas L. Griffiths,et al.  Learning Systems of Concepts with an Infinite Relational Model , 2006, AAAI.

[5]  Michael R. Waldmann,et al.  KNOWLEDGE-BASED CAUSAL INDUCTION , 1996 .

[6]  D. Medin,et al.  The role of covariation versus mechanism information in causal attribution , 1995, Cognition.

[7]  Refractor Vision , 2000, The Lancet.

[8]  Amy M. Masnick,et al.  The Development of Causal Reasoning , 2007 .

[9]  A. Yuille,et al.  Bayesian Models of Judgments of Causal Strength: A Comparison , 2007 .

[10]  S. Carey Knowledge Acquisition: Enrichment or Conceptual Change? , 1991 .

[11]  Permalink Modeling Causal Learning Using Bayesian Generic Priors on Generative and Preventive Powers , 2006 .

[12]  Gregory F. Cooper,et al.  A Bayesian Method for the Induction of Probabilistic Networks from Data , 1992 .

[13]  Thomas L. Griffiths,et al.  A Rational Analysis of Rule-Based Concept Learning , 2008, Cogn. Sci..

[14]  P. Cheng,et al.  Distinguishing Genuine from Spurious Causes: A Coherence Hypothesis , 2000, Cognitive Psychology.

[15]  P. Spirtes,et al.  Causation, prediction, and search , 1993 .

[16]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[17]  David R. Shanks,et al.  The Psychology of Associative Learning , 1995 .

[18]  A. Gopnik,et al.  Why the Child's Theory of Mind Really Is a Theory , 1992 .

[19]  Jacob Feldman,et al.  Minimization of Boolean complexity in human concept learning , 2000, Nature.

[20]  Alan L. Yuille,et al.  Sequential causal learning in humans and rats , 2008 .

[21]  J. Pearl Causality: Models, Reasoning and Inference , 2000 .

[22]  Estes Wk The problem of inference from curves based on group data. , 1956 .

[23]  J. Tenenbaum,et al.  Structure and strength in causal induction , 2005, Cognitive Psychology.

[24]  W. Estes The problem of inference from curves based on group data. , 1956, Psychological bulletin.

[25]  Joshua B Tenenbaum,et al.  Theory-based causal induction. , 2009, Psychological review.

[26]  T. Griffiths,et al.  Modeling individual differences using Dirichlet processes , 2006 .

[27]  I. J. Myung,et al.  Toward an explanation of the power law artifact: Insights from response surface analysis , 2000, Memory & cognition.

[28]  Joshua B. Tenenbaum,et al.  Learning Causal Laws , 2003 .

[29]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[30]  Alan L. Yuille,et al.  The Noisy-Logical Distribution and its Application to Causal Inference , 2007, NIPS.

[31]  Clark Glymour,et al.  Learning Causes: Psychological Explanations of Causal Explanation1 , 1998, Minds and Machines.

[32]  R. Rescorla A theory of pavlovian conditioning: The effectiveness of reinforcement and non-reinforcement , 1972 .

[33]  P. Cheng From covariation to causation: A causal power theory. , 1997 .

[34]  T. Shultz Rules of Causal Attribution. , 1982 .

[35]  P. Cheng,et al.  Assessing interactive causal influence. , 2004, Psychological review.

[36]  Ralph R. Miller,et al.  Outcome additivity and outcome maximality influence cue competition in human causal learning. , 2005, Journal of experimental psychology. Learning, memory, and cognition.

[37]  D. Shanks,et al.  Models of covariation-based causal judgment: A review and synthesis , 2007, Psychonomic bulletin & review.

[38]  D. Sobel Running head: CHILDREN’S CAUSAL INFERENCES Children’s causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers , 2003 .

[39]  H. M. Jenkins,et al.  JUDGMENT OF CONTINGENCY BETWEEN RESPONSES AND OUTCOMES. , 1965, Psychological monographs.

[40]  Noah D. Goodman,et al.  Learning Causal Schemata , 2007 .

[41]  Michael R. Waldmann,et al.  Combining Versus Analyzing Multiple Causes: How Domain Assumptions and Task Context Affect Integration Rules , 2007, Cogn. Sci..

[42]  S. Carey,et al.  The Epigenesis of mind : essays on biology and cognition , 1991 .

[43]  A. Yuille,et al.  Bayesian generic priors for causal learning. , 2008, Psychological review.

[44]  Thomas L. Griffiths,et al.  Structure Learning in Human Causal Induction , 2000, NIPS.

[45]  David M. Sobel,et al.  Detecting blickets: how young children use information about novel causal powers in categorization and induction. , 2000, Child development.

[46]  H. Pashler,et al.  Measuring the Crowd Within , 2008, Psychological science.

[47]  J. Tenenbaum,et al.  Two proposals for causal grammars , 2007 .

[48]  David Hume,et al.  An enquiry concerning human understanding and other writings , 2007 .

[49]  T. Shultz,et al.  Concepts of potency and resistance in causal prediction. , 1989, Child development.

[50]  L. Schulz,et al.  God does not play dice: causal determinism and preschoolers' causal inferences. , 2006, Child development.

[51]  John R. Anderson The Adaptive Character of Thought , 1990 .

[52]  D. Kuhn The development of causal reasoning. , 2012, Wiley interdisciplinary reviews. Cognitive science.

[53]  Learning Causes : Psychological Explanations of Causal Explanation , 1998 .