Bayesian generic priors for causal learning.

The article presents a Bayesian model of causal learning that incorporates generic priors--systematic assumptions about abstract properties of a system of cause-effect relations. The proposed generic priors for causal learning favor sparse and strong (SS) causes--causes that are few in number and high in their individual powers to produce or prevent effects. The SS power model couples these generic priors with a causal generating function based on the assumption that unobservable causal influences on an effect operate independently (P. W. Cheng, 1997). The authors tested this and other Bayesian models, as well as leading nonnormative models, by fitting multiple data sets in which several parameters were varied parametrically across multiple types of judgments. The SS power model accounted for data concerning judgments of both causal strength and causal structure (whether a causal link exists). The model explains why human judgments of causal structure (relative to a Bayesian model lacking these generic priors) are influenced more by causal power and the base rate of the effect and less by sample size. Broader implications of the Bayesian framework for human learning are discussed.

[1]  J. Mill A System of Logic , 1843 .

[2]  G. L. Collected Papers , 1912, Nature.

[3]  Illtyd Trethowan Causality , 1938 .

[4]  H. Simon,et al.  A Behavioral Model of Rational Choice , 1955 .

[5]  O. Penrose The Direction of Time , 1962 .

[6]  H. M. Jenkins,et al.  The display of information and the judgment of contingency. , 1965, Canadian journal of psychology.

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

[8]  L. Kamin Attention-like processes in classical conditioning , 1967 .

[9]  Marshall R. Jones Miami Symposium on the prediction of behavior, 1967 : aversive stimulation , 1968 .

[10]  William Emerson,et al.  The Mathematical Principles of Natural Philosophy , 2013 .

[11]  Jaegwon Kim,et al.  Causes and Events: Mackie on Causation , 1971 .

[12]  R. Rescorla Informational Variables in Pavlovian Conditioning , 1972 .

[13]  R. Rescorla,et al.  A theory of Pavlovian conditioning : Variations in the effectiveness of reinforcement and nonreinforcement , 1972 .

[14]  Rescorla,et al.  [Psychology of Learning and Motivation] Volume 6 || Informational Variables in Pavlovian Conditioning , 1972 .

[15]  H. Kelley The processes of causal attribution. , 1973 .

[16]  J. Earman,et al.  The Cement Of The Universe , 1974 .

[17]  David Lewis Counterfactual Dependence and Time's Arrow , 1979 .

[18]  K. Holyoak,et al.  Analogical problem solving , 1980, Cognitive Psychology.

[19]  L. Allan A note on measurement of contingency between two binary variables in judgment tasks , 1980 .

[20]  R. Sternberg,et al.  Evaluation of evidence in causal inference. , 1981 .

[21]  W. Friedman The Developmental psychology of time , 1982 .

[22]  H. M. Jenkins,et al.  The effect of representations of binary variables on judgment of influence , 1983 .

[23]  Clifton Amsbury,et al.  The Problem of Simplicity , 1984 .

[24]  K. Holyoak,et al.  Induction of category distributions: a framework for classification learning. , 1984, Journal of experimental psychology. Learning, memory, and cognition.

[25]  J. Woodward,et al.  Scientific Explanation and the Causal Structure of the World , 1988 .

[26]  D R Shanks,et al.  Continuous monitoring of human contingency judgment across trials , 1985, Memory & cognition.

[27]  K J Holyoak,et al.  Distributional expectations and the induction of category structure. , 1986, Journal of experimental psychology. Learning, memory, and cognition.

[28]  David R. Shanks,et al.  Acquisition functions in contingency judgment , 1987 .

[29]  John H. Holland,et al.  Induction: Processes of Inference, Learning, and Discovery , 1987, IEEE Expert.

[30]  A. Dickinson,et al.  Associative Accounts of Causality Judgment , 1988 .

[31]  Norberto M. Grzywacz,et al.  A computational theory for the perception of coherent visual motion , 1988, Nature.

[32]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[33]  Edward M. Hundert,et al.  The Cement of the Universe , 1990 .

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

[35]  S. Gelman,et al.  Understanding natural cause: children's explanations of how objects and their properties originate. , 1991, Child development.

[36]  P. Cheng,et al.  Causes versus enabling conditions , 1991, Cognition.

[37]  Norman H. Anderson,et al.  Contributions to information integration theory , 1991 .

[38]  P. Cheng,et al.  Covariation in natural causal induction. , 1992 .

[39]  Michael R. Waldmann,et al.  Predictive and diagnostic learning within causal models: asymmetries in cue competition. , 1992, Journal of experimental psychology. General.

[40]  Edward A. Wasserman,et al.  Assessment of an information integration account of contingency judgment with examination of subjective cell importance and method of information presentation. , 1993 .

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

[42]  F. Vallée-Tourangeau,et al.  Selective associations and causality judgments: Presence of a strong causal factor may reduce judgments of a weaker one. , 1993 .

[43]  Patricia W. Cheng,et al.  Separating Causal Laws from Casual Facts: Pressing the Limits of Statistical Relevance , 1993 .

[44]  I. J. Myung,et al.  Cue Competition Effects: Empirical Tests of Adaptive Network Learning Models , 1993 .

[45]  E. Wasserman,et al.  Rating causal relations: Role of probability in judgments of response-outcome contingency. , 1993 .

[46]  K. Holyoak,et al.  Mental Leaps: Analogy in Creative Thought , 1994 .

[47]  H. Roitblat,et al.  Comparative approaches to cognitive science , 1995 .

[48]  Michael R. Waldmann,et al.  Causal models and the acquisition of category structure , 1995 .

[49]  D. Shanks Is Human Learning Rational? , 1995, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[50]  Geoffrey E. Hinton,et al.  Varieties of Helmholtz Machine , 1996, Neural Networks.

[51]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[52]  E. Wasserman,et al.  Causation and Association , 1996 .

[53]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

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

[55]  H Barlow,et al.  Correspondence Noise and Signal Pooling in the Detection of Coherent Visual Motion , 1997, The Journal of Neuroscience.

[56]  H. Simon,et al.  Cognition and explanation , 1998 .

[57]  R. Shillcock,et al.  Proceedings of the Twenty-Sixth Annual Conference of the Cognitive Science Society , 1998 .

[58]  D. R. Lehman,et al.  Integration of contingency information in judgments of cause, covariation, and probability. , 1998 .

[59]  Laura Martignon,et al.  Bayesian network models of causal learning , 1998 .

[60]  Pascal Mamassian,et al.  Observer biases in the 3D interpretation of line drawings , 1998, Vision Research.

[61]  P. Cheng,et al.  Why Causation Need not Follow From Statistical Association: Boundary Conditions for the Evaluation of Generative and Preventive Causal Powers , 1999 .

[62]  M. Waldmann,et al.  A Bayesian Network Model of Causal Learning , 1999 .

[63]  R. J. Hankinson Explanation and causation , 1999 .

[64]  C. Glymour The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology , 2000 .

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

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

[67]  Peter Dayan,et al.  Explaining Away in Weight Space , 2000, NIPS.

[68]  D. Shanks,et al.  Is causal induction based on causal power? Critique of Cheng (1997). , 2000, Psychological review.

[69]  Patricia W. Cheng,et al.  Causality in the mind: Estimating contextual and conjunctive causal power , 2000 .

[70]  David M. Sobel,et al.  Causal learning mechanisms in very young children: two-, three-, and four-year-olds infer causal relations from patterns of variation and covariation. , 2001, Developmental psychology.

[71]  Refractor Vision , 2000, The Lancet.

[72]  M. Hoch,et al.  [Evolution of the nervous system]. , 2002, Anasthesiologie, Intensivmedizin, Notfallmedizin, Schmerztherapie : AINS.

[73]  Edward H. Adelson,et al.  Motion illusions as optimal percepts , 2002, Nature Neuroscience.

[74]  Elliott Sober,et al.  Simplicity, Inference and Modelling: What is the problem of simplicity? , 2002 .

[75]  Thomas L. Griffiths,et al.  Dynamical Causal Learning , 2002, NIPS.

[76]  Alison Gopnik,et al.  Inferring Hidden Causes , 2003 .

[77]  P. White Making causal judgments from the proportion of confirming instances: the pCI rule. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[78]  N. Chater,et al.  Simplicity: a unifying principle in cognitive science? , 2003, Trends in Cognitive Sciences.

[79]  Joshua B. Tenenbaum,et al.  Inferring causal networks from observations and interventions , 2003, Cogn. Sci..

[80]  K. Holyoak,et al.  A symbolic-connectionist theory of relational inference and generalization. , 2003, Psychological review.

[81]  P. Cheng,et al.  From covariation to causation: a test of the assumption of causal power. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[82]  D. Danks Equilibria of the Rescorla--Wagner model , 2003 .

[83]  Bruno A Olshausen,et al.  Sparse coding of sensory inputs , 2004, Current Opinion in Neurobiology.

[84]  P. White Causal judgment from contingency information: A systematic test of thepCI rule , 2004, Memory & cognition.

[85]  D. Knill,et al.  The Bayesian brain: the role of uncertainty in neural coding and computation , 2004, Trends in Neurosciences.

[86]  S. Sloman,et al.  The advantage of timely intervention. , 2004, Journal of experimental psychology. Learning, memory, and cognition.

[87]  David Danks Constraint-Based Human Causal Learning , 2004, ICCM.

[88]  Alan L. Yuille,et al.  The Rescorla-Wagner Algorithm and Maximum Likelihood Estimation of Causal Parameters , 2004, NIPS.

[89]  David M. Sobel,et al.  A theory of causal learning in children: causal maps and Bayes nets. , 2004, Psychological review.

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

[91]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[92]  Alan L. Yuille,et al.  Ideal Observers for Detecting Motion: Correspondence Noise , 2005, NIPS.

[93]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[94]  Constraints and nonconstraints in causal learning: Reply to White and to Luhmann and Ahn , 2005 .

[95]  Alan L. Yuille,et al.  Augmented Rescorla-Wagner and Maximum Likelihood Estimation , 2005, NIPS.

[96]  Rajesh P. N. Rao,et al.  Bilinear Sparse Coding for Invariant Vision , 2005, Neural Computation.

[97]  Keith J Holyoak,et al.  An fMRI study of causal judgments , 2005, The European journal of neuroscience.

[98]  CAUSAL JUDGMENTS IN THE TRIAL-BY-TRIAL PRESENTATION , 2005 .

[99]  Laura R. Novick,et al.  Constraints and Nonconstraints in Causal Learning: Reply to White (2005) and to Luhmann and Ahn (2005). , 2005 .

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

[101]  J. Tenenbaum,et al.  Secret Agents , 2005, Psychological science.

[102]  Michael R. Waldmann,et al.  Seeing versus doing: two modes of accessing causal knowledge. , 2005, Journal of experimental psychology. Learning, memory, and cognition.

[103]  Alan L. Yuille,et al.  Modeling Causal Learning Using Bayesian Generic Priors on Generative and Preventive Powers , 2011 .

[104]  Rajesh P. N. Rao Neural Models of Bayesian Belief Propagation , 2006 .

[105]  S. Sarkar,et al.  The Philosophy of Science: An Encyclopedia , 2006 .

[106]  Rajesh P. N. Rao,et al.  Bayesian brain : probabilistic approaches to neural coding , 2006 .

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

[108]  Aniket Kittur,et al.  Using Ideal Observers in Higher-order Human Category Learning , 2006 .

[109]  Daniel J. Graham,et al.  Sparse Coding in the Neocortex , 2007 .

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

[111]  M. Oaksford,et al.  The rationality of informal argumentation: a Bayesian approach to reasoning fallacies. , 2007, Psychological review.

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

[113]  David M. Sobel,et al.  Bayes nets and babies: infants' developing statistical reasoning abilities and their representation of causal knowledge. , 2007, Developmental science.

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

[115]  A. Gopnik,et al.  Causal learning : psychology, philosophy, and computation , 2007 .

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

[117]  J. Tenenbaum,et al.  Bayesian Special Section Learning Overhypotheses with Hierarchical Bayesian Models , 2022 .

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

[119]  C. Mckenzie,et al.  A Bayesian view of covariation assessment , 2007, Cognitive Psychology.

[120]  Masasi Hattori,et al.  Adaptive Non-Interventional Heuristics for Covariation Detection in Causal Induction: Model Comparison and Rational Analysis , 2007, Cogn. Sci..

[121]  T. Lombrozo,et al.  Simplicity and probability in causal explanation , 2007, Cognitive Psychology.

[122]  K. McRae,et al.  Proceedings of the 30th Annual Conference of the Cognitive Science Society. , 2008 .

[123]  David R. Shanks,et al.  Judging Covariation and Causation , 2008 .

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

[125]  Keith J Holyoak,et al.  The role of causal models in analogical inference. , 2008, Journal of experimental psychology. Learning, memory, and cognition.

[126]  P. Cheng,et al.  The influence of virtual sample size on confidence and causal-strength judgments. , 2009, Journal of experimental psychology. Learning, memory, and cognition.

[127]  N. Chater,et al.  Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning , 2009, Behavioral and Brain Sciences.

[128]  Steven A. Sloman,et al.  Beyond covariation: Cues to causal structure. , 2010 .