nips nips2000 nips2000-127 nips2000-127-reference knowledge-graph by maker-knowledge-mining
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Author: Joshua B. Tenenbaum, Thomas L. Griffiths
Abstract: We use graphical models to explore the question of how people learn simple causal relationships from data. The two leading psychological theories can both be seen as estimating the parameters of a fixed graph. We argue that a complete account of causal induction should also consider how people learn the underlying causal graph structure, and we propose to model this inductive process as a Bayesian inference. Our argument is supported through the discussion of three data sets.
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[7] J. Pearl (2000). Causality. Cambridge University Press. Graph 1 (he = 1) ~c Model Grapho (he = 0) P(e+lc+) P(e+lc-) ~~c Form of P(elb,c) P(C->E) M' Linear Power Noisy OR-gate we Support Noisy OR-gate Iog P(he=l) __ we 100 075 050 025 000 1 aD 075 050 025100075050100 075 1 aD 100 075 050 025 000075050 025 000 050 025 000 025 000 000 ••• __ •••• 1•• 11 1 1 ___ ••••••• 111 _.:: Humans '°5°:[ I N/ • . : : . _ _ Figure 1: Different theories of human causal induction expressed as different operations on a simple graphical model. The M' and power models correspond to maximum likelihood parameter estimates on a fixed graph (Graph[), while the support model corresponds to a (Bayesian) inference about which graph is the true causal structure. 1 ._ •• _••••••• 11 I _..:' _ _ _ • • • • • • • 111 Support I P(he = O) I••• II.III Figure 2: Computational models compared with the performance of human participants from Buehner and Cheng [1], Experiment lB. Numbers along the top of the figure show stimulus contingencies. [ II.... ............... . .... III........ _ II . .._._-_. ..• III........ p(e+lc+) p(e+lc-) 090 080 070 100 100 100 100 100 080 040 090 066033 000 075 050 025 000 060 040 000 083 I ':: or 1 I I Humans 1.111 ••• :.: 11111111 • .::w.:. •• 1.1 I ••• I.III••• ~ p(e+lc+) P(e+lc-) 20 f ,: 040 070 1 00 090 007 053 1 00 074 002 051 1 00 0 10 1 00 1 00 0 00 030 060 083 0 00 046 093 072 0 00 049 098 0 10 1 00 048 I ___ Humans ~p I • • Support I •• Figure 3: Computational models compared with the performance of human participants from Lober and Shanks [5], Experiments 4-6. [1111 •• I ••• I,:w::.1 II I Support i I Figure 4: Computational models compared with the performance of human participants on a set of stimuli designed to elicit the non-monotonic trends shown in the data of Lober and Shanks [5].