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A theory of causal learning in children: Causal maps and Bayes nets
 PSYCHOLOGICAL REVIEW
, 2004
"... The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events ..."
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Cited by 157 (33 self)
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The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4yearold children construct new causal maps and that their learning is consistent with the Bayes net formalism.
On the Number of Experiments Sufficient and in the Worst Case Necessary to Identify All Causal Relations among N Variables
 In UAI
, 2005
"... We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log 2 (N) + 1 experiments are su#cient and in the worst case necessary to determine the causal relations among N 2 variables when no latent variables, no sample selec ..."
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Cited by 15 (3 self)
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We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log 2 (N) + 1 experiments are su#cient and in the worst case necessary to determine the causal relations among N 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 2 N we provide an upper bound on the number experiments required to determine causal structure when each experiment simultaneously randomizes K variables.
Interventions and causal inference
 Philosophy of Science
, 2007
"... The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an interventi ..."
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Cited by 5 (1 self)
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The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of “hard ” and “soft” interventions, and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the particular experimental setup and the assumptions that can be made.
Automated search for causal relations: Theory and practice
 Heuristics, Probability and Causality: A Tribute to Judea Pearl
, 2010
"... The rapid spread of interest in the last two decades in principled methods of search or estimation of causal relations has been driven in part by technological developments, especially the changing nature of modern data collection and storage techniques, and the increases in the speed and storage ca ..."
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Cited by 2 (0 self)
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The rapid spread of interest in the last two decades in principled methods of search or estimation of causal relations has been driven in part by technological developments, especially the changing nature of modern data collection and storage techniques, and the increases in the speed and storage capacities of computers. Statistics books from 30 years
A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
"... Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules ..."
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Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly identify all arrow orientations shared by all DAGs in a Markov equivalence class, given a member of that class. For DAG models with latent variables, maximal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to construct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is particularly useful for causal inference. 1
Necessary to Identify All Causal Relations Among N Variables
"... We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log2(N) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N ≥ 2 variables when no latent variables, no sample selection bi ..."
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We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log2(N) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N ≥ 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 < K < 1 2N we provide an upper bound on the number experiments required to determine causal structure when each experiment simultaneously randomizes K variables. For large N, these bounds are significantly lower than the N − 1 bound required when each experiment randomizes at most one variable. For kmax < N 2, we show that
Recommended Citation
"... The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an interventi ..."
Abstract
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The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of “hard ” and “soft” interventions, and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the particular experimental setup and the assumptions that can be made.
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence MultiDimensional Causal Discovery
"... We propose a method for learning causal relations within highdimensional tensor data as they are typically recorded in nonexperimental databases. The method allows the simultaneous inclusion of numerous dimensions within the data analysis such as samples, time and domain variables construed as ten ..."
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We propose a method for learning causal relations within highdimensional tensor data as they are typically recorded in nonexperimental databases. The method allows the simultaneous inclusion of numerous dimensions within the data analysis such as samples, time and domain variables construed as tensors. In such tensor data we exploit and integrate nonGaussian models and tensor analytic algorithms in a novel way. We prove that we can determine simple causal relations independently of how complex the dimensionality of the data is. We rely on a statistical decomposition that flattens higherdimensional data tensors into matrices. This decomposition preserves the causal information and is therefore suitable for structure learning of causal graphical models, where a causal relation can be generalised beyond dimension, for example, over all time points. Related methods either focus on a set of samples for instantaneous effects or look at one sample for effects at certain time points. We evaluate the resulting algorithm and discuss its performance both with synthetic and realworld data. 1