Computing Lower and Upper Bounds on the Probability of Causal Statements

Elena Sokolova, Martine Hoogman, Perry Groot, Tom Claassen, Tom Heskes
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:487-498, 2016.

Abstract

Causal discovery provides an opportunity to infer causal relationships from purely observational data and to predict the effect of interventions. Constraint-based methods for causal discovery exploit conditional (in)dependencies to infer the direction of causal relationships. They typically work through forward chaining: given some causal statements, others can be inferred by applying relatively straightforward causal logic such as transitivity and acyclicity. Starting from the premise that we can estimate reliabilities for base causal statements, we propose a novel approach to estimate the reliability of novel statements inferred by forward chaining. Since reliabilities for base statements are clearly dependent, if only because inferred from the same data, exact computation is infeasible. However, lending ideas from the area of imprecise probability theory, we can compute bounds on the reliabilities on inferred statements. Specifically, we make use of the good old Fréchet inequalities and discuss two different variants: greedy and delayed. In simulation experiments, we show that the delayed variant, at the expense of more bookkeeping and computation time, does provide slightly tighter intervals. We illustrate our method on a real-world data set about attention deficit/hyperactivity disorder.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-sokolova16, title = {Computing Lower and Upper Bounds on the Probability of Causal Statements}, author = {Sokolova, Elena and Hoogman, Martine and Groot, Perry and Claassen, Tom and Heskes, Tom}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {487--498}, year = {2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and Campos}, Cassio Polpo}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/sokolova16.pdf}, url = {https://proceedings.mlr.press/v52/sokolova16.html}, abstract = {Causal discovery provides an opportunity to infer causal relationships from purely observational data and to predict the effect of interventions. Constraint-based methods for causal discovery exploit conditional (in)dependencies to infer the direction of causal relationships. They typically work through forward chaining: given some causal statements, others can be inferred by applying relatively straightforward causal logic such as transitivity and acyclicity. Starting from the premise that we can estimate reliabilities for base causal statements, we propose a novel approach to estimate the reliability of novel statements inferred by forward chaining. Since reliabilities for base statements are clearly dependent, if only because inferred from the same data, exact computation is infeasible. However, lending ideas from the area of imprecise probability theory, we can compute bounds on the reliabilities on inferred statements. Specifically, we make use of the good old Fréchet inequalities and discuss two different variants: greedy and delayed. In simulation experiments, we show that the delayed variant, at the expense of more bookkeeping and computation time, does provide slightly tighter intervals. We illustrate our method on a real-world data set about attention deficit/hyperactivity disorder.} }
Endnote
%0 Conference Paper %T Computing Lower and Upper Bounds on the Probability of Causal Statements %A Elena Sokolova %A Martine Hoogman %A Perry Groot %A Tom Claassen %A Tom Heskes %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-sokolova16 %I PMLR %P 487--498 %U https://proceedings.mlr.press/v52/sokolova16.html %V 52 %X Causal discovery provides an opportunity to infer causal relationships from purely observational data and to predict the effect of interventions. Constraint-based methods for causal discovery exploit conditional (in)dependencies to infer the direction of causal relationships. They typically work through forward chaining: given some causal statements, others can be inferred by applying relatively straightforward causal logic such as transitivity and acyclicity. Starting from the premise that we can estimate reliabilities for base causal statements, we propose a novel approach to estimate the reliability of novel statements inferred by forward chaining. Since reliabilities for base statements are clearly dependent, if only because inferred from the same data, exact computation is infeasible. However, lending ideas from the area of imprecise probability theory, we can compute bounds on the reliabilities on inferred statements. Specifically, we make use of the good old Fréchet inequalities and discuss two different variants: greedy and delayed. In simulation experiments, we show that the delayed variant, at the expense of more bookkeeping and computation time, does provide slightly tighter intervals. We illustrate our method on a real-world data set about attention deficit/hyperactivity disorder.
RIS
TY - CPAPER TI - Computing Lower and Upper Bounds on the Probability of Causal Statements AU - Elena Sokolova AU - Martine Hoogman AU - Perry Groot AU - Tom Claassen AU - Tom Heskes BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-sokolova16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 487 EP - 498 L1 - http://proceedings.mlr.press/v52/sokolova16.pdf UR - https://proceedings.mlr.press/v52/sokolova16.html AB - Causal discovery provides an opportunity to infer causal relationships from purely observational data and to predict the effect of interventions. Constraint-based methods for causal discovery exploit conditional (in)dependencies to infer the direction of causal relationships. They typically work through forward chaining: given some causal statements, others can be inferred by applying relatively straightforward causal logic such as transitivity and acyclicity. Starting from the premise that we can estimate reliabilities for base causal statements, we propose a novel approach to estimate the reliability of novel statements inferred by forward chaining. Since reliabilities for base statements are clearly dependent, if only because inferred from the same data, exact computation is infeasible. However, lending ideas from the area of imprecise probability theory, we can compute bounds on the reliabilities on inferred statements. Specifically, we make use of the good old Fréchet inequalities and discuss two different variants: greedy and delayed. In simulation experiments, we show that the delayed variant, at the expense of more bookkeeping and computation time, does provide slightly tighter intervals. We illustrate our method on a real-world data set about attention deficit/hyperactivity disorder. ER -
APA
Sokolova, E., Hoogman, M., Groot, P., Claassen, T. & Heskes, T.. (2016). Computing Lower and Upper Bounds on the Probability of Causal Statements. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:487-498 Available from https://proceedings.mlr.press/v52/sokolova16.html.

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