Cross-validating causal discovery via Leave-One-Variable-Out
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arXiv
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| Format: | Preprint |
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2024
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| author | Schkoda, Daniela Faller, Philipp Blöbaum, Patrick Janzing, Dominik |
| author_facet | Schkoda, Daniela Faller, Philipp Blöbaum, Patrick Janzing, Dominik |
| contents | We propose a new approach to falsify causal discovery algorithms without ground truth, which is based on testing the causal model on a pair of variables that has been dropped when learning the causal model. To this end, we use the "Leave-One-Variable-Out (LOVO)" prediction where $Y$ is inferred from $X$ without any joint observations of $X$ and $Y$, given only training data from $X,Z_1,\dots,Z_k$ and from $Z_1,\dots,Z_k,Y$. We demonstrate that causal models on the two subsets, in the form of Acyclic Directed Mixed Graphs (ADMGs), often entail conclusions on the dependencies between $X$ and $Y$, enabling this type of prediction. The prediction error can then be estimated since the joint distribution $P(X, Y)$ is assumed to be available, and $X$ and $Y$ have only been omitted for the purpose of falsification. After presenting this graphical method, which is applicable to general causal discovery algorithms, we illustrate how to construct a LOVO predictor tailored towards algorithms relying on specific a priori assumptions, such as linear additive noise models. Simulations indicate that the LOVO prediction error is indeed correlated with the accuracy of the causal outputs, affirming the method's effectiveness. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_05625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cross-validating causal discovery via Leave-One-Variable-Out Schkoda, Daniela Faller, Philipp Blöbaum, Patrick Janzing, Dominik Machine Learning Methodology We propose a new approach to falsify causal discovery algorithms without ground truth, which is based on testing the causal model on a pair of variables that has been dropped when learning the causal model. To this end, we use the "Leave-One-Variable-Out (LOVO)" prediction where $Y$ is inferred from $X$ without any joint observations of $X$ and $Y$, given only training data from $X,Z_1,\dots,Z_k$ and from $Z_1,\dots,Z_k,Y$. We demonstrate that causal models on the two subsets, in the form of Acyclic Directed Mixed Graphs (ADMGs), often entail conclusions on the dependencies between $X$ and $Y$, enabling this type of prediction. The prediction error can then be estimated since the joint distribution $P(X, Y)$ is assumed to be available, and $X$ and $Y$ have only been omitted for the purpose of falsification. After presenting this graphical method, which is applicable to general causal discovery algorithms, we illustrate how to construct a LOVO predictor tailored towards algorithms relying on specific a priori assumptions, such as linear additive noise models. Simulations indicate that the LOVO prediction error is indeed correlated with the accuracy of the causal outputs, affirming the method's effectiveness. |
| title | Cross-validating causal discovery via Leave-One-Variable-Out |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2411.05625 |