Constraint-based Causal Discovery from a Collection of Conditioning Sets
Keywords: Causal discovery, causal inference, faithfulness
TL;DR: We propose to learn causal graphs by using CI tests where the conditioning sets are restricted to a given set of conditioning sets including the empty set.
Abstract: In constraint-based causal discovery, existing algorithms systematically use a series of conditional independence (CI) relations observed in the data to recover an equivalence class of causal graphs in the large sample limit. One limitation of these algorithms, such as the PC algorithm, is the reliance on CI tests, which can quickly lose statistical power due to finite samples as the conditioning set size increases or the support of the conditioning set is large. The idea of bounding the size of conditioning sets has been proposed for robust causal discovery. However, the existing algorithms require exhaustive testing of all CI relations with conditioning set sizes up to a certain integer $k$. To further relax this restriction, we propose using CI tests where the conditioning sets are restricted to a given set of conditioning sets including the empty set. We call this set a conditionally closed set $\mathcal{C}$. We define the notion of $\mathcal{C}$-Markov equivalence. We propose a graphical representation to characterize $\mathcal{C}$-Markov equivalence between two causal graphs. We propose a sound constraint-based algorithm called the $\mathcal{C}$-PC algorithm for learning the $\mathcal{C}$-Markov equivalence class. We demonstrate the utility of the proposed algorithm via experiments in scenarios where high-dimensional variables and spurious correlations are present in the data.
Submission Number: 4
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