Recovering Causal Structures from Low-Order Conditional Independencies

• URL: http://arxiv.org/abs/2010.02675v1
• Date: Tue, 6 Oct 2020 12:47:20 GMT
• Title: Recovering Causal Structures from Low-Order Conditional Independencies
• Authors: Marcel Wien\"obst and Maciej Li\'skiewicz
• Abstract summary: We propose an algorithm for a given set of conditional independencies of order less or equal to $k$, where $k$ is a small fixed number. Our results complete and generalize the previous work on learning from pairwise marginal independencies.
• Score: 6.891238879512672
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be performed accurately even for a small number of observations, a reasonable approach to determine casual structures is to base merely on the low-order CIs. Recent research has confirmed that, e.g. in the case of sparse true causal models, structures learned even from zero- and first-order conditional independencies yield good approximations of the models. However, a challenging task here is to provide methods that faithfully explain a given set of low-order CIs. In this paper, we propose an algorithm which, for a given set of conditional independencies of order less or equal to $k$, where $k$ is a small fixed number, computes a faithful graphical representation of the given set. Our results complete and generalize the previous work on learning from pairwise marginal independencies. Moreover, they enable to improve upon the 0-1 graph model which, e.g. is heavily used in the estimation of genome networks.

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