Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches: constraint-based and score-based. A disadvantage of currently existing constraint-based and score-based approaches, however, is the inherent instability in structure estimation. With finite samples small changes in the data can lead to completely different optimal structures. The present work introduces a new score-based causal discovery algorithm that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Structure search is performed over Structural Equation Models. Our approach uses exploratory search but allows incorporation of prior background knowledge to constrain the search space. We show that our approach produces accurate structure estimates on one simulated data set and two real-world data sets for Chronic Fatigue Syndrome and Attention Deficit Hyperactivity Disorder.
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