ParaLiNGAM: Parallel Causal Structure Learning for Linear non-Gaussian Acyclic Models

One of the key objectives in many fields in machine learning is to discover causal relationships among a set of variables from observational data. In linear non-Gaussian acyclic models (LiNGAM), it can be shown that the true underlying causal structure can be identified uniquely from merely observational data. DirectLiNGAM algorithm is a well-known solution to learn the true causal structure in high dimensional setting. DirectLiNGAM algorithm executes in a sequence of iterations and it performs a set of comparisons between pairs of variables in each iteration. Unfortunately, the runtime of this algorithm grows significantly as the number of variables increases. In this paper, we propose a parallel algorithm, called ParaLiNGAM, to learn casual structures based on DirectLiNGAM algorithm. We propose a threshold mechanism that can reduce the number of comparisons remarkably compared with the sequential solution. Moreover, in order to further reduce runtime, we employ a messaging mechanism between workers and derive some mathematical formulations to simplify the execution of comparisons. We also present an implementation of ParaLiNGAM on GPU, considering hardware constraints. Experimental results on synthetic and real data show that the implementation of proposed algorithm on GPU can outperform DirectLiNGAM by a factor up to 4600 X.