A Fast PC Algorithm with Reversed-order Pruning and A Parallelization Strategy

The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an exhaustive-searching manner. This makes the algorithm computationally intractable when the task contains several hundred or thousand nodes, particularly when the true underlying causal graph is dense. We propose a critical observation that the conditional set rendering two nodes independent is non-unique, and including certain redundant nodes do not sacrifice result accuracy. Based on this finding, the innovations of our work are two-folds. First, we innovate on a reserve order linkage pruning PC algorithm which significantly increases the algorithm's efficiency. Second, we propose a parallel computing strategy for statistical independence tests by leveraging tensor computation, which brings further speedup. We also prove the proposed algorithm does not induce statistical power loss under mild graph and data dimensionality assumptions. Experimental results show that the single-threaded version of the proposed algorithm can achieve a 6-fold speedup compared to the PC algorithm on a dense 95-node graph, and the parallel version can make a 825-fold speed-up. We also provide proof that the proposed algorithm is consistent under the same set of conditions with conventional PC algorithm.

Retrofitting Concept Vector Representations of Medical Concepts to Improve Estimates of Semantic Similarity and Relatedness

Estimation of semantic similarity and relatedness between biomedical concepts has utility for many informatics applications. Automated methods fall into two categories: methods based on distributional statistics drawn from text corpora, and methods using the structure of existing knowledge resources. Methods in the former category disregard taxonomic structure, while those in the latter fail to consider semantically relevant empirical information. In this paper, we present a method that retrofits distributional context vector representations of biomedical concepts using structural information from the UMLS Metathesaurus, such that the similarity between vector representations of linked concepts is augmented. We evaluated it on the UMNSRS benchmark. Our results demonstrate that retrofitting of concept vector representations leads to better correlation with human raters for both similarity and relatedness, surpassing the best results reported to date. They also demonstrate a clear improvement in performance on this reference standard for retrofitted vector representations, as compared to those without retrofitting.