Causal Discovery in Biological Data Using Directed Topological Overlap Matrix

Abstract

Most causal discovery tools assume the local causal Markov condition. However, the theoretical assumptions that underline the local causal Markov condition are often not met in practice. This is especially marked in genomics, where the unwanted presence of measurement errors, averaging effects, and feedback loops significantly undermine the legitimacy of the local causal Markov condition. Furthermore, even the most sample efficient causal discovery algorithms require very large samples, orders above what is available even for the largest genomics databases out there. In this paper, by replacing the local causal Markov condition with Reichenbach’s common cause principle, we present directed topological overlap matrix (DTOM): a more flexible approach to causal discovery in genomics settings, robust against the presence of measurement errors, averaging effects, and feedback loops. We study the utility of DTOM for discovering causal relations in biological data using two real gene expression data-sets. We first consider a large-scale gene deletion study in yeast. We show that DTOM allows us to distinguish the deleted gene in a sample knowing only the set of differentially expressed genes in that sample. We then examine the progression of Alzheimer’s disease (AD) under the lens of DTOM. The genes implicated as having a causal role in the progression of AD by our DTOM analysis were significantly enriched in cellular components that had been repeatedly implicated in the progression of AD.