Causal Discovery via Cholesky Factorization

Xu Li, YUNFENG CAI, Mingming Sun, Ping Li

Keywords: DAG Structure Learning, Causal Discovery

Abstract: Discovering the causal relationship via recovering the directed acyclic graph (DAG) structure from the observed data is a challenging combinatorial problem. This paper proposes an extremely fast, easy to implement, and high-performance DAG structure recovering algorithm. The algorithm is based on the Cholesky factorization of the covariance/precision matrix. The time complexity of the algorithm is $\mathcal{O}(p^2n + p^3)$, where $p$ and $n$ are the numbers of nodes and samples, respectively. Under proper assumptions, we show that our algorithm takes $\mathcal{O}(\log(p/\epsilon))$ samples to exactly recover the DAG structure with probability at least $1-\epsilon$. In both time and sample complexities, our algorithm is better than previous algorithms. On synthetic and real-world data sets, our algorithm is significantly faster than previous methods and achieves state-of-the-art performance.

One-sentence Summary: This paper proposes an extremely fast, easy to implement, and high-performance DAG structure recovering algorithm via Cholesky factorization.