A1109
Title: Efficient learning of nonparametric directed acyclic graph with statistical guarantee
Authors: Yibo Deng - shanghai university of finance and economics (China)
Xin He - Shanghai University of Finance and Economics (China) [presenting]
Shaogao Lv - Nanjing Audit University (China)
Abstract: Directed acyclic graph (DAG) models are widely used to represent casual relations among collected nodes. An efficient and consistent method is proposed to learn DAG with a general causal dependence structure, which is in sharp contrast to most existing methods assuming linear dependence of causal relations. The proposed method leverages the concept of a topological layer to facilitate DAG learning. It connects nonparametric DAG learning with kernel ridge regression in a smooth reproducing kernel Hilbert space (RKHS) and learning gradients by showing that the topological layers of a nonparametric DAG can be exactly reconstructed via kernel-based estimation. The parent-child relations can be obtained directly by computing the estimated gradient function. The developed algorithm is computationally efficient in the sense that it attempts to solve a convex optimization problem with an analytic solution, and the gradient functions can be directly computed by using the derivative reproducing property in the smooth RKHS. The asymptotic properties of the proposed method are established in terms of exact DAG recovery without requiring any explicit model specification. Various simulated and real-life examples also support its superior performance.
