A1188
Title: Learning causal graphs via nonlinear sufficient dimension reduction
Authors: Kyongwon Kim - Yonsei University (Korea, South) [presenting]
Eftychia Solea - Queen Mary University of London (United Kingdom)
Bing Li - The Pennsylvania State University (United States)
Abstract: The purpose is to introduce a new nonparametric methodology for estimating a directed acyclic graph (DAG) from observational data. The method is nonparametric in nature: It does not impose any specific form on the joint distribution of the underlying DAG. Instead, it relies on a linear operator on reproducing kernel Hilbert spaces to evaluate conditional independence. However, a fully nonparametric approach would involve conditioning on a large number of random variables, subjecting it to the curse of dimensionality. To solve this problem, nonlinear sufficient dimension reduction is applied to reduce the number of variables before evaluating the conditional independence. An estimator is developed for the DAG, based on a linear operator that characterizes conditional independence, and the consistency and convergence rates of this estimator are established, as well as the uniform consistency of the estimated Markov equivalence class. A modified PC-algorithm is introduced to implement the estimation procedure efficiently, such that the complexity depends on the sparseness of the underlying true DAG. The effectiveness of the methodology is demonstrated through simulations and a real data analysis.
