Estimating Causal Effects From Nonparanormal Observational Data

TL;DR

This paper develops a method to estimate causal effects in large, non-Gaussian observational systems by deriving a functional form and approximation, demonstrated on gene expression data.

Contribution

It introduces a novel approach for causal effect estimation in non-Gaussian systems, extending previous Gaussian-based methods to a broader class of distributions.

Findings

Derived the general functional form of causal effects in non-Gaussian systems

Proposed an effective approximation for causal effect estimation

Validated the method on observational gene expression data

Abstract

One of the basic aims in science is to unravel the chain of cause and effect of particular systems. Especially for large systems this can be a daunting task. Detailed interventional and randomized data sampling approaches can be used to resolve the causality question, but for many systems such interventions are impossible or too costly to obtain. Recently, Maathuis et al. (2010), following ideas from Spirtes et al. (2000), introduced a framework to estimate causal effects in large scale Gaussian systems. By describing the causal network as a directed acyclic graph it is a possible to estimate a class of Markov equivalent systems that describe the underlying causal interactions consistently, even for non-Gaussian systems. In these systems, causal effects stop being linear and cannot be described any more by a single coefficient. In this paper, we derive the general functional form of causal effect in a large subclass of non-Gaussian distributions, called the non- paranormal. We also derive a convenient approximation, which can be used effectively in estimation. We apply the method to an observational gene expression dataset.