Strong Faithfulness and Uniform Consistency in Causal Inference

TL;DR

This paper introduces generalized Faithfulness assumptions in causal inference that enable uniform consistency of algorithms even with unknown time order and latent confounders, expanding reliable causal inference.

Contribution

It proposes two natural generalizations of the Faithfulness assumption that ensure uniform consistency in causal inference algorithms under broader conditions.

Findings

Uniform consistency achieved with generalized Faithfulness assumptions

Algorithms remain reliable even when time order is unknown

Discussion on Faithfulness as a limiting case of stronger assumptions

Abstract

A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most commonly discussed frequentist notions are pointwise consistency and uniform consistency. Uniform consistency is in general preferred to pointwise consistency because the former allows us to control the worst case error bounds with a finite sample size. In the sense of pointwise consistency, several reliable causal inference algorithms have been established under the Markov and Faithfulness assumptions [Pearl 2000, Spirtes et al. 2001]. In the sense of uniform consistency, however, reliable causal inference is impossible under the two assumptions when time order is unknown and/or latent confounders are present [Robins et al. 2000]. In this paper we present two natural generalizations of the Faithfulness assumption in the context of structural equation models, under which we show that the typical algorithms in the literature (in some cases with modifications) are uniformly consistent even when the time order is unknown. We also discuss the situation where latent confounders may be present and the sense in which the Faithfulness assumption is a limiting case of the stronger assumptions.