One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest ``weak'' paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of ``path cancellations'' that will imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice to complement other default tools in observational studies.

Bucur, Ioan Gabriel, Claassen, Tom, Heskes, Tom

Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression exists for the causal effect of one variable on another, given the presence of a third variable. Both rely on faithfulness to infer that the latter only influences the target effect via the cause variable. In reality, it is likely that this assumption only holds approximately and that there will be at least some form of weak interaction. This brings about the paradoxical situation that, in the large-sample limit, no predictions are made, as detecting the weak edge invalidates the setting. We introduce an alternative approach by replacing strict faithfulness with a prior that reflects the existence of many 'weak' (irrelevant) and 'strong' interactions. We obtain a posterior distribution over the target causal effect estimator which shows that, in many cases, we can still make good estimates. We demonstrate the approach in an application on a simple linear-Gaussian setting, using the MultiNest sampling algorithm, and compare it with established techniques to show our method is robust even when strict faithfulness is violated.

Hyttinen, Antti, Eberhardt, Frederick, Hoyer, Patrik O.

Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved in each study. In this article we consider the problem of integrating such knowledge, inferring as much as possible concerning the underlying causal structure with respect to the union of observed variables from such experimental or passive observational overlapping data sets. We do not assume acyclicity or joint causal sufficiency of the underlying data generating model, but we do restrict the causal relationships to be linear and use only second order statistics of the data. We derive conditions for full model identifiability in the most generic case, and provide novel techniques for incorporating an assumption of faithfulness to aid in inference. In each case we seek to establish what is and what is not determined by the data at hand.

Mani, Subramani, Spirtes, Peter L., Cooper, Gregory F.

There are several existing algorithms that under appropriate assumptions can reliably identify a subset of the underlying causal relationships from observational data. This paper introduces the first computationally feasible score-based algorithm that can reliably identify causal relationships in the large sample limit for discrete models, while allowing for the possibility that there are unobserved common causes. In doing so, the algorithm does not ever need to assign scores to causal structures with unobserved common causes. The algorithm is based on the identification of so called Y substructures within Bayesian network structures that can be learned from observational data. An example of a Y substructure is A -> C, B -> C, C -> D. After providing background on causal discovery, the paper proves the conditions under which the algorithm is reliable in the large sample limit.

Zhang, Jiji, Spirtes, Peter L.

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.