Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Strong completeness and faithfulness in Bayesian networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
A discovery algorithm for directed cyclic graphs
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm
The Journal of Machine Learning Research
Detection of Unfaithfulness and Robust Causal Inference
Minds and Machines
Sub-local constraint-based learning of Bayesian networks using a joint dependence criterion
The Journal of Machine Learning Research
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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 (see, e.g. Bickel, Doksum [2001]). 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 constructed 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. 20001. 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.