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Geometry of faithfulness assumption in causal inference
| Content Provider | Semantic Scholar |
|---|---|
| Author | Uhler, Caroline Raskutti, Garvesh Bühlmann, Peter Yu, Bin |
| Copyright Year | 2012 |
| Abstract | Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has non-zero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for algorithms inferring causality based on partial correlations or on conditional independence testing in the Gaussian case. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.stat.berkeley.edu/~binyu/ps/papers2012/UhlerRBY12.pdf |
| Alternate Webpage(s) | http://www.stat.berkeley.edu/~binyu/ps/papers2012/UhlerRBY12.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Assumed Causal filter Causal inference Causality Class Directed acyclic graph Graph - visual representation Normal Statistical Distribution Sampling (signal processing) Statistical Estimation algorithm |
| Content Type | Text |
| Resource Type | Article |
