Reproduce “A Consistent Estimator for Confounding Strength” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Luca Rendsburg, Leena Chennuru Vankadara, Debarghya Ghoshdastidar, Ulrike von Luxburg
The authors estimate confounding strength, the squared gap between observational regression and causal effect, under an independent-mechanisms model. High-dimensional concentration makes this scalar estimable without identifying vectors. They show the population estimator is consistent, while its sample plug-in version is generally biased when dimension grows proportionally with sample size. An RMT correction is asymptotically consistent under additional assumptions, not a finite-sample guarantee.
Key insights
- While the theoretical "population estimator" for confounding strength is consistent in high dimensions under the independent causal mechanisms (ICM) assumption, practical plug-in estimators using sample statistics introduce significant and quantifiable asymptotic biases.
- The plug-in estimator for $\tau_{pop}$ is asymptotically biased by a factor of $(1-\gamma)^{-1}$, where $\gamma = d/n$.
- Random matrix theory provides the necessary framework to correct these biases, enabling the derivation of a consistent estimator for confounding strength even when the data dimension is large relative to the sample size.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.