
On the implied weights of linear regression for causal inference
In this paper, we derive and analyze the implied weights of linear regre...
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Nonparametric efficient causal mediation with intermediate confounders
Interventional effects for mediation analysis were proposed as a solutio...
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A unifying approach for doublyrobust ℓ_1 regularized estimation of causal contrasts
We consider inference about a scalar parameter under a nonparametric mo...
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Distributional Anchor Regression
Prediction models often fail if train and test data do not stem from the...
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Asymptotic normality of the timedomain generalized least squares estimator for linear regression models
In linear models, the generalized least squares (GLS) estimator is appli...
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Estimating Treatment Effects with Observed Confounders and Mediators
Given a causal graph, the docalculus can express treatment effects as f...
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Measuring Sample Path Causal Influences with Relative Entropy
We present a sample path dependent measure of causal influence between t...
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Distributional Robustness of Kclass Estimators and the PULSE
In causal settings, such as instrumental variable settings, it is well known that estimators based on ordinary least squares (OLS) can yield biased and nonconsistent estimates of the causal parameters. This is partially overcome by twostage least squares (TSLS) estimators. These are, under weak assumptions, consistent but do not have desirable finite sample properties: in many models, for example, they do not have finite moments. The set of Kclass estimators can be seen as a nonlinear interpolation between OLS and TSLS and are known to have improved finite sample properties. Recently, in causal discovery, invariance properties such as the moment criterion which TSLS estimators leverage have been exploited for causal structure learning: e.g., in cases, where the causal parameter is not identifiable, some structure of the nonzero components may be identified, and coverage guarantees are available. Subsequently, anchor regression has been proposed to tradeoff invariance and predictability. The resulting estimator is shown to have optimal predictive performance under bounded shift interventions. In this paper, we show that the concepts of anchor regression and Kclass estimators are closely related. Establishing this connection comes with two benefits: (1) It enables us to prove robustness properties for existing Kclass estimators when considering distributional shifts. And, (2), we propose a novel estimator in instrumental variable settings by minimizing the mean squared prediction error subject to the constraint that the estimator lies in an asymptotically valid confidence region of the causal parameter. We call this estimator PULSE (puncorrelated least squares estimator) and show that it can be computed efficiently, even though the underlying optimization problem is nonconvex. We further prove that it is consistent.
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