Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding

Guo, Zijian; Ćevid, Domagoj; Bühlmann, Peter

doi:10.48550/arxiv.2004.03758

Cited by 8 publications

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We review some of our more recent contributions on deconfounding, distributional robustness and replicability, and causality (Rothenhäusler et al, 2018;Bühlmann, 2020;Ćevid et al, 2018;Guo et al, 2020). A unified treatment might enable us to clarify the connections more clearly.…”

Section: The Current Workmentioning

confidence: 99%

“…(A3) The compatibility constant of n −1 XT X is of the same order as the minimal eigenvalue λ min (Σ) of Σ = Cov(X i ). Ćevid et al (2018) give a detailed discussion when these assumptions hold, see also Guo et al (2020). In particular, (A1) is an assumption on dense confounding: for example, if p/q → ∞ and the number of non-zero columns of γ is of the order p (order p components of X are affected by H) and each of the non-zero columns of γ is sampled i.i.d.…”

Section: Guarantees For the Lasso After The Trim Transformmentioning

confidence: 99%

“…We briefly review here the approach of Guo et al (2020) on the doubly debiased Lasso to obtain hypothesis tests and confidence intervals for single regression coefficients β 0 j in model ( 1) in presence of hidden confounding.…”

Section: The Doubly Debiased Lassomentioning

confidence: 99%

See 2 more Smart Citations

Deconfounding and Causal Regularization for Stability and External Validity

Bühlmann,

Ćevid

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: The Current Workmentioning

confidence: 99%

Section: Guarantees For the Lasso After The Trim Transformmentioning

confidence: 99%

See 1 more Smart Citation

Deconfounding and Causal Regularization for Stability and External Validity

Bühlmann,

Ćevid

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A recent paper in the Lasso literature considers the interplay of sparse and low rank assumptions. [33] consider the model…”

Section: Error-in-variables Regressionmentioning

confidence: 99%

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

Agarwal¹,

Singh²

2021

Preprint

View full text Add to dashboard Cite

Even the most carefully curated economic data sets have variables that are noisy, missing, discretized, or privatized. The standard workflow for empirical research involves data cleaning followed by data analysis that typically ignores the bias and variance consequences of data cleaning. We formulate a semiparametric model for causal inference with corrupted data to encompass both data cleaning and data analysis. We propose a new end-to-end procedure for data cleaning, estimation, and inference with data cleaning-adjusted confidence intervals. We prove √ n-consistency, Gaussian approximation, and semiparametric efficiency for our estimator of the causal parameter by finite sample arguments. Our key assumption is that the true covariates are approximately low rank. In our analysis, we provide nonasymptotic theoretical contributions to matrix completion, statistical learning, and semiparametric statistics. We verify the coverage of the data cleaning-adjusted confidence intervals in simulations.

show abstract

“…Kong et al (2019) consider a binary outcome with a univariate confounder and prove identification under a linear factor model for multiple treatments and a parametric outcome model via a meticulous analysis of the link distribution; but their approach cannot generalize to the multivariate confounder setting as we illustrate with a counterexample in the supplement. Grimmer et al (2020); Ćevid et al (2018); Guo et al (2020); Chernozhukov et al (2017) consider linear outcome models with high-dimensional treatments that are confounded or mismeasured; in this case, identification is implied by the fact that confounding on each treatment vanishes as the number of treatments goes to infinity. In contrast, we take a fundamentally causal approach to confounding and to identification of treatment effects by allowing the outcome model to be nonparametric, the treatment-confounder distribution to lie in a more general, though not unrestricted, class of models, the number of treatments to be finite, and confounding to not vanish.…”

Section: Related Workmentioning

confidence: 99%

Identifying effects of multiple treatments in the presence of unmeasured confounding

Wang¹,

Hu²,

Ogburn³

et al. 2020

Preprint

View full text Add to dashboard Cite

Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to bridge the gap between these statistical approaches and causal inference, but these attempts have either been shown to be flawed or have relied on fully parametric assumptions. In this paper, we propose two strategies for identifying and estimating causal effects of multiple treatments in the presence of unmeasured confounding. The auxiliary variables approach leverages auxiliary variables that are not causally associated with the outcome; in the case of a univariate confounder, our method only requires one auxiliary variable, unlike existing instrumental variable methods that would require as many instruments as there are treatments. An alternative null treatments approach relies on the assumption that at least half of the confounded treatments have no causal effect on the outcome, but does not require a priori knowledge of which treatments are null. Our identification strategies do not impose parametric assumptions on the outcome model and do not rest on estimation of the confounder.

show abstract

Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding

Cited by 8 publications

References 0 publications

Deconfounding and Causal Regularization for Stability and External Validity

Deconfounding and Causal Regularization for Stability and External Validity

Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

Identifying effects of multiple treatments in the presence of unmeasured confounding

Contact Info

Product

Resources

About