Spectral Deconfounding via Perturbed Sparse Linear Models

Abstract

Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be represented as a high-dimensional linear model where the sparse coefficient vector is perturbed. For this model, we develop and investigate a class of methods that are based on running the Lasso on preprocessed data. The preprocessing step consists of applying certain spectral transformations that change the singular values of the design matrix. We show that, under some assumptions, one can achieve the optimal ${\ell }_1$-error rate for estimating the underlying sparse coefficient vector. Our theory also covers the Lava estimator (Chernozhukov et al. [2017]) for a special model class. The performance of the method is illustrated on simulated data and a genomic dataset.

References in corpus (3)

• The Blessings of Multiple Causes
• Detecting non-causal artifacts in multivariate linear regression models
• RSVP-graphs: Fast High-dimensional Covariance Matrix Estimation under Latent Confounding

Cited by in corpus (4)

• Higher-order least squares: assessing partial goodness of fit of linear causal models
• Deconfounding and Causal Regularization for Stability and External Validity
• Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding
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