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Spectrally Deconfounded Random Forests

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Abstract

We introduce a modification of Random Forests to estimate functions when unobserved confounding variables are present. The technique is tailored for high-dimensional settings with many observed covariates. We employ spectral deconfounding techniques to minimize a deconfounded version of the least squares objective, resulting in the Spectrally Deconfounded Random Forests (SDForests). We demonstrate how the omitted variable bias in estimating a direct effect approaches zero, assuming dense confounding and high-dimensional data. We compare the performance of SDForests with that of classical Random Forests in a simulation study and a semi-synthetic setting using single-cell gene expression data. Empirical results suggest that SDForests outperform classical Random Forests in estimating the direct regression function, even if the theoretical assumptions are not perfectly met, and that SDForests and classical Random Forests have comparable performance in the non-confounded case. We provide an R-Package for SDForest, and supplementary materials for this article are available online.

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