Estimation of spectral transformation

Estimates the spectral transformation Q for spectral deconfounding by shrinking the leading singular values of the covariates.

get_Q(X, type, trim_quantile = 0.5, q_hat = 0, gpu = FALSE, scaling = TRUE)

Arguments

X: Numerical covariates of class matrix.
type: Type of deconfounding, one of 'trim', 'pca', 'no_deconfounding'. 'trim' corresponds to the Trim transform (Ćevid et al. 2020) as implemented in the Doubly debiased lasso (Guo et al. 2022) , 'pca' to the PCA transformation(Paul et al. 2008) and 'no_deconfounding' to the Identity.
trim_quantile: Quantile for Trim transform, only needed for trim.
q_hat: Assumed confounding dimension, only needed for pca.
gpu: If TRUE, the calculations are performed on the GPU. If it is properly set up.
scaling: Whether X should be scaled before calculating the spectral transformation.

Value

Q of class matrix, the spectral transformation matrix.

References

Ćevid D, Bühlmann P, Meinshausen N (2020). “Spectral Deconfounding via Perturbed Sparse Linear Models.” J. Mach. Learn. Res., 21(1). ISSN 1532-4435, http://jmlr.org/papers/v21/19-545.html.

Guo Z, Ćevid D, Bühlmann P (2022). “Doubly debiased lasso: High-dimensional inference under hidden confounding.” The Annals of Statistics, 50(3). ISSN 0090-5364, doi:10.1214/21-AOS2152 .

Paul D, Bair E, Hastie T, Tibshirani R (2008). ““Preconditioning” for feature selection and regression in high-dimensional problems.” The Annals of Statistics, 36(4). ISSN 0090-5364, doi:10.1214/009053607000000578 .

Author

Markus Ulmer

Examples

set.seed(1)
X <- matrix(rnorm(50 * 20), nrow = 50)
Q_trim <- get_Q(X, 'trim')
Q_pca <- get_Q(X, 'pca', q_hat = 5)
Q_plain <- get_Q(X, 'no_deconfounding')