get_W: Estimation of anchor transformation

In SDModels: Spectrally Deconfounded Models

Estimation of anchor transformation

Description

Estimates the anchor transformation for the Anchor-Objective. The anchor transformation is W = I-(1-\sqrt{\gamma}))\Pi_A, where \Pi_A = A(A^TA)^{-1}A^T. For \gamma = 1 this is just the identity. For \gamma = 0 this corresponds to residuals after orthogonal projecting onto A. For large \gamma this is close to the orthogonal projection onto A, scaled by \gamma. The estimator \text{argmin}_f ||W(Y - f(X))||^2 corresponds to the Anchor-Regression Estimator \insertCiteRothenhausler2021AnchorCausalitySDModels, \insertCiteBuhlmann2020InvarianceRobustnessSDModels.

Usage

get_W(A, gamma, intercept = FALSE, gpu = FALSE)

Arguments

A	Numerical Anchor of class matrix.
gamma	Strength of distributional robustness, \gamma \in [0, \infty].
intercept	Logical, whether to include an intercept in the anchor.
gpu	If TRUE, the calculations are performed on the GPU. If it is properly set up.

Value

W of class matrix, the anchor transformation matrix.

Author(s)

Markus Ulmer

References

\insertAllCited

Examples

set.seed(1)
n <- 50
X <- matrix(rnorm(n * 1), nrow = n)
Y <- 3 * X + rnorm(n)
W <- get_W(X, gamma = 0)
resid <- W %*% Y

SDModels documentation built on April 11, 2025, 5:50 p.m.