get_W

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 
Rothenhausler2021AnchorCausalitySDModels, Buhlmann2020InvarianceRobustnessSDModels.

Screen for and analyze non-linear sparse direct effects in the presence of unobserved confounding using the spectral deconfounding techniques (Ćevid, Bühlmann, and Meinshausen (2020)<jmlr.org/papers/v21/19-545.html>, Guo, Ćevid, and Bühlmann (2022) <doi:10.1214/21-AOS2152>). These methods have been shown to be a good estimate for the true direct effect if we observe many covariates, e.g., high-dimensional settings, and we have fairly dense confounding. Even if the assumptions are violated, it seems like there is not much to lose, and the deconfounded models will, in general, estimate a function closer to the true one than classical least squares optimization. 'SDModels' provides functions SDAM() for Spectrally Deconfounded Additive Models (Scheidegger, Guo, and Bühlmann (2025) <doi:10.1145/3711116>) and SDForest() for Spectrally Deconfounded Random Forests (Ulmer, Scheidegger, and Bühlmann (2025) <doi:10.48550/arXiv.2502.03969>).

Markus Ulmer

SDModels

Spectrally Deconfounded Models

Cyrill Scheidegger

get_W function

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

Arguments

Author

Estimation of anchor transformation — get_W

<dl>

<dt>A</dt>
<dd>Numerical Anchor of class <code>matrix</code>.</dd>


<dt>gamma</dt>
<dd>Strength of distributional robustness, \(\gamma \in [0, \infty]\).</dd>


<dt>intercept</dt>
<dd>Logical, whether to include an intercept in the anchor.</dd>


<dt>gpu</dt>
<dd>If <code>TRUE</code>, the calculations are performed on the GPU. 
If it is properly set up.</dd>

</dl>

get_W: Estimation of anchor transformation

Description

Usage

Value

Arguments

Author

References

Examples