f_four

Function of x on a fourier basis with a subset of covariates 
having a causal effect on Y using the parameters beta.
The function is given by:
$$f(x_i) = \sum_{j = 1}^p 1_{j \in js} \sum_{k = 1}^K (\beta_{j, k}^{(1)} \cos(0.2 k x_j) +
\beta_{j, k}^{(2)} \sin(0.2 k x_j))$$

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

f_four function

<dl><dt>x</dt>
<dd>a vector of covariates</dd>
<dt>beta</dt>
<dd>the parameter vector for the function f(X)</dd>
<dt>js</dt>
<dd>the indices of the causal covariates in X</dd></dl>

Arguments

Author

Function of x on a fourier basis — f_four

<dl>

<dt>x</dt>
<dd>a vector of covariates</dd>


<dt>beta</dt>
<dd>the parameter vector for the function f(X)</dd>


<dt>js</dt>
<dd>the indices of the causal covariates in X</dd>

</dl>

f_four: Function of x on a fourier basis

Description

Usage

Value

Arguments

Author

See Also

Examples