compute_dW_dlambda_wrapper

Wrapper function for computing the derivative of the weight matrix w.r.t lambda \(\lambda\).
This involves computing terms related to the derivative of \(1/(1+\textbf{x}^{T}\textbf{U}\textbf{G}\textbf{x})\).

internal

Implements Lagrangian multiplier smoothing splines for flexible
nonparametric regression and function estimation. Provides tools for fitting,
prediction, and inference using a constrained optimization approach to
enforce smoothness.
Supports generalized linear models, Weibull accelerated failure time (AFT) models,
quadratic programming problems, and customizable arbitrary correlation structures.
Options for fitting in parallel are provided. The method builds upon the framework described
by Ezhov et al. (2018) <doi:10.1515/jag-2017-0029> using Lagrangian multipliers
to fit cubic splines. For more information on correlation structure estimation,
see Searle et al. (2009) <ISBN:978-0470009598>. For quadratic programming and
constrained optimization in general, see Nocedal & Wright (2006) <doi:10.1007/978-0-387-40065-5>.
For a comprehensive background on smoothing splines, see Wahba (1990)
<doi:10.1137/1.9781611970128> and Wood (2006) <ISBN:978-1584884743>
"Generalized Additive Models: An Introduction with R".

Matthew Davis

lgspline

Lagrangian Multiplier Smoothing Splines for Smooth Function
Estimation

compute_dW_dlambda_wrapper function

<dl><dt>G</dt>
<dd>A list of penalty matrices \(\textbf{G}\) for each partition</dd>
<dt>A</dt>
<dd>Constraint matrix \(\textbf{A}\)</dd>
<dt>GXX</dt>
<dd>List of \(\textbf{G}\textbf{X}^{T}\textbf{X}\) products</dd>
<dt>Ghalf</dt>
<dd>List of \(\textbf{G}^{1/2}\) matrices</dd>
<dt>dG_dlambda</dt>
<dd>List of \(d\textbf{G}/d\lambda\) matrices</dd>
<dt>dGhalf_dlambda</dt>
<dd>List of \(d\textbf{G}^{1/2}/d\lambda\) matrices</dd>
<dt>AGAInv</dt>
<dd>Inverse of \(\textbf{A}^{T}\textbf{G}\textbf{A}\)</dd>
<dt>nc</dt>
<dd>Number of columns</dd>
<dt>K</dt>
<dd>Number of partitions minus 1 (\(K\))</dd>
<dt>parallel</dt>
<dd>Logical to enable parallel processing</dd>
<dt>cl</dt>
<dd>Cluster object for parallel computation</dd>
<dt>chunk_size</dt>
<dd>Size of chunks for parallel processing</dd>
<dt>num_chunks</dt>
<dd>Number of chunks</dd>
<dt>rem_chunks</dt>
<dd>Remainder chunks</dd></dl>

Arguments

Compute Derivative of Penalty Matrix G with Respect to Lambda (Wrapper) — compute_dW_dlambda_wrapper

<dl>

<dt>G</dt>
<dd>A list of penalty matrices \(\textbf{G}\) for each partition</dd>


<dt>A</dt>
<dd>Constraint matrix \(\textbf{A}\)</dd>


<dt>GXX</dt>
<dd>List of \(\textbf{G}\textbf{X}^{T}\textbf{X}\) products</dd>


<dt>Ghalf</dt>
<dd>List of \(\textbf{G}^{1/2}\) matrices</dd>


<dt>dG_dlambda</dt>
<dd>List of \(d\textbf{G}/d\lambda\) matrices</dd>


<dt>dGhalf_dlambda</dt>
<dd>List of \(d\textbf{G}^{1/2}/d\lambda\) matrices</dd>


<dt>AGAInv</dt>
<dd>Inverse of \(\textbf{A}^{T}\textbf{G}\textbf{A}\)</dd>


<dt>nc</dt>
<dd>Number of columns</dd>


<dt>K</dt>
<dd>Number of partitions minus 1 (\(K\))</dd>


<dt>parallel</dt>
<dd>Logical to enable parallel processing</dd>


<dt>cl</dt>
<dd>Cluster object for parallel computation</dd>


<dt>chunk_size</dt>
<dd>Size of chunks for parallel processing</dd>


<dt>num_chunks</dt>
<dd>Number of chunks</dd>


<dt>rem_chunks</dt>
<dd>Remainder chunks</dd>

</dl>

compute_dW_dlambda_wrapper: Compute Derivative of Penalty Matrix G with Respect to Lambda (Wrapper)

Description

Usage

Value

Arguments