cpp.airwls.glmstep

Internal function to compute one Fisher scoring step for GLMs.
It constitutes the building block of the AIRWLS algorithm for the
estimation of GMF models.

internal

Efficient framework to estimate high-dimensional generalized matrix factorization models using penalized maximum likelihood under a dispersion exponential family specification. Either deterministic and stochastic methods are implemented for the numerical maximization. In particular, the package implements the stochastic gradient descent algorithm with a block-wise mini-batch strategy to speed up the computations and an efficient adaptive learning rate schedule to stabilize the convergence. All the theoretical details can be found in Castiglione et al. (2024, <doi:10.48550/arXiv.2412.20509>). Other methods considered for the optimization are the alternated iterative re-weighted least squares and the quasi-Newton method with diagonal approximation of the Fisher information matrix discussed in Kidzinski et al. (2022, <http://jmlr.org/papers/v23/20-1104.html>).

Cristian Castiglione

sgdGMF

Estimation of Generalized Matrix Factorization Models via
Stochastic Gradient Descent

Davide Risso

Alexandre Segers

cpp.airwls.glmstep function

<dl><dt>beta</dt>
<dd>current value of the regression coefficients to be updated</dd>
<dt>y</dt>
<dd>response vector</dd>
<dt>X</dt>
<dd>design matrix</dd>
<dt>familyname</dt>
<dd>model family name</dd>
<dt>linkname</dt>
<dd>link function name</dd>
<dt>varfname</dt>
<dd>variance function name</dd>
<dt>offset</dt>
<dd>vector of constants to be added to the linear predictor</dd>
<dt>weights</dt>
<dd>vector of constants non-negative weights</dd>
<dt>penalty</dt>
<dd>penalty parameter of a ridge-type penalty</dd></dl>

Arguments

Compute one Fisher scoring step for GLMs — cpp.airwls.glmstep

<dl>

<dt>beta</dt>
<dd>current value of the regression coefficients to be updated</dd>


<dt>y</dt>
<dd>response vector</dd>


<dt>X</dt>
<dd>design matrix</dd>


<dt>familyname</dt>
<dd>model family name</dd>


<dt>linkname</dt>
<dd>link function name</dd>


<dt>varfname</dt>
<dd>variance function name</dd>


<dt>offset</dt>
<dd>vector of constants to be added to the linear predictor</dd>


<dt>weights</dt>
<dd>vector of constants non-negative weights</dd>


<dt>penalty</dt>
<dd>penalty parameter of a ridge-type penalty</dd>

</dl>

cpp.airwls.glmstep: Compute one Fisher scoring step for GLMs

Description

Usage

Arguments