cpp.airwls.glmfit

Internal function implementing the Fisher scoring algorithms for the
estimation of GLMs. It is used in 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.glmfit function

<dl><dt>beta</dt>
<dd>initial value of the regression coefficients to be estimated</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>
<dt>nsteps</dt>
<dd>number of iterations</dd>
<dt>stepsize</dt>
<dd>stepsize parameter of the Fisher scoring algorithm</dd>
<dt>print</dt>
<dd>if <code>TRUE</code>, print the algorithm history</dd></dl>

Arguments

Fisher scoring algorithm for GLMs — cpp.airwls.glmfit

<dl>

<dt>beta</dt>
<dd>initial value of the regression coefficients to be estimated</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>


<dt>nsteps</dt>
<dd>number of iterations</dd>


<dt>stepsize</dt>
<dd>stepsize parameter of the Fisher scoring algorithm</dd>


<dt>print</dt>
<dd>if <code>TRUE</code>, print the algorithm history</dd>

</dl>

cpp.airwls.glmfit: Fisher scoring algorithm for GLMs

Description

Usage

Arguments