eigengap.onatski

Select the number of significant principal components of a matrix via the
Onatski method

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

eigengap.onatski function

<dl><dt>covmat</dt>
<dd>matrix to be decomposed</dd>
<dt>maxcomp</dt>
<dd>maximum number of eigenvalues to compute</dd>
<dt>maxiter</dt>
<dd>maximum number of iterations</dd></dl>

Arguments

Rank selection via the Onatski method — eigengap.onatski

<dl>

<dt>covmat</dt>
<dd>matrix to be decomposed</dd>


<dt>maxcomp</dt>
<dd>maximum number of eigenvalues to compute</dd>


<dt>maxiter</dt>
<dd>maximum number of iterations</dd>

</dl>

eigengap.onatski: Rank selection via the Onatski method

Description

Usage

Arguments

References