The Perturbed Prox-Preconditioned SPIDER algorithm for EM-based large scale learning

Gersende Fort (1) , Eric Moulines (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 X-DEP-MATHAPP - Département de Mathématiques Appliquées de l'École polytechnique
3 XPOP - Modélisation en pharmacologie de population

Incremental Expectation Maximization (EM) algorithms were introduced to design EM for the large scale learning framework by avoiding the full data set to be processed at each iteration. Nevertheless, these algorithms all assume that the conditional expectations of the sufficient statistics are explicit. In this paper, we propose a novel algorithm named Perturbed Prox-Preconditioned SPIDER (3P-SPIDER), which builds on the Stochastic Path Integral Differential EstimatoR EM (SPIDER-EM) algorithm. The 3P-SPIDER algorithm addresses many intractabilities of the E-step of EM; it also deals with non-smooth regularization and convex constraint set. Numerical experiments show that 3P-SPIDER outperforms other incremental EM methods and discuss the role of some design parameters.

Mots clés: Statistical Learning; Large Scale Learning; Expectation Maximization algorithm; Finite-sum Optimization; Accelerated Stochastic Approximation; Control Variates

Domaines: Machine Learning [stat.ML]; Méthodologie [stat.ME]; Traitement du signal et de l'image [eess.SP]

Gersende Fort, Eric Moulines. The Perturbed Prox-Preconditioned SPIDER algorithm for EM-based large scale learning. SSP 2021 - IEEE Statistical Signal Processing Workshop, Jul 2021, Rio de Janeiro, Brazil. ⟨hal-03183774v2⟩