# Fast incremental expectation maximization for finite-sum optimization: nonasymptotic convergence

@article{Fort2020FastIE, title={Fast incremental expectation maximization for finite-sum optimization: nonasymptotic convergence}, author={Gersende Fort and P. Gach and {\'E}ric Moulines}, journal={Statistics and Computing}, year={2020}, volume={31} }

Fast incremental expectation maximization (FIEM) is a version of the EM framework for large datasets. In this paper, we first recast FIEM and other incremental EM type algorithms in the Stochastic Approximation within EM framework. Then, we provide nonasymptotic bounds for the convergence in expectation as a function of the number of examples n and of the maximal number of iterations Kmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage…

## 6 Citations

### Stochastic Variable Metric Proximal Gradient with variance reduction for non-convex composite optimization

- Computer ScienceArXiv
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This paper introduces a novel algorithm, the Perturbed Proximal Preconditioned SPIDER algorithm, which allows approximate preconditioned forward operator and uses a variable metric proximity operator as the backward operator; it also proposes a mini-batch strategy with variance reduction to address the ﬁnite sum setting.

### Geom-Spider-EM: Faster Variance Reduced Stochastic Expectation Maximization for Nonconvex Finite-Sum Optimization

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- 2021

This paper proposes an extension of the Stochastic Path-Integrated Differential EstimatoR EM (SPIDER-EM) and derives complexity bounds for this novel algorithm, designed to solve smooth nonconvex finite-sum optimization problems.

### An online Minorization-Maximization algorithm

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It is shown that an online version of the Minorization–Maximization (MM) algorithm, which in-cludes the online EM algorithm as a special case, can be constructed in a similar manner.

### The Perturbed Prox-Preconditioned Spider Algorithm: Non-Asymptotic Convergence Bounds

- Computer Science, Mathematics2021 IEEE Statistical Signal Processing Workshop (SSP)
- 2021

A novel algorithm named PerturbedProx-Preconditioned SPIDER (3P-SPIDER) is introduced. It is a stochastic variancereduced proximal-gradient type algorithm built on Stochastic Path Integral…

### Federated Expectation Maximization with heterogeneity mitigation and variance reduction

- Computer ScienceArXiv
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FedEM is a new communication method, which handles partial participation of local devices, and is robust to heterogeneous distributions of the datasets, and develops and analyzes an extension of FedEM to further incorporate a variance reduction scheme.

### The Perturbed Prox-Preconditioned Spider Algorithm for EM-Based Large Scale Learning

- Computer Science2021 IEEE Statistical Signal Processing Workshop (SSP)
- 2021

The 3P-SPIDER algorithm addresses many intractabilities of the E-step of EM; it also deals with non-smooth regularization and convex constraint set and discusses the role of some design parameters.

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