# Properties of the Stochastic Approximation EM Algorithm with Mini-batch Sampling

## TL;DR

This paper introduces a mini-batch Monte Carlo EM algorithm for large datasets, demonstrating its convergence, efficiency, and practical benefits in latent variable models.

## Contribution

It proposes a mini-batch sampling approach for the stochastic approximation EM algorithm, showing convergence and improved speed in large-scale data scenarios.

## Key findings

- Mini-batch sampling accelerates convergence of the EM algorithm.
- The algorithm converges under classical conditions for exponential models.
- Mini-batch size influences the limit distribution of estimators.

## Abstract

To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classicalconditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models.In particular, we highlight that mini-batch sampling results in an important speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented. Finally, we illustrate how to use mini-batch sampling in practice to improve results when a constraint on the computing time is given.