Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Deterministic Approximate EM Algorithm; Application to the Riemann Approximation EM and the Tempered EM

Abstract : The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with hidden variables. Many authors modified its simple design to fit more specific situations. For instance the Expectation (E) step has been replaced by Monte Carlo (MC) approximations, Markov Chain Monte Carlo approximations, tempered approximations... Most of the well-studied approximations belong to the stochastic class. By comparison, the literature is lacking when it comes to deterministic approximations. In this paper, we introduce a theoretical framework, with state-of-the-art convergence guarantees, for any deterministic approximation of the E step. We analyse theoretically and empirically several approximations that fit into this framework. First, for cases with intractable E steps, we introduce a deterministic alternative to the MC-EM, using Riemann sums. This method is easy to implement and does not require the tuning of hyper-parameters. Then, we consider the tempered approximation, borrowed from the Simulated Annealing optimisation technique and meant to improve the EM solution. We prove that the tempered EM verifies the convergence guarantees for a wide range of temperature profiles. We showcase empirically how it is able to escape adversarial initialisations. Finally, we combine the Riemann and tempered approximations to accomplish both their purposes.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas
Contributor : Thomas Lartigue <>
Submitted on : Friday, December 18, 2020 - 4:59:53 PM
Last modification on : Wednesday, February 10, 2021 - 4:16:05 PM


  • HAL Id : hal-02513593, version 2
  • ARXIV : 2003.10126


Thomas Lartigue, Stanley Durrleman, Stéphanie Allassonnière. Deterministic Approximate EM Algorithm; Application to the Riemann Approximation EM and the Tempered EM. 2020. ⟨hal-02513593v2⟩



Record views


Files downloads