Convergence of the Monte Carlo expectation maximization for curved exponential families

By Gersende Fort, Eric Moulines. 2003

159 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8e3c2bfce1157c88a9ecdc693ed196ee7a283642

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Citations in the corpus

Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion) (2006, methodology): “It is well documented (see for example Fort and Moulines (2003), and references therein) that the number of MC samples that are used to approximate the expectation should increase with the EM iterations.”
On Convergence Properties of the Monte Carlo EM Algorithm (2012, methodology): “Fort and Moulines (2003) Fort and Moulines (2003) used the ergodic theory of Markov chains to prove the almost sure (a.s.) convergence of a variation of the Monte Carlo EM algorithm.”
Adaptive methods for sequential importance sampling with application to state space models (2008, methodology): “The convergence of this algorithm can be established along the same lines as the convergence of the MCEM algorithm; see Fort and Moulines (2003).”
On stochastic proximal gradient algorithms (2014, background): “Assume that (the proof is postponed below) for any M > 0, lim n→∞ |V (θ n+1 ) − V (T γ (θ n ))| 1 θn−θ≤M = 0, P − a.s. (47) Since {θ n , n ≥ 0} remains almost surely in a compact set by assumption, the theorem follows from (Fort and Moulines, 2003, Proposition 9).”
Adaptive sequential Monte Carlo by means of mixture of experts (2011, background): “Although the right hand side of (3.9) is most often not directly computable, such a quantity can be approximated on-the-ﬂy using the weighted sample already generated; the resulting algorithms (Algorithms 1 and 2; see Sect.”
On Perturbed Proximal Gradient Algorithms (2014, background): “The second one is established in ( Fort and Moulines , 2003 , Proposition 12 ) .”
Language Evolution by Iterated Learning With Bayesian Agents (2007, methodology): “The number of samples, m n , typically increases with n, producing similar convergence guarantees to those of the standard EM algorithm (Sherman, Ho, & Dalal, 1999; Fort & Moulines, 2003).”
An efficient stochastic approximation EM algorithm using conditional particle filters (2013, methodology): “A problem with MCEM, however, is that it relies on the number of simulations M k to increase with k to be convergent [2] [15].”